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Maths and Stats Success (MASS)
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Maths and Stats Success
Do you feel that you need refreshing in maths skills, worry about the maths element of your course or struggle with stats? Maths and Stats Success (MASS) is a service available to students which aims to help with the maths element of courses, irrespective of students' current capabilities. Friendly one –to–one support is offered by separate Colleges via informal weekly drop in sessions – there's no need to make an appointment. Additional learning resources can be accessed online.
On-line resources: We have a variety of resources available online, which students can access 24 hours a day, 7 days a week through the Blackboard Virtual Learning Environment (VLE). Please click here to find out more information about the engineering in mathmatics resources.
In the Department of Biosciences, we run a weekly Statistics Help service for all students, undergraduate and postgraduate, in our department. These are put on by a rota of academic staff with a wide range of mathematical biology and statistical experience. All bioscience students are sent an email at the start of term announcing the current venue for the drop-in sessions, and up to date information about the time and locations can be found on the departmental timetable on the intranet.
These are drop-in sessions in which we aim to help any Biosciences student with any quantitative issue, from basic data presentation (graphs and tables) to statistical analysis and maths. We are not experts in everything mathematical but we can almost certainly provide some degree of help.
This service is not a substitute for the taught courses in data analysis that are currently offered at all levels in Biosciences, from Foundation Year to MSc. The aim is to point you in the right direction, not to do it for you! So, bring specific questions and data and don't leave it until the last minute (e.g. the week before handing in a research project!). | 677.169 | 1 |
Algebra students: Get Friendly with your Calculator!
The start of a new term is the best time to learn more about using your calculator. Whether you need to master basic functions or conquer more advanced tasks, using the calculator is essential to doing well in Algebra and scoring on the Common Core test this spring. Here's the link to the graphing calculator manual: Yes, the manual can be boring. But it's the most direct way to learn the steps for a specific task: just look it up in the table of contents and click on the link for that function. I'll be posting links to calculator lessons on YouTube soon, but for now download this manual onto your phone or to the computer you use outside of school and then practice all the moves you've been confused about. Have fun! | 677.169 | 1 |
Calendar
VIDEO GALLERIES: List of Video Playlist from the University of New South Wales (UNSW) Here are video galleries from UNSW's You'll find various collections of video courses from that program. Many of the videos are about one hour or so in length. Below is a list of video galleries from the University of New South [...] . . . → Read More: Video Galleries from the University of New South Wales
Here is a short explanation on x- and y-intercepts for a given linear equation. The rendering below is a step-by-step example and response to a question I answered to a student in Some of the links in the post above are "affiliate links." This means if you click on the link and purchase the [...] . . . → Read More: Pre-Algebra Homework Help and Tutorial: Intercepts for a Linear Equation
The set of videos is organized so that it has easy navigation to the set of videos. The course covers basic arithmetic operations on signed numbers as well as covering concepts about symbols, and its notation, solutions of linear and quadratic equations. The course covers factoring, powers, and elementary graphing. Online learning for this topic [...] . . . → Read More: Pre-Algebra Homework Help: Overview to Step-By-Step Introduction to Algebra Videos | 677.169 | 1 |
MATH201 Real Analysis
First Semester
18 points
MATH 201 is an introduction to the basic techniques of real analysis in the familiar context of single-variable calculus.
Paper details
Analysis is, broadly, the part of mathematics which deals with limiting processes. The main examples students have met in school and first-year university are from calculus, where the derivative and integral are defined using quite different limiting processes. Real analysis is about real-valued functions of a real variable — in fact, exactly the kind of functions which are studied in calculus. The methods of analysis have been developed over the past two centuries to give mathematicians rigorous methods for deciding whether a formal calculation is correct or not. This paper discusses the basic ideas of analysis, and uses them to explain how calculus works. At the end of the semester, students should have a broader overview of calculus and a grounding in the methods of analysis which will prove invaluable in later years.
Potential students
MATH 201 is compulsory for the Mathematics major and is of particular relevance also for students majoring in Statistics, Physics or any discipline requiring a quantitative analysis of systems and how they change with space and time. It is a prerequisite for MATH 301 (Hilbert spaces) and MATH 302 (Complex Analysis).
Lecturer
Lectures
Tutorial
2 per week: (Times TBA) Tutorials start in the second week of semester.
Assessment
The internal assessment is made up of 50% from 4 assignments and 50% from a class test. Test mark
all expressed out of 100, then your final mark F in this paper will be calculated according to this formula:
F = max(E, (4E + A + T)/6) | 677.169 | 1 |
The content of California Pre-Algebra offers complete coverage of California's Grade 7 Mathematics Content Standards. Mathematics standards from previous grades are reviewed to help understand Grade 7 standards. Activities are provided to develop Grade 7 concepts. Each lesson has ample skill practice so that students can master the important mathematical processes taught in Grade 7. California Pre-Algebra also teaches valuable techniques for solving purely mathematical as well as real-world problems. Throughout each chapter students will engage in error analysis and mathematical reasoning to build critical thinking skills and to construct logical arguments. California Pre-Algebra thus provides a balance between basic skills, conceptual understanding, and problem solving – all supported by mathematical reasoning. California Pre-Algebra will also help students become better at taking notes and taking tests. Look for a notetaking strategy at the beginning of each chapter as well as helpful marginal notes throughout each chapter. The marginal notes give students support in keeping a notebook, studying math, reading algebra and geometry, doing homework, using technology, and reviewing for tests.
NB: Glossary, English-to-Spanish Glossary, and Index are NOT included the pdf version of the textbook. | 677.169 | 1 |
A Stroll Through Calculus is an easygoing tour of the main concepts of calculus without fussing over dotting every i and crossing every t. Despite what many think, the basic content of calculus is understandable at an elementary level. People who aren't afraid of a little high school algebra can discover in these pages why calculus is so important and so powerful—without getting bogged down in theory or subtle computations. | 677.169 | 1 |
Math4991 Capstone Project in Pure Mathematics
A typical 4-year curriculum in mathematics is quite limited in its scope. In this class, a diverse group of professors and distinguished scholars who will present topics in various old and new branches of mathematics. These lectures will illustrate the beauty and diverse applications of mathematics. The class will be talk in the style of presentations, albeit there will be more discussions. The lectures will be delivered by several professors over the semester. The course is intended for the pure math track, and knowing how mathematics can be applied to the real world is necessary to gain deeper appreciation for mathematics.
There will be some exercises after each class to reinforce the concepts from the lectures. These exercises will be collected weekly. Furthermore, there might be some open ended questions to test your imagination and your ability to think independently. You are encouraged to go online to look for related articles. This gives you a feel for how mathematical research is done, and is where the project comes in. You will be asked to form small groups to do a project on a topic of your choice. I hope that, by the end of the course, you will be excited about mathematics and eager to look for a topic to do your own research.
Attendance is mandatory because the course is structured like a workshop, and there is no textbook. Your attendance will count toward the final grade.
Homework, 30 points
Exercises will be given after a lecture. The homework is usually due on Friday (for September lectures) or Wednesday (for October and November lectures) in the following week after the lecture. There may also be discussion problems or open ended questions that are not required to be turned in, but can be the basis for your term project. Homework will count for 30% of your total final grade.
The typesetting tool for mathematics is LaTeX. You need to learn LaTeX in the first four weeks, and are required to submit your homework in LaTeX after Oct 1.
You are allowed to discuss homework with your fellow students. However, copying is suspected because of the similarity of an unusual argument, especially if the argument is wrong, those suspected of copying will be called into Prof. Yan's office and questioned. If copying is confirmed, an automatic reduction of 10 points in the final homework grade will be made to all involved parties for each incidence.
Project, 50 points
The project is team based. The team decides the topic and how to collaborate. A team normally has 3 members, and may have 2 in exceptional cases. The project consists of a presentation and a written final report.
Each team gives one presentation of around 20 minutes. The professor will randomly choose presenter and may switch presenter in the middle of presentation. A panel of professors determines the grade of the presentation, which is 25 out of total of 50.
The report must be written separately by each individual. Copying and any form of plagiarism from the web or team members is strictly forbidden, and will result in 0 point for all parties involved, regardless who copied from who. The report should be at least 5 pages long, but should not be overly long. The grade of the report is another 25 out of total of 50.
Not doing a project, or submitting an unacceptable project, will result in an F grade regardless how well you do in attendance and homework.
Each professor will make himself available to you for that week and beyond. In addition, your TAs should also be available to help you. You are encouraged to talk to the professor and TA regarding your homework and project.
Showing respect to the professors and your fellow students is a basic courtesy all of you should understand and practice in all your classes. There is no exception in this class. During the class, please turn your cell phone to the silent mode. Also, you are not allowed to turn on your laptop or tablet unless it is for note-taking. Anyone who violates this code of conduct will receive a warning. A second violation will result in dismissal from the class, as well as a 10 points deduction on the attendance grade. | 677.169 | 1 |
Overview
Single Variable Calculus / Edition 7
James Stewart's well-received SINGLE VARIABLE InEditorial Reviews
In the new edition of this introductory text, Stewart (McMaster U.) presents all topics geometrically, numerically, algebraically, and verbally, for better conceptual understanding by students. Topics include functions and models; derivatives; differential equations; and infinite sequences and series. Annotation c. by Book News, Inc., Portland, Or.
Most Helpful Customer Reviews
sold a book they didn't own, no return emails until got B&N involved, then had to fight for refund. Book was never going to come and they were never going to contact me to let me know. Very similar to other complaints listed in reviews. Be careful, you may not get what you pay for EVER. And it will take alot of effort on your end to get a refund that you are due. Would have given them 0 stars if could.
Anonymous
More than 1 year ago
A very well organized text. Only goes up to what is typically Calc I and II in universities (but I think there is a version that goes up to Calc III). Haven't gone through the entire thing yet, but from what I've read and done as far as examples and practice problems it's a very reasonable text. Not outstandingly better than previous calculus texts I've used, but preferable (for me). Anyone getting this book is probably doing so for a course and has no choice, but if you are the rare person learning calculus on your own for fun, this text would easy enough to follow.
With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself
apart from all others in advanced calculus. Besides the classical capstones—the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss ...
This best selling author team explains concepts simply and clearly, without glossing over difficult points.
Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and ...
Full of relevant, diverse, and current real-world applications students can relate to, Stefan Waner and
Steven Costenoble's APPLIED CALCULUS, 7th Edition, helps your students see the relevance of mathematics to their interests. A large number of the applications are based ...
BIOCALCULUS: CALCULUS, PROBABILITY, AND STATISTICS FOR THE LIFE SCIENCES shows students how calculus relates to
biology, with a style that maintains rigor without being overly formal. The text motivates and illustrates the topics of calculus with examples drawn from many ...
New from James Stewart and Daniel Clegg, BRIEF APPLIED CALCULUS takes an intuitive, less formal
approach to calculus without sacrificing the mathematical integrity. Featuring a wide range of applications designed to motivate students with a variety of interests, clear examples ...
The second of a three-volume work, this is the result of the authors'experience teaching calculus
at Berkeley. The book covers techniques and applications of integration, infinite series, and differential equations, the whole time motivating the study of calculus using its ... | 677.169 | 1 |
We have 7 Units to cover in 8th grade math. A summary of each unit is listed below.
Mathematics Grade 8 Unit Descriptions
The eighth grade standards are designed to prepare students to bridge from middle grades mathematics to high school courses that will ensure all students are college and career ready by the conclusion of their fourth high school course.
The Standards for Mathematical Practice are a key component as they are applied in each course to equip students in making sense of problems and building a set of tools they can use in real world situations. Rather than racing to cover many topics in a "mile-wide, inch-deep curriculum", the standards ask mathematics teachers to significantly narrow and deepen the way time and energy are spent
in the classroom. Much of the eighth grade mathematics curriculum focuses on functions and linear relationships as building blocks to algebra and geometry.
Unit 1: The first unit centers around geometry standards related to transformations – translations, reflections, rotations, and dilations, both on and off the coordinate plane – and the notion of congruence and similarity. Students will understand congruence and similarity using
physical models, transparencies, or geometry software. Students learn to use informal arguments to establish proof of angle sum and exterior angle relationships related to parallel lines and two dimensional polygons.
Unit 2: Students will explore and understand that there are numbers that are not rational, called irrational numbers, and will approximate their value by using rational numbers. Clear understanding of irrational numbers will be demonstrated using models, number lines, and
expressions of estimates and approximations. Students will work with radicals and express very large and very small numbers using integer exponents.
Unit 3:
Students will extend their work with irrational numbers by applying the Pythagorean Theorem to situations involving right triangles, including finding distance. Proof of the Pythagorean Theorem and its converse allow students to demonstrate understanding of the theorem. Real-world problems are solved involving volume of cylinders, cones, and spheres.
Unit 4:
The fourth unit introduces students to relations and functions, and defines a function as a relation whose every input corresponds with a single output. From this understanding, students define, evaluate, and compare functions. Functions are described and modeled using a variety of representations, including algebraically, graphically, numerically in tables, and verbally.
Unit 5: In unit five, functions are further explored, focusing on the study of linear functions. Students will understand the connections between proportional relationships, lines, and linear equations, and solve mathematical and real-life problems involving such relationships. Slope is formally introduced, and students work with equations for slope in different forms, including comparing proportional relationships represented in different ways (graphically, tabular, algebraically, verbally).
Unit 6:
Students will extend the study of linear relationships by exploring models and tables. They will use functions to model relationships between quantities and describe the rate of change. The study of statistics expands from more simplistic samples and collections in sixth and seventh grade, to bivariate data, which can be graphed and a line of best fit determined.
Unit 7:
The final unit broadens the study of linear equations to situations involving simultaneous equations. Using graphing, substitution, and elimination, students learn to solve systems of equations algebraically, and make applications to real-world situations.
USA Test Prep Practice
LCMS Student - Welcome to USATESTPREP.COM
Directions for getting on USATESTPREP.COM:
Go to usatestprep.com. Click on "Login" at the top right of your page.
For the Account ID: type in lumpkinmiddlega
Your username is your GTID number
Your password is lumpkin
Click on "Login Now"
Click on "Join a Class". (Hint: this is the orange button found at the bottom left of the page)
From the drop-down box choose a teacher, and then choose the class that you are enrolled in. Finally click "Join Class".
You have now joined! Good Job! Now you can return to complete assignments or take a benchmark (quiz or test).
Please note, that benchmarks will require a code. Your teacher will give you those codes in | 677.169 | 1 |
This exam practice book for AS contains detailed advice and tips on how to improve marks and overall grade. The authors are experienced examiners who have been involved with the development of the new AS Maths exams. This book gives students much-needed guidance on how to tackle these new-style questions. Exam Practice AS Maths includes: / Exam questions across all boards / Students' answers with hints and tips / 'Don't make these mistakes' sections / 'Key points to remember' sections / 'Questions to try' plus examiner's hints / 'How to score full marks' sections / Answers and guidance at the back.
"synopsis" may belong to another edition of this title.
About the Author:
John Berry is Professor of Mathematics Education at the University of Plymouth and Mathematics Professor in Residence at Well Cathedral School, Somerset. He teaches mathematics at A-level, able and gifted pupils at KS3 and has acted as a consultant for QCA. Ted Graham is the Director fo the Centre for Teaching Mathematics and a Senior Lecturer in the School of Mathematics and Statistics at the University of Plymouth. He has worked as a chief examiner for ten years and is currently a chief examiner in Mechanics for a major examining board. Roger Williamson is a former Senior Lecturer in Statistics at Manchester Metropolitan University. He is Chief Examiner in Statistics and a former Chief Moderator for a major examining group.
Book Description Collins 28194902
Book Description Collins 28/014902
Book Description Collins 284902
Book Description Collins 284902
Book Description Collins 28/01194902 | 677.169 | 1 |
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The A-Plus Notes for Beginning Algebra: Pre-Algebra and Algebra 1 by Rong Yang includes topics on Algebra such as Real Numbers, Decimals, Number Theory, Fractions, Percents, Equations, Functions & Graphs, Factoring, Inequalties & Absolute Value, Systems of Equations, Systems of Inequalities, Radicals, Quadratic Equations, Quadratic Functions, Rational Expressions and Statistics & Probability along with standardized sample questions & tests. The book can be best used for SAT, ACT, NTE, CBEST, STAR TEST & HS EXIT and outlines the concepts, formulas & theorems in Algebra. With over 18,000 simple & complex examples and exercises, the book facilitates the learning process in problem solving. Rong Yang, the author of A-Plus Notes for Beginning Algebra, has written other books as well such as A-Plus Notes for Algebra, A-Plus Notes for Algebra 2 and Pre-Calculus and A-Plus Notes for SAT Math.
An excerpt from the book:
Real numbers are the one which can be located on the number line. Each point on the number line is called the graph of the number on the line. The number is called the coordinate of the point. The coordinate of point A is -5. The graph of -5 is point A. The graph of 0 is the point called origin. The coordinate of the origin is 0. Real numbers include rational numbers and irrational numbers.
Rational numbers can be written as the ratio of two integers. 0.1 = 1/10, 0.5 = 5/10, 1.2 = 12/10 = 6/5, 0.1 = 1/9, 0.54 = 54/99 = 6/11. Every rational number can be expressed as either a terminating decimal or as a repeating decimal.
Irrational numbers cannot be written as the ratio of two integers. They are nonterminating (infinite), nonrepeating decimals.
On a number line, the numbers to the right of the origin are positive, and the numbers to the left of the origin are negative. On a number line, the number on the right is greater than the number on the left.
Rule of rounding: When an exact computation is not needed for the answer of a problem, we use the rules of rounding to estimate numbers. We can round each number to the nearest 10, 100, 1000,… It depends on how accurate the answer we need. If the digit to the right of the digit to be rounded is 5 or more, we round up by increasing the digit to be rounded by 1 and replacing the digits to the right with zeros. If the digit to the right of the digit to be rounded is less than 5, we round down by leaving the digit to be rounded the same and replacing the digits to the right with zeros. | 677.169 | 1 |
Geometry: A Metric Approach with Models (Undergraduate Texts in Mathematics)
"Geometry: A Metric Approach with Models", imparts a real feeling for Euclidean and non-Euclidean (in particular, hyperbolic) geometry. Intended as a rigorous first course, the book introduces and develops the various axioms slowly, and then, in a departure from other texts, continually illustrates the major definitions and axioms with two or three models, enabling the reader to picture the idea more clearly. Topics covered include the fundamentals of neutral (absolute) geometry; the theory of parallels; hyperbolic geometry; classical Euclidean geometry; proof of the existence of an area function; the cut and reassemble theory of Bolyai; and the classification of isometries of a neutral geometry. Over 700 problems and 250 figures are included in this revised second edition. This second edition has been expanded to include a selection of expository exercises. Additionally, the authors have designed software with computational problems to accompany the text. This software may be obtained from George Parker. This textbook on geometry is intended for undergraduate students in mathematics. | 677.169 | 1 |
worksheets on logarithms, in increasing difficulty.
Detailed typed answers are provided to every question. I hope you find it useful. You can get more free worksheets on many topics, mix and match, with detailed step-by-step solutions at
Here is a summary containing all the important facts that you must know about travel logarithms.
It contains:
- Definition of logarithm
- Common and natural logarithms
-Examples
- Logarithm rules.
- 25 exercises with answer key.
I hope you find it useful.
Please rate this resource so I can improve as I go on!!
SAVE with foldables for units 1 - 3 of your Pre-Calculus course.
Sets include:
- Color-coded graphic organizers*
- Black-line master graphic organizers
- Color coded notes with examples.
- Practice problems or activity such as puzzle or card sort (good for homework)
- Answer key for practice problemsStudents are guided through a set of investigative prompts that explore exponential change in real-life situations, allowing them to build up an understanding of what exponential growth/decay actually means and how it can be expressed algebraically and graphically - and why. An accompanying commentary provides answers with explanations. After using this resource, most students can create models of the type y=k(a^x), explain the graphical behaviour of this function and give examples of real life occurrences.Including all the Power point presentations for the Topic 1 - Algebra based on the IB Mathematics SL Syllabus. The sub topics are:
Patterns and Sequences
Arithmetic sequences
Geometric sequences
Sigma notation
Arithmetic series
Geometric series
Convergent series and sums to infinity
Applications of geometric and arithmetic patterns
Exponents
Solving exponential equations
Properties of logarithms
Laws of logarithms
Change of base
Exponential and logarithmic equations
Pascal triangle
Binomial expansion
Mathematics of Finance is one of the topic which is covered during Mathematics lectures and seminars in order to enhance students knowledge.
During this Lecture and Seminar we are covering following subtopics (Agenda):
- Indices and logarithms and their rules
- Exponential functions
- Applications of exponential functions
- Limit and continuity of functions
In this File you will find:
- 1 Mathematics of Finance Lecture Power Point Presentation 28 Slides
- 1 Seminar Plan
- 19 Seminar Activities with full answer list for students
All covered materials are taught for bachelor level students Level 3.
Please write your comments once you purchase this lesson in order to have some suggestions for further improvements of teaching materials. | 677.169 | 1 |
Differential Equations Modeling with MATLAB
ISBN-10: 013736539X
ISBN-13: 9780137365395 engineering and science courses in Differential Equations. This progressive text on differential equations utilizes MATLAB's state-of-the-art computational and graphical tools right from the start to help students probe a variety of mathematical models. Ideas are examined from four perspectives: geometric, analytic, numeric, and physical. Students are encouraged to develop problem-solving skills and independent judgment as they derive models, select approaches to their analysis, and find answers to the original, physical questions. Both qualitative and algebraic tools are stressed | 677.169 | 1 |
Calculus hasn't changed, but your students have. Today's students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. Thomas' Calculus, Twelfth Edition, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, and improved conceptual flow.
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. | 677.169 | 1 |
Saturday, April 21, 2012
But last week I have received couple of pushy emails that wanted to know how to study mathematics.
So here I go.
Maths is a subject of concepts and techniques to apply those concepts.
Vectors, derivatives, complex numbers etc are all concepts to link and explain the physical world. If you don't understand them, no amount of practice of solving them will be useful.
You need to understand what this concept is and then do practice questions to apply those concepts.
Most Maths books just concentrate on the techniques to solve but if you have access to Internet, then understanding concepts behind Maths is much simpler now.
Head over to the videos of khan academy ( ) and cement those concepts first. I didn't have them, when I was studying, but now I never miss a chance to head over these videos to cement my understanding.
He used to teach us a topic and the next day, first thing he used to do was write couple of exercise numbers on the board and asked us to do those exercise question in ten minutes before he began his next lesson.
This was the ritual. The practice of this random exercises from the old taught topics was great. It cemented the understanding and this regularity kept the concepts alive.
So these are the two steps that I used to do in my Maths study in aesi.
Learn the concept. Understand it. First from the teacher and then by myself.
Once this was done. I went to the exercise of the book. Will systematically solve all exercise, but also incorporated the habit of giving myself 10 minutes to do random exercises question from the previous exercises. This ten minutes were how I used to start studying Maths.
Every math study session began with doing a ten minute random exercises from previously understood concepts.
Hope this helps. I am far removed from doing Maths right now but I feel this principal that I learnt in class vii from my Maths teacher still works and will be helpful to anyone applying it.
What are your ways of studying Maths? Do you have a nobel technique to share?
Thursday, April 19, 2012
The above screen shot shows a part of the e-conversation with the Senior General Manager of Reliance Industries. Everyone's hope is FDI.
What do you think about allowing FDI @ Aviation ? Let's discuss !
I love to interact with so many students and I always try to share my experience with them. Just a couple of hours before, I received a message from a student. She asked me some questions which can be seen in the below picture. I'm very happy to see that students are actually enjoying AeSI these days and have started interacting with each other using social media platforms.
My learning in embedded technology
## I want to be very honest while replying. It's a fact that a couple of months back, I wasn't even aware that whether a resistor has polarity or not ? what exactly a capacitor does ? how to use voltmeter ?
## I learnt Embedded Technology just because I have seen that it's a trend going on in Bangalore and most of the guys use to choose this path.
## I was good in C language but when I joined the institute, I came to know what is the difference between the C language taught in a normal institute and what is required by an industry? Till 2011, I wasn't aware about graphics.h. I never thought that we can turn OFF/ON keyboard keys using C program.
Playing with LCD, :LED, MOTORS and .................
(It doesn't mean only turning On & Off.... example : intensity variation of LED, glowing and blinking of a set of LED in multiple pattern, Displaying various things in various ways on LCD, controlling the speed of motors.)\
I have used Atmel's Atmega8 and Atmega16 microcontrollers in basic and Atmega128 as in advanced embedded. Software used were Code Vision AVR and AVR Studio. There is a difference between C and Embedded C. I have learnt the basics of Embedded-C at the institute and I'm still on the way of learning excellence in Embedded-C. But some company also uses Embedded-Java.
****************************
Learning a technology is always good, but do it only and only if you have passion to learn. Don't just do it like me. In my case I have done it just because of the trend going on that time and I was not having enough people to communicate with. Let's leave it. AesiAA & the team's intention is to help others so that the future of Aesi students can be polished.
The girl who has sent this message, wrote that she has knowledge in some languages like java, c , c++, unix, linux etc. It's good but I want to suggest that rather then thinking in all directions, think in one direction but with a shadow of perfection. I'm confident that one day you'll become the role model for others. People will give your examples to others.
Linux is very good because of it's nature of virus free activities. When you work with micro controller, It's always necessary to work in a virus free platform because we burn files into micro controller. and due to some other reasons as well.
Take an example of flight control system or fly by wire system. Just close your eyes and imagine How it's possible that flaps of star board is going upwards and flaps of port wing is going downwards? How it's possible that after moving to a particular degree it stop its movements? How does an aircraft understand that how much deviation from original position it require ? How does the light blink which is located in the belly of aircraft? Anti-collision system : How is it working ? Is there any concept of sensor in the operation of this system ? Specific warning comes only at specific job... Why and How ?
The answers are hidden in just one word which is none other then "EMBEDDED"
Case 1 : B.Tech (Aeronautical) Vs B.Tech (Electronics)
Case 2 : B.Tech+M.Tech (Aeronautical) Vs B.tech(Electronics)+M.Tech(Aeronautical)
My experience says that a company is more interested in the profile which is marked bold because of a fact that a regular student of electronics will obviously know more about electronics. In all operations of FMS (Flight management system) the technology used is fully devoted to electronics. One just need a cloud of Aviation to be the best. Even in case 1, company has good trainers who have the ability to teach the ABC of aviation to electronics students. My intention is not to demotivate the students rather I just want to show them the reality. So It's a world of competition, if we want to kiss success, so we have to try hard, try making new projects, refer magazines like electronics for you ! digit ! and all...
But It's a fact that AeSI students have more knowledge (not practical), if a chance of learning is given, they are going to rock. It's time to say and prove that
Tuesday, April 17, 2012
It's time for me to get ready and go to office so can't share everything in detail as if now. I'm sharing a presentation to all electronics hobbyists who love to play with micro controllers and have an attitude to learn and grow. In case if you do have any query related to it so feel free to post your comments and please note that I'm not getting anything to refer you in the industry. It's just because I've seen students saying that "No company recruits freshers and I want to help my Aesi friends."
Everything you say is true. But what you don't know or realize is that we the seniors and aesiaa are doing a lot behind the scene for addressing those concerns. The heat is on. Its only when the water boils we realize the fire is on.
This post about the glowing testimonial we got for aesi graduates from director ADE is a result of lot of efforts and dedication from our side.
Yes things are still bad and needs improvement. But this is a gradual process and it will take time.
When I say be proud of your degree, I mean be proud of the efforts you have put in your degree. Be proud of the knowledge it has given you. Once you are in the industry, you will truly see the height, studying for AeSI has taken you. Look at these posts in myaesi and you will understand what I am saying.
When we realize the value of this education after we graduate. We can't expect people to understand it without experiencing it. It's a job for the bureaucrats at AeSI buts it's a way of life for us.
Building the brand of AeSI is what we at AeSIAA has chosen to do. IIT's are not only famous for the education they provide but for the things the IIT graduates do. We want to do the same for AeSI.
AeSI should be known for its graduates. And with students like you and many others from whom I regularly get mail from, I am assured the future for AeSI and its graduates is bright.
Cheers and reach for the stars.
The conversation on the posts is continuing in the comment section of the post. Head over to the post and join the conversation.
Sunday, April 15, 2012
After my recent post on update from aesiaa, I received this email from an aesi student. And I am posting his email here for giving it a wider audience.
I am changing the name for obvious reasons. But the points raised by him are genuine and worth to ponder.
I have sent a brief reply to this email to him, will post the same here, latter this week.
Now over to the student of aesi......
hello sir,
I am tony, AVIONICS stream , cleared 16 papers so far(65.2%). I don't know what to say and what to expect from this email but still you asked me to shoot you a mail, so i'm writing this. When you wrote the last blog , then i got a little carried away and wrote things that shouldn't be said or atleast the way i put it .
I'm sorry for that, but truely sir what i wrote was straight from the heart and if you think from our student side, then it won't be that wrong if you see.
What AESIAA is doing or trying to do, is very impressive and yes every one has a life and sorry for putting it that way. What i want is that someone could carry my words to AESI, as i can't do it myself as long as i haven't completed it, thats it, what i meant when i wrote it . I thing AESI doesnt deserve that kind of pride 'cause of the negligence it shows to students like us,and the lady who picks up the phone she is over smart, i think, don't even know the proper rules,
Why AESI is not up to the mark for me?
1) Absolutely no motivation from their side, u don't get credit on merit , nor deserving students are offered any job after completion, so when there is no motivation how one is supposed to study,
2) very elusive policies and rules, the rules regarding training and projects in sec-b are not clearly mentioned in any written notice, u have to call AESI to seek information and that stupid lady hungs up without even listening to your queries,
3) Syllabus not upto the mark what industry seeks from avionics, students, nor it is suitable for GATE, we have to study a hell lot extra to cover it up, its not so in case of aero-mechanical though,
4)Wont give authority to any college , like IGNOU so they can train us the way they want and practical can be included.
5) i don't understand every organisation wants to see its growth , but why not AESI ? its going the other way round, its being decades since the foundation of AESI, progress is nil not slow,
6) The curriculum does n't encourages quality students, most of the students who are present in AESI are simply 'cause they didn't get chance in good colleges not like me who want to study aeronautics ,,
7) there is a huge void between passing of 20 papers and getting a job 'cause :- a) No one knows AESI that well b) % marks are not good of majority of students c) no practical knowledge only theoretical, so that effects confidence of the student itself d) to gain practical knowledge u have to get training from organisations which are mostly unpaid and u have to pay them instead, so that kills time, money ,patience and aesi is not be bothered about it
8) "u are 21 \22 yr u are an engineer and working for a good company " chances for either of this case or both to occur is tending to 0% i believe
Sir , i have spit it out, i don't know how will you take it but i certainly can't feel proud of an organization which lacks this qualities, i'm very sorry sir, my apology again.
Thursday, April 12, 2012
AeSI Graduates received this great and best possible recommendation from none other than Shri PS Krishnan, Distinguished Scientist & Director ADE.
Have a look!!.
The text for your reference.
I am writing this letter for the high possible recommendation for the graduates of the Aeronautical Society of India. I have seen many of the AeSI Grads working at various positions under many UAV programs at Aeronautical Development Establishment for couple of decades. I found them very sincere and diligent.
They have shown commitment for work and have impressed me and my establishment with their extraordinary understanding of the engineering fundamentals. They have contributed well with the scientists community in the lab and outside, taken opportunities to discover more about their fields of work. They have independently taken initiative of refining the methods of simulation rather than just concentrating on the results. They have also proven themselves to be adoptable and efficient manager of the resources. As an illustration of their calibre, those scientist of this stream selected in DRDO have risen to the positions even up to the Director of the labs and retired as Scientist G's as a minimum.
As per my impression of them, they would be an asset for any organisation they are a part of and i truly believe that they will always excel in their career.
Wednesday, April 11, 2012
Sunday, April 08, 2012
A quick update on the recent commendation that AeSIAA received at the recently concluded AeSI Bangalore AGM.
Dear Fellow Alumnus, It is my great pleasure to announce that AeSIAA has received a tremendous attention and support during the recently concluded AGM of AeSI Bangalore Branch and received the commendation from Shri T Mohana Rao, Chairman, AeSI BB.
"We place on record our deep sense of appreciation for excellent services rendered by you in furthering the cause of Aeronautical Fraternity through Aeronautical Society of India, Bangalore Branch. .................T Mohana Rao, Chairman, AeSI BB"
Friends, this is just the beginning. With your continued support and endevours, we are likely to excel further in our activity. We need to create a brand of AeSI like IITs/IIMs and we the graduates are the ingredients of this. Each one of us in our respective organisations should feel proud and be the ambassador of AeSIAA. We need to map all our alumnus across all organisations and bring them into single umbrellas for mutual benefit of all. Let pledge to do so. Help AeSIAA, Help yourself by joining and taking active interest in furthering the cause of Aeronautical Fraternity through our AeSIAA.
With this motto in mind we are planning a general body meeting and requesting participation of all AeSI Grads/alumnus settled/working in and around Bangalore in our AGM on Saturday, May 12, 2012 at AeSI Bangalore Branch.
Kindly spare your valuable time and be the part of the ongoing efforts of AeSIAA creating BRAND AeSIAA. The agenda and notice of the meeting will follow soon. We also seek generous donations for creating funds for awards in the following category like Distinguished Alumni Award, Best Students etc. The same will be debated and discussed during the scheduled AGM. All are welcome to give their valuable inputs.
The awards can be named after the donors if the donations are sufficient. Alumnus settled abroad or with High net worth are requested to join this privileged move.
I'm confident that all of us know that "Winners don't do different things but they do the things differently".
Yeah ! It's the fact of clearing papers of Aesi. Doing things differently doesn't mean that the answer of a question will become 1 from 0. It means to add values by using Graphs, Flow Charts, Diagrams etc...
As Mr. Singh always says that garnishing your answer sheet matters a lot. Practice last years question papers and always remember that "doing mistakes at the class room is better than doing mistakes in the exam hall." Good luck to all the students who are about to give exams in June,2012 session. | 677.169 | 1 |
Pass the screening test. Remote screening test for non-local applicants would be held in March, 2017. The screening test for local applicants will be held on June 10, 2017 (Saturday).
Class Day: Tuesday, Thursday & Friday
Course Description
This course is designed to introduce students to the fundamental concepts of mathematics such as sets, number systems, relations, functions and cardinality. It also serves as a bridge between computational and proof-based courses. By means of a wide variety of proof-writing and oral presentation practice, students will learn to communicate mathematics emphasizing precise logic and clear exposition. We hope that this course can invite students to explore mathematics more deeply and even entice some of them to become mathematics majors. | 677.169 | 1 |
The quadratic formula expresses the solution of the degree two equation ax2 + bx + c = 0, where a is not zero, in terms of its coefficients a, b and c.
Algebra (from Arabic"al-jabr" meaning "reunion of broken parts"[1]) is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols;[2] it is a unifying thread of almost all of mathematics.[3] As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.
Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values,[4] for example, in x+2=5{\displaystyle x+2=5} the letter x{\displaystyle x} is unknown, but the law of inverses can be used to discover its value: x=3{\displaystyle x=3}. In E = mc2, the letters E{\displaystyle E} and m{\displaystyle m} are variables, and the letter c{\displaystyle c} is a constant, the speed of light in a vacuum. Algebra gives methods for solving equations and expressing formulas that are much easier (for those who know how to use them) than the older method of writing everything out in words.
The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an "algebra", and the word is used, for example, in the phrases linear algebra and algebraic topology.
Etymology
The word algebra comes from the Arabicالجبر (al-jabr lit. "the reunion of broken parts") from the title of the book Ilm al-jabr wa'l-muḳābala by the Persian mathematician and astronomer al-Khwarizmi. The word entered the English language during the fifteenth century, from either Spanish, Italian, or Medieval Latin, it originally referred to the surgical procedure of setting broken or dislocated bones. The mathematical meaning was first recorded in the sixteenth century.[5]
Different meanings of "algebra"
The word "algebra" has several related meanings in mathematics, as a single word or with qualifiers.
As a single word without an article, "algebra" names a broad part of mathematics.
As a single word with an article or in plural, "an algebra" or "algebras" denotes a specific mathematical structure, whose precise definition depends on the author. Usually the structure has an addition, multiplication, and a scalar multiplication (see Algebra over a field). When some authors use the term "algebra", they make a subset of the following additional assumptions: associative, commutative, unital, and/or finite-dimensional. In universal algebra, the word "algebra" refers to a generalization of the above concept, which allows for n-ary operations.
Algebra as a branch of mathematics
Algebra began with computations similar to those of arithmetic, with letters standing for numbers,[4] this allowed proofs of properties that are true no matter which numbers are involved. For example, in the quadratic equation
ax2+bx+c=0,{\displaystyle ax^{2}+bx+c=0,}
a,b,c{\displaystyle a,b,c} can be any numbers whatsoever (except that a{\displaystyle a} cannot be 0{\displaystyle 0}), and the quadratic formula can be used to quickly and easily find the values of the unknown quantity x{\displaystyle x} which satisfy the equation. That is to say, to find all the solutions of the equation.
Historically, and in current teaching, the study of algebra starts with the solving of equations such as the quadratic equation above. Then more general questions, such as "does an equation have a solution?", "how many solutions does an equation have?", "what can be said about the nature of the solutions?" are considered. These questions lead to ideas of form, structure and symmetry,[6] this development permitted algebra to be extended to consider non-numerical objects, such as vectors, matrices, and polynomials. The structural properties of these non-numerical objects were then abstracted to define algebraic structures such as groups, rings, and fields.
Before the 16th century, mathematics was divided into only two subfields, arithmetic and geometry. Even though some methods, which had been developed much earlier, may be considered nowadays as algebra, the emergence of algebra and, soon thereafter, of infinitesimal calculus as subfields of mathematics only dates from the 16th or 17th century, from the second half of 19th century on, many new fields of mathematics appeared, most of which made use of both arithmetic and geometry, and almost all of which used algebra.
The Hellenistic mathematicians Hero of Alexandria and Diophantus[12] as well as Indian mathematicians such as Brahmagupta continued the traditions of Egypt and Babylon, though Diophantus' Arithmetica and Brahmagupta's Brāhmasphuṭasiddhānta are on a higher level.[13] For example, the first complete arithmetic solution (including zero and negative solutions) to quadratic equations was described by Brahmagupta in his book Brahmasphutasiddhanta. Later, Persian and Arabic mathematicians developed algebraic methods to a much higher degree of sophistication, although Diophantus and the Babylonians used mostly special ad hoc methods to solve equations, Al-Khwarizmi's contribution was fundamental. He solved linear and quadratic equations without algebraic symbolism, negative numbers or zero, thus he had to distinguish several types of equations.[14]
In the context where algebra is identified with the theory of equations, the Greek mathematician Diophantus has traditionally been known as the "father of algebra" but in more recent times there is much debate over whether al-Khwarizmi, who founded the discipline of al-jabr, deserves that title instead.[15].[16],[17] and that he gave an exhaustive explanation of solving quadratic equations,[18] supported by geometric proofs, while treating algebra as an independent discipline in its own right.[19]".[20]
Another Persian mathematician Omar Khayyam is credited with identifying the foundations of algebraic geometry and found the general geometric solution of the cubic equation, his book Treatise on Demonstrations of Problems of Algebra (1070), which laid down the principles of algebra, is part of the body of Persian mathematics that was eventually transmitted to Europe.[21] Yet another Persian mathematician, Sharaf al-Dīn al-Tūsī, found algebraic and numerical solutions to various cases of cubic equations,[22] he also developed the concept of a function.[23] The Indian mathematicians Mahavira and Bhaskara II, the Persian mathematician Al-Karaji,[24]Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī (1412–1486) took ''the first steps toward the introduction of algebraic symbolism''.He also computed ∑n2, ∑n3 and used the method of successive approximation to determine square roots.[25] As the Islamic world was declining, the European world was ascending. And it is here that algebra was further developed.
Areas of mathematics with the word algebra in their name
Some areas of mathematics that fall under the classification abstract algebra have the word algebra in their name; linear algebra is one example. Others do not: group theory, ring theory, and field theory are examples. In this section, we list some areas of mathematics with the word "algebra" in the name.
Elementary algebra, the part of algebra that is usually taught in elementary courses of mathematics.
Elementary algebra
Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic; in arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In algebra, numbers are often represented by symbols called variables (such as a, n, x, y or z). This is useful because:
It allows the general formulation of arithmetical laws (such as a + b = b + a for all a and b), and thus is the first step to a systematic exploration of the properties of the real number system.
It allows the reference to "unknown" numbers, the formulation of equations and the study of how to solve these. (For instance, "Find a number x such that 3x + 1 = 10" or going a bit further "Find a number x such that ax + b = c". This step leads to the conclusion that it is not the nature of the specific numbers that allows us to solve it, but that of the operations involved.)
It allows the formulation of functional relationships. (For instance, "If you sell x tickets, then your profit will be 3x − 10 dollars, or f(x) = 3x − 10, where f is the function, and x is the number to which the function is applied".)
Polynomials
A polynomial is an expression that is the sum of a finite number of non-zero terms, each term consisting of the product of a constant and a finite number of variables raised to whole number powers. For example, x2 + 2x − 3 is a polynomial in the single variable x. A polynomial expression is an expression that may be rewritten as a polynomial, by using commutativity, associativity and distributivity of addition and multiplication, for example, (x − 1)(x + 3) is a polynomial expression, that, properly speaking, is not a polynomial. A polynomial function is a function that is defined by a polynomial, or, equivalently, by a polynomial expression, the two preceding examples define the same polynomial function.
Two important and related problems in algebra are the factorization of polynomials, that is, expressing a given polynomial as a product of other polynomials that can not be factored any further, and the computation of polynomial greatest common divisors. The example polynomial above can be factored as (x − 1)(x + 3). A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable.
Education
It has been suggested that elementary algebra should be taught to students as young as eleven years old,[28] though in recent years it is more common for public lessons to begin at the eighth grade level (≈ 13 y.o. ±) in the United States.[29] However, in some US schools, algebra is started in ninth grade.
Since 1997, Virginia Tech and some other universities have begun using a personalized model of teaching algebra that combines instant feedback from specialized computer software with one-on-one and small group tutoring, which has reduced costs and increased student achievement.[30]
Abstract algebra
Abstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts. Here are listed fundamental concepts in abstract algebra.
Sets: Rather than just considering the different types of numbers, abstract algebra deals with the more general concept of sets: a collection of all objects (called elements) selected by property specific for the set. All collections of the familiar types of numbers are sets. Other examples of sets include the set of all two-by-two matrices, the set of all second-degree polynomials (ax2 + bx + c), the set of all two dimensional vectors in the plane, and the various finite groups such as the cyclic groups, which are the groups of integers modulon. Set theory is a branch of logic and not technically a branch of algebra.
Binary operations: The notion of addition (+) is abstracted to give a binary operation, ∗ say. The notion of binary operation is meaningless without the set on which the operation is defined, for two elements a and b in a set S, a ∗ b is another element in the set; this condition is called closure. Addition (+), subtraction (−), multiplication (×), and division (÷) can be binary operations when defined on different sets, as are addition and multiplication of matrices, vectors, and polynomials.
Identity elements: The numbers zero and one are abstracted to give the notion of an identity element for an operation. Zero is the identity element for addition and one is the identity element for multiplication, for a general binary operator ∗ the identity element e must satisfy a ∗ e = a and e ∗ a = a, and is necessarily unique, if it exists. This holds for addition as a + 0 = a and 0 + a = a and multiplication a × 1 = a and 1 × a = a. Not all sets and operator combinations have an identity element; for example, the set of positive natural numbers (1, 2, 3, ...) has no identity element for addition.
Inverse elements: The negative numbers give rise to the concept of inverse elements. For addition, the inverse of a is written −a, and for multiplication the inverse is written a−1. A general two-sided inverse element a−1 satisfies the property that a ∗ a−1 = e and a−1 ∗ a = e, where e is the identity element.
Associativity: Addition of integers has a property called associativity. That is, the grouping of the numbers to be added does not affect the sum, for example: (2 + 3) + 4 = 2 + (3 + 4). In general, this becomes (a ∗ b) ∗ c = a ∗ (b ∗ c). This property is shared by most binary operations, but not subtraction or division or octonion multiplication.
Commutativity: Addition and multiplication of real numbers are both commutative. That is, the order of the numbers does not affect the result, for example: 2 + 3 = 3 + 2. In general, this becomes a ∗ b = b ∗ a. This property does not hold for all binary operations, for example, matrix multiplication and quaternion multiplication are both non-commutative.
Groups
Combining the above concepts gives one of the most important structures in mathematics: a group. A group is a combination of a set S and a single binary operation ∗, defined in any way you choose, but with the following properties:
An identity element e exists, such that for every member a of S, e ∗ a and a ∗ e are both identical to a.
Every element has an inverse: for every member a of S, there exists a member a−1 such that a ∗ a−1 and a−1 ∗ a are both identical to the identity element.
The operation is associative: if a, b and c are members of S, then (a ∗ b) ∗ c is identical to a ∗ (b ∗ c).
If a group is also commutative—that is, for any two members a and b of S, a ∗ b is identical to b ∗ a—then the group is said to be abelian.
For example, the set of integers under the operation of addition is a group; in this group, the identity element is 0 and the inverse of any element a is its negation, −a. The associativity requirement is met, because for any integers a, b and c, (a + b) + c = a + (b + c)
The nonzero rational numbers form a group under multiplication. Here, the identity element is 1, since 1 × a = a × 1 = a for any rational number a. The inverse of a is 1/a, since a × 1/a = 1.
The integers under the multiplication operation, however, do not form a group, this is because, in general, the multiplicative inverse of an integer is not an integer. For example, 4 is an integer, but its multiplicative inverse is ¼, which is not an integer.
Semigroups, quasigroups, and monoids are structures similar to groups, but more general. They comprise a set and a closed binary operation, but do not necessarily satisfy the other conditions. A semigroup has an associative binary operation, but might not have an identity element. A monoid is a semigroup which does have an identity but might not have an inverse for every element. A quasigroup satisfies a requirement that any element can be turned into any other by either a unique left-multiplication or right-multiplication; however the binary operation might not be associative.
Rings and fields
Groups just have one binary operation. To fully explain the behaviour of the different types of numbers, structures with two operators need to be studied, the most important of these are rings, and fields.
A ring has two binary operations (+) and (×), with × distributive over +. Under the first operator (+) it forms an abelian group. Under the second operator (×) it is associative, but it does not need to have identity, or inverse, so division is not required, the additive (+) identity element is written as 0 and the additive inverse of a is written as −a.
Distributivity generalises the distributive law for numbers. For the integers (a + b) × c = a × c + b × c and c × (a + b) = c × a + c × b, and × is said to be distributive over +.
The integers are an example of a ring, the integers have additional properties which make it an integral domain.
A field is a ring with the additional property that all the elements excluding 0 form an abelian group under ×. The multiplicative (×) identity is written as 1 and the multiplicative inverse of a is written as a−1.
The rational numbers, the real numbers and the complex numbers are all examples of fields.
See also
Notes
^I. N. Herstein, Topics in Algebra, "An algebraic system can be described as a set of objects together with some operations for combining them." p. 1, Ginn and Company, 1964
^I. N. Herstein, Topics in Algebra, "...it also serves as the unifying thread which interlaces almost all of mathematics." p. 1, Ginn and Company, 1964
^ abc(Boyer 1991, "Europe in the Middle Ages" p. 258) "In the arithmetical theorems in Euclid's Elements VII-IX, numbers had been represented by line segments to which letters had been attached, and the geometric proofs in al-Khwarizmi's Algebra made use of lettered diagrams; but all coefficients in the equations used in the Algebra are specific numbers, whether represented by numerals or written out in words. The idea of generality is implied in al-Khwarizmi's exposition, but he had no scheme for expressing algebraically the general propositions that are so readily available in geometry."
^(Boyer 1991, "The Arabic Hegemony" p. 229) "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation."
^(Boyer 1991, "The Arabic Hegemony" p. 230) "The six cases of equations given above exhaust all possibilities for linear and quadratic equations having positive root. So systematic and exhaustive was al-Khwarizmi's exposition that his readers must have had little difficulty in mastering the solutions."
^Gandz and Saloman (1936), The sources of al-Khwarizmi's algebra, Osiris i, p. 263–277: "In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers".
^(Boyer 1991, "The Arabic Hegemony" p. 239) "Abu'l Wefa was a capable algebraist as well as a trigonometer. ... His successor al-Karkhi evidently used this translation to become an Arabic disciple of Diophantus – but without Diophantine analysis! ... In particular, to al-Karkhi is attributed the first numerical solution of equations of the form ax2n + bxn = c (only equations with positive roots were considered),"
1. center-stage Banks portrays the human Fassin Taak, a Slow Seer at the Court of the Nasqueron Dwellers. They are the major species outside the control of the Mercatoria. Dweller societies try not to get involved with Quick species, those with sentient beings who experience life at around the human beings experience it. Dwellers are one of the Slow species who experience life at a much slower temporal rate, Dweller individuals live for millions of years, and the species has existed for billions of years, long before the foundation of the Mercatoria. Taak, looking forward to a life of scholarship, is astonished to be drafted into one of the Mercatorias religio-military orders. However, the Dweller List is only a list of star systems, portals are relatively small and can be anywhere within a system so long as it is a point of zero net gravitational attraction, such as a Lagrange point. The list is useless without a certain mathematical transform needed to give the location of the portals. Taak must go on an expedition to Nasqueron in order to find the Transform. A Mercatoria counter-attack fleet hurries to defend Ulubis against the Starveling Cult ships, however, both fleets are forced to travel at sub light speeds, leaving the inhabitants of the Ulubis system anxiously wondering which will arrive first. Taaks hunt for the Transform takes him on a dizzying journey and it is also revealed that the Dwellers have been harbouring artificial intelligences from Mercatoria persecution. The Beyonder/Starveling forces arrive and easily overwhelm Ulubiss native defences, however, they discover to their dismay that the counter-attack force is arriving much sooner than predicted, and is superior. The Beyonder factions despair of locating Taak and the secret in the time available before the recapture of Ulubis and he makes a last-ditch attempt to force the Dwellers to yield up Taak, threatening them with antimatter weapons. The Dwellers respond with devastating blows on his fleet, Taak returns from his journey with his memory partly erased. However, he is able to piece together the secret from the remaining clues. The Dwellers have hidden wormhole portals in the cores of all their occupied planets, however, it remains unclear whether the Dwellers will give the necessary cooperation in allowing other species access to their network, now that the secret is out. The novel ends with Taak, having left Ulubis and joined the Beyonders, in an interview in 2004, Banks stated that It probably could become a trilogy, but for now it's a standalone novel
2. unknown, while a, b, and c are constants with a not equal to 0, one can verify that the quadratic formula satisfies the quadratic equation, by inserting the former into the latter. With the above parameterization, the formula is, x = − b ± b 2 −4 a c 2 a. Each of the solutions given by the formula is called a root of the quadratic equation. Geometrically, these represent the x values at which any parabola, explicitly given as y = ax2 + bx + c. The quadratic formula can be derived with an application of technique of completing the square. For this reason, the derivation is sometimes left as an exercise for students, the explicit derivation is as follows. Divide the quadratic equation by a, which is allowed because a is non-zero, subtract c/a from both sides of the equation, yielding, x 2 + b a x = − c a. The quadratic equation is now in a form to which the method of completing the square can be applied, accordingly, after rearranging the terms on the right hand side to have a common denominator, we obtain,2 = b 2 −4 a c 4 a 2. The square has thus been completed, taking the square root of both sides yields the following equation, x + b 2 a = ± b 2 −4 a c 2 a. Isolating x gives the formula, x = − b ± b 2 −4 a c 2 a. The plus-minus symbol ± indicates that both x = − b + b 2 −4 a c 2 a and x = − b − b 2 −4 a c 2 a are solutions of the quadratic equation. There are many alternatives of this derivation with minor differences, mostly concerning the manipulation of a and these result in slightly different forms for the solution, but are otherwise equivalent. A lesser known quadratic formula, as used in Mullers method, without going into parabolas as geometrical objects on a cone, a parabola is any curve described by a second-degree polynomial, i. e. The first and foremost geometrical application of the formula is that it will define the points along the x-axis where the parabola will cross it. If this distance term were to decrease to zero, the axis of symmetry would be the x value of the zero, algebraically, this means that √b2 − 4ac =0, or simply b2 − 4ac =0, for its term to be reduced to zero
35 supers67. analysis may be distinguished from geometry, however, it can be applied to any space of mathematical objects that has a definition of nearness or specific distances between objects. Mathematical analysis formally developed in the 17th century during the Scientific Revolution, early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, a geometric sum is implicit in Zenos paradox of the dichotomy. The explicit use of infinitesimals appears in Archimedes The Method of Mechanical Theorems, in Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle. Zu Chongzhi established a method that would later be called Cavalieris principle to find the volume of a sphere in the 5th century, the Indian mathematician Bhāskara II gave examples of the derivative and used what is now known as Rolles theorem in the 12th century. In the 14th century, Madhava of Sangamagrama developed infinite series expansions, like the power series and his followers at the Kerala school of astronomy and mathematics further expanded his works, up to the 16th century. The modern foundations of analysis were established in 17th century Europe. During this period, calculus techniques were applied to approximate discrete problems by continuous ones, in the 18th century, Euler introduced the notion of mathematical function. Real analysis began to emerge as an independent subject when Bernard Bolzano introduced the definition of continuity in 1816. In 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra widely used in earlier work, instead, Cauchy formulated calculus in terms of geometric ideas and infinitesimals. Thus, his definition of continuity required a change in x to correspond to an infinitesimal change in y. He also introduced the concept of the Cauchy sequence, and started the theory of complex analysis. Poisson, Liouville, Fourier and others studied partial differential equations, the contributions of these mathematicians and others, such as Weierstrass, developed the -definition of limit approach, thus founding the modern field of mathematical analysis. In the middle of the 19th century Riemann introduced his theory of integration, the last third of the century saw the arithmetization of analysis by Weierstrass, who thought that geometric reasoning was inherently misleading, and introduced the epsilon-delta definition of limit. Then, mathematicians started worrying that they were assuming the existence of a continuum of numbers without proof. Around that time, the attempts to refine the theorems of Riemann integration led to the study of the size of the set of discontinuities of real functions, also, monsters began to be investigated
8.
Group (mathematics)
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In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element. The operation satisfies four conditions called the group axioms, namely closure and it allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way while retaining their essential structural aspects. The ubiquity of groups in areas within and outside mathematics makes them a central organizing principle of contemporary mathematics. Groups share a kinship with the notion of symmetry. The concept of a group arose from the study of polynomial equations, after contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory—an active mathematical discipline—studies groups in their own right, to explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups. A theory has developed for finite groups, which culminated with the classification of finite simple groups. Since the mid-1980s, geometric group theory, which studies finitely generated groups as objects, has become a particularly active area in group theory. One of the most familiar groups is the set of integers Z which consists of the numbers, −4, −3, −2, −1,0,1,2,3,4. The following properties of integer addition serve as a model for the group axioms given in the definition below. For any two integers a and b, the sum a + b is also an integer and that is, addition of integers always yields an integer. This property is known as closure under addition, for all integers a, b and c, + c = a +. Expressed in words, adding a to b first, and then adding the result to c gives the final result as adding a to the sum of b and c. If a is any integer, then 0 + a = a +0 = a, zero is called the identity element of addition because adding it to any integer returns the same integer. For every integer a, there is a b such that a + b = b + a =0. The integer b is called the element of the integer a and is denoted −a. The integers, together with the operation +, form a mathematical object belonging to a class sharing similar structural aspects. To appropriately understand these structures as a collective, the abstract definition is developed
9. the conceptualization of rings started in the 1870s and completed in the 1920s. Key contributors include Dedekind, Hilbert, Fraenkel, and Noether, rings were first formalized as a generalization of Dedekind domains that occur in number theory, and of polynomial rings and rings of invariants that occur in algebraic geometry and invariant theory. Afterward, they proved to be useful in other branches of mathematics such as geometry. A ring is a group with a second binary operation that is associative, is distributive over the abelian group operation. By extension from the integers, the group operation is called addition. Whether a ring is commutative or not has profound implications on its behavior as an abstract object, as a result, commutative ring theory, commonly known as commutative algebra, is a key topic in ring theory. Its development has greatly influenced by problems and ideas occurring naturally in algebraic number theory. The most familiar example of a ring is the set of all integers, Z, −5, −4, −3, −2, −1,0,1,2,3,4,5. The familiar properties for addition and multiplication of integers serve as a model for the axioms for rings, a ring is a set R equipped with two binary operations + and · satisfying the following three sets of axioms, called the ring axioms 1. R is a group under addition, meaning that, + c = a + for all a, b, c in R. a + b = b + a for all a, b in R. There is an element 0 in R such that a +0 = a for all a in R, for each a in R there exists −a in R such that a + =0. R is a monoid under multiplication, meaning that, · c = a · for all a, b, c in R. There is an element 1 in R such that a ·1 = a and 1 · a = a for all a in R.3. Multiplication is distributive with respect to addition, a ⋅ = + for all a, b, c in R. · a = + for all a, b, c in R. As explained in § History below, many follow a alternative convention in which a ring is not defined to have a multiplicative identity. This article adopts the convention that, unless stated, a ring is assumed to have such an identity
10.11. algebraic notation and an understanding of the general rules of the operators introduced in arithmetic. Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real, the use of variables to denote quantities allows general relationships between quantities to be formally and concisely expressed, and thus enables solving a broader scope of problems. Many quantitative relationships in science and mathematics are expressed as algebraic equations, algebraic notation describes how algebra is written. It follows certain rules and conventions, and has its own terminology, a term is an addend or a summand, a group of coefficients, variables, constants and exponents that may be separated from the other terms by the plus and minus operators. By convention, letters at the beginning of the alphabet are used to represent constants. They are usually written in italics, algebraic operations work in the same way as arithmetic operations, such as addition, subtraction, multiplication, division and exponentiation. and are applied to algebraic variables and terms. Multiplication symbols are usually omitted, and implied when there is no space between two variables or terms, or when a coefficient is used. For example,3 × x 2 is written as 3 x 2, usually terms with the highest power, are written on the left, for example, x 2 is written to the left of x. When a coefficient is one, it is usually omitted, likewise when the exponent is one. When the exponent is zero, the result is always 1, however 00, being undefined, should not appear in an expression, and care should be taken in simplifying expressions in which variables may appear in exponents. Other types of notation are used in algebraic expressions when the required formatting is not available, or can not be implied, such as where only letters, for example, exponents are usually formatted using superscripts, e. g. x 2. In plain text, and in the TeX mark-up language, the symbol ^ represents exponents. In programming languages such as Ada, Fortran, Perl, Python and Ruby, many programming languages and calculators use a single asterisk to represent the multiplication symbol, and it must be explicitly used, for example,3 x is written 3*x. Elementary algebra builds on and extends arithmetic by introducing letters called variables to represent general numbers and this is useful for several reasons. Variables may represent numbers whose values are not yet known, for example, if the temperature of the current day, C, is 20 degrees higher than the temperature of the previous day, P, then the problem can be described algebraically as C = P +20. Variables allow one to describe general problems, without specifying the values of the quantities that are involved, for example, it can be stated specifically that 5 minutes is equivalent to 60 ×5 =300 seconds
12. with their homomorphisms, form mathematical categories. Category theory is a formalism that allows a way for expressing properties. Universal algebra is a subject that studies types of algebraic structures as single objects. For example, the structure of groups is an object in universal algebra. As in other parts of mathematics, concrete problems and examples have played important roles in the development of abstract algebra, through the end of the nineteenth century, many – perhaps most – of these problems were in some way related to the theory of algebraic equations. Numerous textbooks in abstract algebra start with definitions of various algebraic structures. This creates an impression that in algebra axioms had come first and then served as a motivation. The true order of development was almost exactly the opposite. For example, the numbers of the nineteenth century had kinematic and physical motivations. An archetypical example of this progressive synthesis can be seen in the history of group theory, there were several threads in the early development of group theory, in modern language loosely corresponding to number theory, theory of equations, and geometry. Leonhard Euler considered algebraic operations on numbers modulo an integer, modular arithmetic, lagranges goal was to understand why equations of third and fourth degree admit formulae for solutions, and he identified as key objects permutations of the roots. An important novel step taken by Lagrange in this paper was the view of the roots, i. e. as symbols. However, he did not consider composition of permutations, serendipitously, the first edition of Edward Warings Meditationes Algebraicae appeared in the same year, with an expanded version published in 1782. Waring proved the theorem on symmetric functions, and specially considered the relation between the roots of a quartic equation and its resolvent cubic. Kronecker claimed in 1888 that the study of modern algebra began with this first paper of Vandermonde, cauchy states quite clearly that Vandermonde had priority over Lagrange for this remarkable idea, which eventually led to the study of group theory. Paolo Ruffini was the first person to develop the theory of permutation groups and his goal was to establish the impossibility of an algebraic solution to a general algebraic equation of degree greater than four
1314. its energy-content. One of his Annus Mirabilis papers, Einstein was the first to propose that the equivalence of mass and energy is a general principle and a consequence of the symmetries of space and time. A consequence of the equivalence is that if a body is stationary, it still has some internal or intrinsic energy, called its rest energy. When the body is in motion, its energy is greater than its rest energy. The mass-energy formula also serves to convert units of mass to units of energy, the formula was initially written in many different notations, and its interpretation and justification was further developed in several steps. In Does the inertia of a body depend upon its energy content, Einstein used V to mean the speed of light in a vacuum and L to mean the energy lost by a body in the form of radiation. A remark placed above it informed that the equation was approximated by neglecting magnitudes of fourth, subsequently, in October 1907, this was rewritten as M0 = E0/c2 and given a quantum interpretation by Johannes Stark, who assumed its validity and correctness. In December 1907, Einstein expressed the equivalence in the form M = μ + E0/c2 and concluded, A mass μ is equivalent, as regards inertia and it appears far more natural to consider every inertial mass as a store of energy. In 1909, Gilbert N. Lewis and Richard C. Tolman used two variations of the formula, m = E/c2 and m0 = E0/c2, with E being the energy of a body, E0 its rest energy, m the relativistic mass. In 1911, Max von Laue gave a more comprehensive proof of M0 = E0/c2 from the stress–energy tensor, which was later generalized by Felix Klein. Einstein returned to the once again after World War II. Mass and energy can be seen as two names for the underlying, conserved physical quantity. Thus, the laws of conservation of energy and conservation of mass are equivalent, Einstein elaborated in a 1946 essay that the principle of the conservation of mass proved inadequate in the face of the special theory of relativity. If the conservation of mass law is interpreted as conservation of rest mass, the rest energy of a particle can be converted, not to energy, but rather to other forms of energy that require motion, such as kinetic energy, thermal energy, or radiant energy. Similarly, kinetic or radiant energy can be converted to other kinds of particles that have rest energy, in the transformation process, neither the total amount of mass nor the total amount of energy changes, since both properties are connected via a simple constant. Its momentum and energy continue to increase without bounds, whereas its speed approaches a constant value—the speed of light
15. an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns, such equations are naturally represented using the formalism of matrices and vectors. Linear algebra is central to both pure and applied mathematics, for instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces, combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Because linear algebra is such a theory, nonlinear mathematical models are sometimes approximated by linear models. The study of linear algebra first emerged from the study of determinants, determinants were used by Leibniz in 1693, and subsequently, Gabriel Cramer devised Cramers Rule for solving linear systems in 1750. Later, Gauss further developed the theory of solving linear systems by using Gaussian elimination, the study of matrix algebra first emerged in England in the mid-1800s. In 1844 Hermann Grassmann published his Theory of Extension which included foundational new topics of what is called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for womb, while studying compositions of linear transformations, Arthur Cayley was led to define matrix multiplication and inverses. Crucially, Cayley used a letter to denote a matrix. In 1882, Hüseyin Tevfik Pasha wrote the book titled Linear Algebra, the first modern and more precise definition of a vector space was introduced by Peano in 1888, by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its form in the first half of the twentieth century. The use of matrices in quantum mechanics, special relativity, the origin of many of these ideas is discussed in the articles on determinants and Gaussian elimination. Linear algebra first appeared in American graduate textbooks in the 1940s, following work by the School Mathematics Study Group, U. S. high schools asked 12th grade students to do matrix algebra, formerly reserved for college in the 1960s. In France during the 1960s, educators attempted to teach linear algebra through finite-dimensional vector spaces in the first year of secondary school and this was met with a backlash in the 1980s that removed linear algebra from the curriculum. To better suit 21st century applications, such as mining and uncertainty analysis
16. sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a group is again a free group. Below are some of the areas studied in algebraic topology, In mathematics. The first and simplest homotopy group is the group, which records information about loops in a space. Intuitively, homotopy groups record information about the shape, or holes. In homology theory and algebraic topology, cohomology is a term for a sequence of abelian groups defined from a co-chain complex. That is, cohomology is defined as the study of cochains, cocycles. Cohomology can be viewed as a method of assigning algebraic invariants to a space that has a more refined algebraic structure than does homology. Cohomology arises from the algebraic dualization of the construction of homology, in less abstract language, cochains in the fundamental sense should assign quantities to the chains of homology theory. A manifold is a space that near each point resembles Euclidean space. Typically, results in algebraic topology focus on global, non-differentiable aspects of manifolds, knot theory is the study of mathematical knots. While inspired by knots that appear in daily life in shoelaces and rope, in precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R3. A simplicial complex is a space of a certain kind, constructed by gluing together points, line segments, triangles. Simplicial complexes should not be confused with the abstract notion of a simplicial set appearing in modern simplicial homotopy theory. The purely combinatorial counterpart to a complex is an abstract simplicial complex. A CW complex is a type of space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, an older name for the subject was combinatorial topology, implying an emphasis on how a space X was constructed from simpler ones grouped1920. parentheses were rearranged on each line, the values of the expressions were not altered, since this holds true when performing addition and multiplication on any real numbers, it can be said that addition and multiplication of real numbers are associative operations. Associativity is not to be confused with commutativity, which addresses whether or not the order of two operands changes the result. For example, the order doesnt matter in the multiplication of numbers, that is. Associative operations are abundant in mathematics, in fact, many algebraic structures explicitly require their binary operations to be associative, however, many important and interesting operations are non-associative, some examples include subtraction, exponentiation and the vector cross product. Z = x = xyz for all x, y, z in S, the associative law can also be expressed in functional notation thus, f = f. If a binary operation is associative, repeated application of the produces the same result regardless how valid pairs of parenthesis are inserted in the expression. This is called the generalized associative law, thus the product can be written unambiguously as abcd. As the number of elements increases, the number of ways to insert parentheses grows quickly. Some examples of associative operations include the following, the two methods produce the same result, string concatenation is associative. In arithmetic, addition and multiplication of numbers are associative, i. e. + z = x + = x + y + z z = x = x y z } for all x, y, z ∈ R. x, y, z\in \mathbb. }Because of associativity. Addition and multiplication of numbers and quaternions are associative. Addition of octonions is also associative, but multiplication of octonions is non-associative, the greatest common divisor and least common multiple functions act associatively. Gcd = gcd = gcd lcm = lcm = lcm } for all x, y, z ∈ Z. x, y, z\in \mathbb. }Taking the intersection or the union of sets, ∩ C = A ∩ = A ∩ B ∩ C ∪ C = A ∪ = A ∪ B ∪ C } for all sets A, B, C. Slightly more generally, given four sets M, N, P and Q, with h, M to N, g, N to P, in short, composition of maps is always associative. Consider a set with three elements, A, B, and C, thus, for example, A=C = A
21. needed there are operations, such as division and subtraction. The commutative property is a property associated with binary operations and functions. If the commutative property holds for a pair of elements under a binary operation then the two elements are said to commute under that operation. The term commutative is used in several related senses, putting on socks resembles a commutative operation since which sock is put on first is unimportant. Either way, the result, is the same, in contrast, putting on underwear and trousers is not commutative. The commutativity of addition is observed when paying for an item with cash, regardless of the order the bills are handed over in, they always give the same total. The multiplication of numbers is commutative, since y z = z y for all y, z ∈ R For example,3 ×5 =5 ×3. Some binary truth functions are also commutative, since the tables for the functions are the same when one changes the order of the operands. For example, the logical biconditional function p ↔ q is equivalent to q ↔ p and this function is also written as p IFF q, or as p ≡ q, or as Epq. Further examples of binary operations include addition and multiplication of complex numbers, addition and scalar multiplication of vectors. Concatenation, the act of joining character strings together, is a noncommutative operation, rotating a book 90° around a vertical axis then 90° around a horizontal axis produces a different orientation than when the rotations are performed in the opposite order. The twists of the Rubiks Cube are noncommutative and this can be studied using group theory. Some non-commutative binary operations, Records of the use of the commutative property go back to ancient times. The Egyptians used the property of multiplication to simplify computing products. Euclid is known to have assumed the property of multiplication in his book Elements
22. operation of arity zero, or 0-ary operation is a constant, the mixed product is an example of an operation of arity 3, or ternary operation. Generally, the arity is supposed to be finite, but infinitary operations are sometimes considered, in this context, the usual operations, of finite arity are also called finitary operations. There are two types of operations, unary and binary. Unary operations involve only one value, such as negation and trigonometric functions, binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, and exponentiation. Operations can involve mathematical objects other than numbers, the logical values true and false can be combined using logic operations, such as and, or, and not. Vectors can be added and subtracted, rotations can be combined using the function composition operation, performing the first rotation and then the second. Operations on sets include the binary operations union and intersection and the operation of complementation. Operations on functions include composition and convolution, operations may not be defined for every possible value. For example, in the numbers one cannot divide by zero or take square roots of negative numbers. The values for which an operation is defined form a set called its domain, the set which contains the values produced is called the codomain, but the set of actual values attained by the operation is its range. For example, in the numbers, the squaring operation only produces non-negative numbers. A vector can be multiplied by a scalar to form another vector, and the inner product operation on two vectors produces a scalar. An operation may or may not have certain properties, for example it may be associative, commutative, anticommutative, idempotent, the values combined are called operands, arguments, or inputs, and the value produced is called the value, result, or output. Operations can have fewer or more than two inputs, an operation is like an operator, but the point of view is different. An operation ω is a function of the form ω, V → Y, where V ⊂ X1 × … × Xk. The sets Xk are called the domains of the operation, the set Y is called the codomain of the operation, thus a unary operation has arity one, and a binary operation has arity two
23. order to achieve the goal by 2015, the United Nations estimated that all children at the entry age for primary school would have had to have been attending classes by 2009. This would depend on the duration of the level, as well as how well the schools retain students until the end of the cycle. As of 2010, the number of new teachers needed in sub-Saharan Africa alone, however, the gender gap for children not in education had also been narrowed. Between 1999 and 2008, the number of not in education worldwide had decreased from 57 percent to 53 percent, however it should also be noted that in some regions. According to the United Nations, there are things in the regions that have already been accomplished. The country doubled its enrollment ratio over the same period, other regions in Latin America such as Guatemala and Nicaragua as well as Zambia in Southern Africa broke through the 90 percent towards greater access to primary education. In Australia, students undertake preschool then 13 years of schooling before moving to vocational or higher education, Primary schooling for most children starts after they turn 5 years old. In most states, children can be enrolled earlier at the discretion of individual school principals on the basis of intellectual giftedness, in Victoria, New South Wales, Northern Territory, ACT and Tasmania students then move through Kindergarten/Preparatory School/Reception and Years 1 to 6 before starting high school. Pre-School/Kindergarten,4 to 5 years old Prep, currently, at the age of 6 children attend from the grade 1 to 4 what is called Ensino Primário, and afterwards from grade 5 to 9 the Ensino Fundamental. At the age of 15 the teenagers go to Ensino Médio, which is equivalent High School in other countries, Primary school is mandatory and consists in nine years called Ensino Fundamental, separated in Ensino Fundamental I and Ensino Fundamental II. Primary school is followed by the three years called Ensino Médio. 1st grade, 15- to 16-year-olds, 2nd grade, 16- to 17-year-olds, 3rd grade, in Canada, primary school usually begins at ages three or four, starting with either Kindergarten or Grade 1 and lasts until age 13 or 14. Many places in Canada have a split between primary and elementary schools, in Nova Scotia elementary school is the most common term. The provincial government of Nova Scotia uses the term Primary instead of Kindergarten, most children are pupils in the Danish Folkeskolen, which has the current grades, Kindergarten, 3–6 years https, //meta. wikimedia. The first three grades of school are called Algkool which can be translated as beginning school and can be confused with primary school
24. higher education. In most countries it is compulsory for students between the ages 11 and 16, Compulsory education sometimes extends to age 19. In classical and mediaeval times secondary education was provided by the church for the sons of nobility and to boys preparing for universities, as trade required navigational and scientific skills the church reluctantly expanded the curriculum and widened the intake. As late as 1868, secondary schools were organised to satisfy the needs of different social classes with the labouring classes getting 4yrs, the merchant class 5yrs, only then did it become accepted that girls could be sent to school. The rights to an education were codified after 1945, and countries are still working to achieve the goal of mandatory. It is at this education level, particularly in its first cycle. Within a country these can be implemented in different ways, with different age levels, Level 1 and Level 2, that is primary education and lower secondary together form basic education. Though they may be dated they do provide a set of definitions. The educational aim is to complete provision of education, completing the delivery of basic skills. The end of secondary education often coincides with the end of compulsory education in countries where that exists. There are also vocational schools that last only three years. Secondary schools supply students with primary subjects needed for the work environment in Croatia. People who completed secondary school are classified as medium expertise, there are currently around 90 gymnasiums and some 300 vocational schools in Croatia. The public secondary schools are under the jurisdiction of regional government, the two secondary phases are the Gymnasium followed by Eniaio Lykeio or Unified Lyceum. The third phase is the Post-secondary education consisting of public institutions or universities. Due to historic reasons, the Czech school system is almost the same as the German school system, the school system is free and mandatory until age 15
25. 1930s, in older texts, the name infinitesimal group is used. Lie algebras are related to Lie groups, which are groups that are also smooth manifolds. Any Lie group gives rise to a Lie algebra, conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to covering. This correspondence between Lie groups and Lie algebras allows one to study Lie groups in terms of Lie algebras, alternativity, =0 for all x in g. The Jacobi identity, + + =0 for all x, y, z in g, if the fields characteristic is not 2 then anticommutativity implies alternativity. It is customary to express a Lie algebra in lower-case fraktur, if a Lie algebra is associated with a Lie group, then the spelling of the Lie algebra is the same as that Lie group. For example, the Lie algebra of SU is written as s u. Elements of a Lie algebra g are said to be generators of the Lie algebra if the smallest subalgebra of g containing them is g itself. The dimension of a Lie algebra is its dimension as a space over F. The cardinality of a generating set of a Lie algebra is always less than or equal to its dimension. The Lie bracket is not associative in general, meaning that need not equal, nonetheless, much of the terminology that was developed in the theory of associative rings or associative algebras is commonly applied to Lie algebras. A subspace h ⊆ g that is closed under the Lie bracket is called a Lie subalgebra, if a subspace I ⊆ g satisfies a stronger condition that ⊆ I, then I is called an ideal in the Lie algebra g. A homomorphism between two Lie algebras is a map that is compatible with the respective Lie brackets, f, g → g ′, f =. The set of x such that =0 for all s in S forms a subalgebra called the centralizer of S. The centralizer of g itself is called the center of g, similar to centralizers, if S is a subspace, then the set of x such that is in S for all s in S forms a subalgebra called the normalizer of S. Let g be a Lie algebra and i an ideal of g, if the canonical map g → g / i splits, then g is said to be a semidirect product of i and g / i, g = g / i ⋉ i. Levis theorem says that a finite-dimensional Lie algebra is a product of its radical
26. in 1986, in the course of this construction, one employs a Fock space that admits an action of vertex operators attached to lattice vectors. They observed that many vertex algebras that appear in nature have an additional structure. Motivated by this observation, they added the Virasoro action and bounded-below property as axioms and we now have post-hoc motivation for these notions from physics, together with several interpretations of the axioms that were not initially known. While related, these chiral algebras are not precisely the same as the objects with the name that physicists use. More sophisticated examples such as affine W-algebras and the chiral de Rham complex on a complex manifold arise in geometric representation theory, a vertex algebra is a collection of data that satisfy certain axioms. A vector space V, called the space of states, the underlying field is typically taken to be the complex numbers, although Borcherdss original formulation allowed for an arbitrary commutative ring. An identity element 1 ∈ V, sometimes written |0 ⟩ or Ω to indicate a vacuum state, an endomorphism T, V → V, called translation. A linear multiplication map Y, V ⊗ V → V and this structure is alternatively presented as an infinite collection of bilinear products unv, or as a left-multiplication map V → End, called the state-field correspondence. For each u ∈ V, the operator-valued formal distribution Y is called an operator or a field. The standard notation for the multiplication is u ⊗ v ↦ Y v = ∑ n ∈ Z u n v z − n −1 and these data are required to satisfy the following axioms, Identity. For any u ∈ V, Yu = u = uz0, T =0, and for any u, v ∈ V, v = T Y v − Y T v = d d z Y v Locality. For any u, v ∈ V, there exists a positive integer N such that, the Locality axiom has several equivalent formulations in the literature, e. g. In particular, the coefficients of this vertex operator endow V with an action of the Virasoro algebra with central charge c, L0 acts semisimply on V with integer eigenvalues that are bounded below. Under the grading provided by the eigenvalues of L0, the multiplication on V is homogeneous in the sense that if u and v are homogeneous, the identity 1 has degree 0, and the conformal element ω has degree 2. A homomorphism of vertex algebras is a map of the vector spaces that respects the additional identity, translation. Homomorphisms of vertex operator algebras have weak and strong forms, depending on whether they respect conformal vectors, a vertex algebra V is commutative if all vertex operators commute with each other
27. integers. Commutative algebra is the main tool in the local study of schemes. The study of rings that are not necessarily commutative is known as noncommutative algebra, it includes ring theory, representation theory, Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry. In algebraic number theory, the rings of integers are Dedekind rings. Considerations related to modular arithmetic have led to the notion of a valuation ring, the notion of localization of a ring is one of the main differences between commutative algebra and the theory of non-commutative rings. It leads to an important class of rings, the local rings that have only one maximal ideal. The set of the ideals of a commutative ring is naturally equipped with a topology. All these notions are widely used in geometry and are the basic technical tools for the definition of scheme theory. Many other notions of commutative algebra are counterparts of geometrical notions occurring in algebraic geometry and this is the case of Krull dimension, primary decomposition, regular rings, Cohen–Macaulay rings, Gorenstein rings and many other notions. The subject, first known as theory, began with Richard Dedekinds work on ideals, itself based on the earlier work of Ernst Kummer. Later, David Hilbert introduced the ring to generalize the earlier term number ring. Hilbert introduced an abstract approach to replace the more concrete and computationally oriented methods grounded in such things as complex analysis. In turn, Hilbert strongly influenced Emmy Noether, who recast many earlier results in terms of an ascending chain condition, another important milestone was the work of Hilberts student Emanuel Lasker, who introduced primary ideals and proved the first version of the Lasker–Noether theorem. He established the concept of the Krull dimension of a ring, first for Noetherian rings before moving on to expand his theory to cover general valuation rings, to this day, Krulls principal ideal theorem is widely considered the single most important foundational theorem in commutative algebra. These results paved the way for the introduction of commutative algebra into algebraic geometry, much of the modern development of commutative algebra emphasizes modules. Both ideals of a ring R and R-algebras are special cases of R-modules, though it was already incipient in Kroneckers work, the modern approach to commutative algebra using module theory is usually credited to Krull and Noether. The notion of a Noetherian ring is of importance in both commutative and noncommutative ring theory, due to the role it plays in simplifying the ideal structure of a ring
28. two elements of the ring to a third. They are called addition and multiplication and commonly denoted by + and ⋅, e. g. a + b, the identity elements for addition and multiplication are denoted 0 and 1, respectively. If the multiplication is commutative, i. e. a ⋅ b = b ⋅ a, in the remainder of this article, all rings will be commutative, unless explicitly stated otherwise. An important example, and in some sense crucial, is the ring of integers Z with the two operations of addition and multiplication, as the multiplication of integers is a commutative operation, this is a commutative ring. It is usually denoted Z as an abbreviation of the German word Zahlen, a field is a commutative ring where every non-zero element a is invertible, i. e. has a multiplicative inverse b such that a ⋅ b =1. Therefore, by definition, any field is a commutative ring, the rational, real and complex numbers form fields. An example is the set of matrices of divided differences with respect to a set of nodes. If R is a commutative ring, then the set of all polynomials in the variable X whose coefficients are in R forms the polynomial ring. The same holds true for several variables, if V is some topological space, for example a subset of some Rn, real- or complex-valued continuous functions on V form a commutative ring. The same is true for differentiable or holomorphic functions, when the two concepts are defined, such as for V a complex manifold, in contrast to fields, where every nonzero element is multiplicatively invertible, the theory of rings is more complicated. There are several notions to cope with that situation, first, an element a of ring R is called a unit if it possesses a multiplicative inverse. Another particular type of element is the zero divisors, i. e. a non-zero element a such that there exists an element b of the ring such that ab =0. If R possesses no zero divisors, it is called an integral domain since it resembles the integers in some ways. Many of the following notions also exist for not necessarily commutative rings, for example, all ideals in a commutative ring are automatically two-sided, which simplifies the situation considerably. Given any subset F = j ∈ J of R, the ideal generated by F is the smallest ideal that contains F. Equivalently, an ideal generated by one element is called a principal ideal. A ring all of whose ideals are principal is called a principal ideal ring, any ring has two ideals, namely the zero ideal and R, the whole ring
29. equation were known as early as 2000 BC. A quadratic equation with real or complex coefficients has two solutions, called roots and these two solutions may or may not be distinct, and they may or may not be real. It may be possible to express a quadratic equation ax2 + bx + c =0 as a product =0. In some cases, it is possible, by inspection, to determine values of p, q, r. If the quadratic equation is written in the form, then the Zero Factor Property states that the quadratic equation is satisfied if px + q =0 or rx + s =0. Solving these two linear equations provides the roots of the quadratic, for most students, factoring by inspection is the first method of solving quadratic equations to which they are exposed. As an example, x2 + 5x +6 factors as, the more general case where a does not equal 1 can require a considerable effort in trial and error guess-and-check, assuming that it can be factored at all by inspection. Except for special cases such as where b =0 or c =0 and this means that the great majority of quadratic equations that arise in practical applications cannot be solved by factoring by inspection. The process of completing the square makes use of the identity x 2 +2 h x + h 2 =2. Starting with an equation in standard form, ax2 + bx + c =0 Divide each side by a. Subtract the constant term c/a from both sides, add the square of one-half of b/a, the coefficient of x, to both sides. This completes the square, converting the left side into a perfect square, write the left side as a square and simplify the right side if necessary. Produce two linear equations by equating the square root of the side with the positive and negative square roots of the right side. Completing the square can be used to derive a formula for solving quadratic equations. The mathematical proof will now be briefly summarized and it can easily be seen, by polynomial expansion, that the following equation is equivalent to the quadratic equation,2 = b 2 −4 a c 4 a 2. Taking the square root of both sides, and isolating x, gives, x = − b ± b 2 −4 a c 2 a and these result in slightly different forms for the solution, but are otherwise equivalent
30. certain requirements, called axioms. Euclidean vectors are an example of a vector space and they represent physical quantities such as forces, any two forces can be added to yield a third, and the multiplication of a force vector by a real multiplier is another force vector. In the same vein, but in a more geometric sense, Vector spaces are the subject of linear algebra and are well characterized by their dimension, which, roughly speaking, specifies the number of independent directions in the space. Infinite-dimensional vector spaces arise naturally in mathematical analysis, as function spaces and these vector spaces are generally endowed with additional structure, which may be a topology, allowing the consideration of issues of proximity and continuity. Among these topologies, those that are defined by a norm or inner product are commonly used. This is particularly the case of Banach spaces and Hilbert spaces, historically, the first ideas leading to vector spaces can be traced back as far as the 17th centurys analytic geometry, matrices, systems of linear equations, and Euclidean vectors. Today, vector spaces are applied throughout mathematics, science and engineering, furthermore, vector spaces furnish an abstract, coordinate-free way of dealing with geometrical and physical objects such as tensors. This in turn allows the examination of local properties of manifolds by linearization techniques, Vector spaces may be generalized in several ways, leading to more advanced notions in geometry and abstract algebra. The concept of space will first be explained by describing two particular examples, The first example of a vector space consists of arrows in a fixed plane. This is used in physics to describe forces or velocities, given any two such arrows, v and w, the parallelogram spanned by these two arrows contains one diagonal arrow that starts at the origin, too. This new arrow is called the sum of the two arrows and is denoted v + w, when a is negative, av is defined as the arrow pointing in the opposite direction, instead. Such a pair is written as, the sum of two such pairs and multiplication of a pair with a number is defined as follows, + = and a =. The first example above reduces to one if the arrows are represented by the pair of Cartesian coordinates of their end points. A vector space over a field F is a set V together with two operations that satisfy the eight axioms listed below, elements of V are commonly called vectors. Elements of F are commonly called scalars, the second operation, called scalar multiplication takes any scalar a and any vector v and gives another vector av. In this article, vectors are represented in boldface to distinguish them from scalars
31. general32. variety of areas of mathematics and science. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra, the word polynomial joins two diverse roots, the Greek poly, meaning many, and the Latin nomen, or name. It was derived from the binomial by replacing the Latin root bi- with the Greek poly-. The word polynomial was first used in the 17th century, the x occurring in a polynomial is commonly called either a variable or an indeterminate. When the polynomial is considered as an expression, x is a symbol which does not have any value. It is thus correct to call it an indeterminate. However, when one considers the function defined by the polynomial, then x represents the argument of the function, many authors use these two words interchangeably. It is a convention to use uppercase letters for the indeterminates. However one may use it over any domain where addition and multiplication are defined, in particular, when a is the indeterminate x, then the image of x by this function is the polynomial P itself. This equality allows writing let P be a polynomial as a shorthand for let P be a polynomial in the indeterminate x. A polynomial is an expression that can be built from constants, the word indeterminate means that x represents no particular value, although any value may be substituted for it. The mapping that associates the result of substitution to the substituted value is a function. This can be expressed concisely by using summation notation, ∑ k =0 n a k x k That is. Each term consists of the product of a number—called the coefficient of the term—and a finite number of indeterminates, because x = x1, the degree of an indeterminate without a written exponent is one. A term and a polynomial with no indeterminates are called, respectively, a constant term, the degree of a constant term and of a nonzero constant polynomial is 0. The degree of the polynomial,0, is generally treated as not defined
33.34.35. general36.ions such as sets, rings, several terms used in category theory, including the term morphism, are used differently from their uses in the rest of mathematics. In category theory, morphisms obey conditions specific to category theory itself, Category theory has practical applications in programming language theory, in particular for the study of monads in functional programming. Categories represent abstraction of other mathematical concepts, many areas of mathematics can be formalised by category theory as categories. Hence category theory uses abstraction to make it possible to state and prove many intricate, a basic example of a category is the category of sets, where the objects are sets and the arrows are functions from one set to another. However, the objects of a category need not be sets, any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category—and all the results of category theory apply to it. The arrows of category theory are said to represent a process connecting two objects, or in many cases a structure-preserving transformation connecting two objects. There are, however, many applications where more abstract concepts are represented by objects. The most important property of the arrows is that they can be composed, in other words, linear algebra can also be expressed in terms of categories of matrices. A systematic study of category theory allows us to prove general results about any of these types of mathematical structures from the axioms of a category. The class Grp of groups consists of all objects having a group structure, one can proceed to prove theorems about groups by making logical deductions from the set of axioms. For example, it is immediately proven from the axioms that the identity element of a group is unique, in the case of groups, the morphisms are the group homomorphisms. The study of group homomorphisms then provides a tool for studying properties of groups. Not all categories arise as structure preserving functions, however, the example is the category of homotopies between pointed topological spaces. If one axiomatizes relations instead of functions, one obtains the theory of allegories, a category is itself a type of mathematical structure, so we can look for processes which preserve this structure in some sense, such a process is called a functor. Diagram chasing is a method of arguing with abstract arrows joined in diagrams. Functors are represented by arrows between categories, subject to specific defining commutativity conditions, functors can define categorical diagrams and sequences
37. which can be studied both through their homology and cohomology. A powerful tool for doing this is provided by spectral sequences, from its very origins, homological algebra has played an enormous role in algebraic topology. K-theory is an independent discipline which draws upon methods of homological algebra, the chain complex is the central notion of homological algebra. The elements of Cn are called n-chains and the homomorphisms dn are called the maps or differentials. The chain groups Cn may be endowed with extra structure, for example, the differentials must preserve the extra structure if it exists, for example, they must be linear maps or homomorphisms of R-modules. For notational convenience, restrict attention to abelian groups, a theorem by Barry Mitchell implies the results will generalize to any abelian category. Every chain complex defines two further sequences of groups, the cycles Zn = Ker dn and the boundaries Bn = Im dn+1, where Ker d and Im d denote the kernel. Since the composition of two consecutive boundary maps is zero, these groups are embedded into each other as B n ⊆ Z n ⊆ C n, a chain complex is called acyclic or an exact sequence if all its homology groups are zero. Chain complexes arise in abundance in algebra and algebraic topology, in the case of topological spaces, we arrive at the notion of singular homology, which plays a fundamental role in investigating the properties of such spaces, for example, manifolds. On a technical level, homological algebra provides the tools for manipulating complexes, two objects X and Y are connected by a map f between them. Homological algebra studies the relation, induced by the map f and this is generalized to the case of several objects and maps connecting them. Phrased in the language of category theory, homological algebra studies the properties of various constructions of chain complexes. An object X admits multiple descriptions or the complex C ∙ is constructed using some presentation of X, note that the sequence of groups and homomorphisms may be either finite or infinite. A similar definition can be made for other algebraic structures. For example, one could have a sequence of vector spaces and linear maps, or of modules. More generally, the notion of an exact sequence makes sense in any category with kernels and cokernels, the most common type of exact sequence is the short exact sequence
1.
The Algebraist
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Euclid in Raphael 's School of AthensArabic is the sole official language
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Bilingual traffic sign in Qatar
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A strange attractor arising from a differential equation. Differential equations are an important area of mathematical analysis with many applications to science and engineering.
Group (mathematics)
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In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element. The operation satisfies four conditions called the group axioms, namely closure and it allows entities with highly diverse mathematical origins in abstract algebra and beyond to be hand
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A periodic wallpaper pattern gives rise to a wallpaper group.
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The manipulations of this Rubik's Cube form the Rubik's Cube group.
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Richard Dedekind, one of the founders of ring theory.
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Chapter IX of David Hilbert 's Die Theorie der algebraischen Zahlkörper. The chapter title is Die Zahlringe des Körpers, literally "the number rings of the field". The word "ring" is the contraction of "Zahlring".
algeb
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A typical algebra problem.
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Two-dimensional plot (magenta curve) of the algebraic equation
wit
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The permutations of Rubik's Cube form a group, a fundamental concept within abstract algebra.
i
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The mass–energy equivalence formula was displayed on Taipei 101 during the event of the World Year of Physics 2005.
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Task Force One, the world's first nuclear-powered task force. Enterprise, Long Beach and Bainbridge in formation in the Mediterranean, 18 June 1964. Enterprise crew members are spelling out Einstein's mass–energy equivalence formula E = mc 2 on the flight deck.
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The popular connection between Einstein, E = mc 2, and the atomic bomb was prominently indicated on the cover of Time magazine in July 1946 by the writing of the equation on the mushroom cloud.
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The three-dimensional Euclidean space R 3 is a vector space, and lines and planes passing through the origin are vector subspaces in R 3.
sometime
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A torus, one of the most frequently studied objects in algebraic topologyian parenthese
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A binary operation ∗ on the set S is associative when this diagram commutes. That is, when the two paths from S × S × S to S compose to the same function from S × S × S to S.
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This image illustrates that addition is commutative.
op
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A large elementary school in Magome, Japan
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Children and teacher in a primary school classroom in Laos
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An elementary school in California, United States
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A poster at the United Nations Headquarters in New York City, New York, USA, showing the Millennium Development Goals.
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High school in Bratislava, Slovakia (Gymnázium Grösslingová 18)
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Sydney Boys High School
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Krabbesholm Højskole
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Helsingin normaalilyseo
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String theory
integer
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A 1915 postcard from one of the pioneers of commutative algebra, Emmy Noether, to E. Fischer, discussing her work in commutative algebra.
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The spectrum of Z.
equat ce
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The graph of a polynomial function of degree 3
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Schematic representation of a category with objects X, Y, Z and morphisms f, g, g ∘ f. (The category's three identity morphisms 1 X, 1 Y and 1 Z, if explicitly represented, would appear as three arrows, next to the letters X, Y, and Z, respectively, each having as its "shaft" a circular arc measuring almost 360 degrees.)
wh
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A diagram used in the snake lemma, a basic result in homological algebra.A page of Fibonacci's Liber Abaci from the Biblioteca Nazionale di Firenze showing (in box on right) the Fibonacci sequence with the position in the sequence labeled in Roman numerals and the value in Hindu-Arabic numerals. | 677.169 | 1 |
Andrew Pressley is Professor of Mathematics at King's College London, UK.
more
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates.
Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout.
New features of this revised and expanded second edition include:
a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book.
Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.
Around 200 additional exercises, and a full solutions manual for instructors, available via
Praise for the first edition:
"The text is nicely illustrated, the definitions are well-motivated and the proofs are particularly well-written and student-friendly…this book would make an excellent text for an undergraduate course, but could also well be used for a reading course, or simply read for pleasure."
Australian Mathematical Society Gazette
"Excellent figures supplement a good account, sprinkled with illustrative examples."
Curves in the plane and in space.- How much does a curve curve?.- Global properties of curves.- Surfaces in three dimensions.- Examples of surfaces.- The first fundamental form.- Curvature of surfaces.- Gaussian, mean and principal curvatures.- Geodesics.- Gauss' Theorema Egregium.- Hyperbolic geometry.- Minimal surfaces.- The Gauss–Bonnet theorem. | 677.169 | 1 |
MacAnova
A Program for Statistical Analysis and Matrix Algebra MacAnova is a free, open source, interactive statistical analysis program for Windows, Macintosh, and Linux written by Gary W. Oehlert and Christopher Bingham, both of the School of Statistics, University of Minnesota. ...
March 12th 2013
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Math-o-mir
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wxMaxima is a document based interface for the computer algebra system Maxima. wxMaxima uses wxWidgets and runs natively on Windows, X11 and Mac OS X. wxMaxima provides menus and dialogs for many common maxima commands, autocompletion, inline plots and simple ...
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fMath Editor - CKEditor Plugin
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Aquarius Soft PC Binary Converter 1.6c
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Yorick for Windows
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FlatGraph
Plotting functions (usual and parametric) with more possibilities. Differentiation of any order (with simplification). Construction of tangents to the graph. The simple and clear interface with the detailed documentation and examples of work. The program is designed both for inexperienced ...
fMath Formula - GWT Widget
fMath Formula - GWT Widget provide a simple way to display equations or mathematics formula on your GWT applications (Google Web Toolkit). It has more than 20000 symbols to display using MathML or in LaTeX. The widget is free of ...
SPSS Statistics | 677.169 | 1 |
College Algebra
Program Details
This College Algebra online course provides students with a working knowledge of college-level algebra and its applications, emphasizing methods for solving linear and quadratic equations, word problems, and polynomial, rational, and radical equations. Students perform operations on real numbers and polynomials and simplify algebraic, rational, and radical expressions.Course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities.
Similar Programs:
Program Overview
Degree Level:
Certificate
Delivery Format:
100% Online
Tuition Basis :
Per Course
International Students Accepted:
Yes
Accelerated Degree:
No
Requirements
Accreditation & Licensing
Distance Education Accrediting Council (DEAC | 677.169 | 1 |
BEGINNING ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master algebraic concepts, problem solving, and communication skills. Students learn how to solve problems generated from realistic applications, instead of learning techniques without conceptual understanding. The authors have developed several key ideas to make concepts real and vivid for students.
First, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension.
Second, the authors integrate applications, drawing on realistic data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application.
Third, the authors develop key concepts as students progress through the course. For example, the distributive property is introduced in real numbers, covered when students are learning how to multiply a polynomial by a constant, and finally when students learn how to multiply a polynomial by a monomial. These concepts are reinforced through applications in the text.
Last, the authors' approach prepares students for intermediate algebra by including an introduction to material such as functions and interval notation as well as the last chapter that covers linear and quadratic modeling.
Meet the Authors
Mark Clark,
Palomar College
Mark Clark graduated from California State University, Long Beach, and holds bachelor's and master's degrees in Mathematics. A full-time associate professor at Palomar College, since 1996, Mark is committed to teaching using applications and technology to help students understand mathematics in context and communicate results clearly. Intermediate algebra is one of his favorite courses to teach and he continues to teach several sections of this course each year. He is co-author of BEGINNING ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS, INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS, and BEGINNING AND INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS published by Cengage. Mark shares his passion for using applications to teach mathematical concepts by delivering workshops and talks to other instructors at local and national conferences.
Cynthia Anfinson,
Palomar College
Cynthia (Cindy) Anfinson graduated from the University of California, San Diego, with a bachelor's degree in Mathematics and is a member of Phi Beta Kappa. Under the Army Science and Technology Graduate Fellowship, she earned a master's degree in Applied Mathematics from Cornell University. She is currently an associate professor of Mathematics at Palomar College where her experience includes working with the First-Year Experience and Summer Bridge programs. Her leadership experience includes directing the Mathematics Learning Center for a three-year term and serving on multiple committees, including the Basic Skills Committee and the Student Success and Equity Council. She is the co-author of BEGINNING ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS, INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS, AND BEGINNING AND INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS published by Cengage.
Features
Prealgebra Review. The text begins in Chapter R by reviewing some prealgebra concepts, providing students with a review of those topics most necessary for beginning algebra such as arithmetic with signed numbers, fractions, decimals and percents. This chapter also reviews other traditional student weak spots--absolute value, the idea of opposites, and the order-of-operations agreement, ending with coverage of the real number system.
Chapter Projects. To enhance critical thinking, end-of-chapter projects can be assigned either individually or as group work. Instructors can choose which projects best suit the focus of their class and give their students the chance to show how well they can tie together the concepts they have learned in that chapter. Some of these projects include online research or activities that students must perform to analyze data and make conclusions.
Cumulative Reviews. Cumulative reviews appear after every two chapters, and group together the major topics across chapters. Answers to all the exercises are available to students in the answer appendix.
Practical Help for Instructors. Practical tips are provided in the Annotated Instructor's Edition on how to approach and pace chapters as well as integrate features such as Concept Investigations. In addition, for every student example in the student text, there is a different instructor classroom example in the AIE, with accompanying answers that can be used for additional in-class practice and/or homework.
An Innovative Critical-Thinking Feature: Concept Investigations. The directed-discovery activities called Concept Investigations are ideal as group work during class, incorporated as part of a lecture, or as individual assignments to investigate concepts further. Inserted at key points within the chapter, each Concept Investigation helps students explore patterns and relationships such as the graphical and algebraic representations of the concepts being studied.
Worked Examples with In-Text Practice Problems. This text provides a broad range of examples that give students more practical experience with mathematics. Other examples reinforce patterns of problem solving by using a step-by-step approach, breaking down an example into more basic concepts or techniques and then following it immediately with a practice problem that is similar to that example.
Integrated "Student" Work. Clearly identifiable examples of "student" work appear throughout the exercises in the text. These boxes ask students to find and correct common errors in "student" work.
Margin Notes. The margin contains three kinds of notes written to help the student with specific types of information: Skill Connections provide a just-in-time review of core mathematical concepts, reinforcing student skill sets; Connecting the Concepts reinforce a concept by showing relationships across sections; and specific vocabulary of mathematics and the applications are helpfully defined and reinforced through margin notes called "What's That Mean?"
Reinforcement of Visual Learning through Graphs and Tables. Graphs and tables are used throughout the book to organize data, examine trends, and have students gain knowledge of graphing linear and quadratic equations. The graphical and numeric approach helps support visual learners, incorporating realistic situations into the text and reinforcing the graphs and data that students see in their daily lives.
Exercise Sets. The exercise sets include a balance of both applications and skill-based problems developed with a clear level of progression in terms of difficulty level. Some exercise sets begin with a few warm-up problems before focusing on applications. Exercise sets typically end with additional skill practice to help students master the concepts when needed. A balance of graphical, numerical, and algebraic skill problems is included throughout the book to help students see mathematics from several different views.
Flexible Use of the Calculator. The core exercises do not require calculator usage, although the book has been written to support the use of a scientific calculator. Calculator Details Margin boxes will appear as necessary to instruct students on the correct use of a scientific calculator. In certain Concept Investigations, the calculator is used to help students with arithmetic so that they may concentrate on looking for patterns. In selected applications, the calculator is used to do the numerical computations so that students can work with more realistic problem situations.
Extensive End-of-Chapter Material includes Chapter Summaries, Review Exercises, Chapter Tests, Chapter Projects, and Cumulative Reviews. Chapter Summaries revisit the big ideas of the chapter and reinforce them with new worked-out examples. Students can also review and practice what they have learned with the Chapter Review exercises before taking the Chapter Test.
FOR INSTRUCTORS
ISBN: 9780538736756
Each section of the main text is discussed in uniquely designed Teaching Guides containing instruction tips, examples, activities, worksheets, overheads, assessments, and solutions to all worksheets and activities. The community site for this FREE Instructor's supplement provides more detail for instructors. In addition, the puzzles and activities are included in a Student Workbook that are saleable.
ISBN: 9780840054692
This CD-ROM (or DVD) provides the instructor with dynamic media tools for teaching. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing Featuring Algorithmic Equations. Easily build solution sets for homework or exams using Solution Builder's online solutions manual. Microsoft® PowerPoint® lecture slides and figures from the book are also included on this CD-ROM (or DVD).
Complete Solutions Manual
ISBN: 9780534465346
The Complete Solutions Manual provides worked-out solutions to all of the problems in the text.
Solution Builder
ISBN: 9780840054661
This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. Visit
Text-Specific DVD
ISBN: 9780534465353
Honored with two Tellys, a Communicator Award, and an international Aurora Award, these ten- to twenty-minute problem-solving lessons cover almost every learning objective from each chapter. Rena Petrello--recipient of the "Mark Dever Award for Excellence in Teaching"--presents each lesson using her experience teaching online mathematics courses. It was through this online teaching experience that Petrello discovered the lack of suitable content for online instructors, prompting her to develop her own video lessons and ultimately create this video project. Students will love the additional guidance and support when they miss a class or when they are preparing for an upcoming quiz or exam.
Student Workbook
ISBN: 9781111568900
Providing the perfect head start, the Student Workbook contains all of the assessments, activities, and worksheets from the Instructor's Resource Binder for classroom discussions, in-class activities, and group work.
Student Solutions Manual
ISBN: 9780534465339
Contains fully worked-out solutions to all of the odd-numbered end-of section exercises as well as the complete worked-out solutions to all of the exercises included at the end of each chapter in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. | 677.169 | 1 |
Description
The Simplex Tutor helps you solve simple linear programming problems. Arithmetic for pivoting can be tedious and mistakes can be hard to catch, so use the tutor to check your work.
• Hints will guide you to a solution
• Tutor completes pivots for you
• Simplex solver
• Mail solver's solutions
• Exact answers are shown as fractions
• Review linear programming, with examples
• Review simplex method, with examples
• 32 sample problem templates included
• Enter your own problems
• Enter data as fractions or decimals
• Custom keyboard for easy data entry
• Export matrices as HTML or CSV
• Save matrices as pictures
• Work problems with up to six constraints and six initial variables
If you are stuck and not sure how to proceed with a problem, you can request a hint guiding you to the solution. The more hints you ask for, the more guidance you will receive. Eventually the tutor will tell you a correct location to pivot on if the problem is solvable, or it will tell you that there is no solution. In this way the rules of the simplex method are continually reinforced and soon you will not need to ask for hints.
If you want more than hints, turn on the solver from the settings view. Now step by step solutions using the simplex method will be given.
Turn problems into fully worked examples with the Simplex Tutor.
If the Simplex Tutor has been helpful to you, please leave a review. If you have a suggestion, please contact us at Many thanks!
For help solving two dimensional linear programming problems graphically, or to plot linear inequalities, see the Linear Program Plotter.
For practice with row operations, the Gauss-Jordan method, or finding matrix inverses, see the Row Operations Tutor | 677.169 | 1 |
two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using The Geometer's Sketchpad. The book's truly discovery-based approach guides readers to learn geometry through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries. In the process, readers hone their understanding of geometry and their ability to write rigorous mathematical proofs. | 677.169 | 1 |
Algebra I (1 Credit)
Algebra
This course introduces students to the rules and properties to apply to integers, solving and graphing linear equations, inequalities and systems of equations, the use of ratios and functions to solve algebraic problems using triangles. The student will also learn to multiply polynomials and factor trinomials, and to combine like terms for problems involving exponents and polynomials. | 677.169 | 1 |
Homework Helpers: Basic Math and Pre-Algebra is a straightforward and easy-to-read review of arithmetic skills. It includes topics that are intended to help prepare students to successfully learn algebra, including:
This book will help build a solid mathematical foundation and enable students to gain the confidence they need to continue their education in mathematics. Particular attention is placed on topics that students traditionally struggle with the most. The final chapter in the book covers word problems in detail, and several problem-solving strategies are discussed. While this book could be used to supplement standard pre-algebra textbooks, it could also be used to refresh your arithmetic and problem-solving skills.
The topics are explained in everyday language before the examples are worked. The problems are solved clearly and systematically, with step-by-step instructions provided. Problem-solving skills and good habits, such as checking your answers after every problem, are emphasized. There are practice problems throughout each book, and the answers to all of the practice problems are provided.
"synopsis" may belong to another edition of this title.
About the Author:
Denise Szecsei earned Bachelor of Science degrees in Physics, Chemistry and Mathematics from the University of Redlands. She served four years as a technical instructor in the U.S. Navy before she went on to receive her doctorate degree in Mathematics from the Florida State University. She has been teaching since 1985 and is currently teaching Mathematics at Stetson University. | 677.169 | 1 |
maths models
As research increases the range and scope of our understanding of the economics and mathematics of financial markets, we need books such as this that summarise and explain the topic's different models.
In this volume, authors Jaksa Cvitanic and Fernando Zapatero do more than provide an introduction to the subject. Within its 500 pages they give a comprehensive overview of the different mathematical models that form the foundation of current thinking in financial economics, financial engineering and mathematical finance.
There are sections covering all the main developments in the field on markets, derivative securities and equilibrium models, and within each section there is a description of all the familiar - and not-so-familiar - models in finance: the capital asset pricing model, factor models, Black-Scholes and so on. Usefully, where appropriate, the authors discuss the empirical evidence. In handling these topics, they have adopted a consistent approach throughout, explaining each model in an intuitive way, without seeking to provide a rigorous proof.
As an overview of the mathematics of finance, the book is suitable as a primer for graduate programmes and advanced courses in finance and financial economics. It will aid PhD students' understanding of this important area in finance and economics. It provides useful end-of-chapter problems and suggested further reading.
An instructor's guide available from the publishers' and the authors'
website provides downloadable copies of the graphics in the text.
Peter Moles is lecturer in finance, Edinburgh University.
Introduction to the Economics and Mathematics of Financial Markets. First edition | 677.169 | 1 |
Description - Geometry by Dan Pedoe
Lucid, well-written introduction to elementary geometry usually included in undergraduate and first-year graduate courses in mathematics. Topics include vector algebra in the plane, circles and coaxial systems, mappings of the Euclidean plane, similitudes, isometries, mappings of the intensive plane, much more. Includes over 500 exercises. | 677.169 | 1 |
Calculus by Laura Taalman, Peter Kohn
Many calculus textbooks glance to interact scholars with margin notes, anecdotes, and different units. yet many teachers locate those distracting, who prefer to captivate their technology and engineering scholars with the wonderful thing about the calculus itself. Taalman and Kohn's clean new textbook is designed to assist teachers do exactly that.
Taalman and Kohn's Calculus bargains a streamlined, dependent exposition of calculus that mixes the readability of vintage textbooks with a contemporary standpoint on techniques, abilities, purposes, and conception. Its glossy, uncluttered layout removes sidebars, old biographies, and asides to maintain scholars all for what's so much important—the foundational ideas of calculus which are so vital to their destiny educational careers.
This is often pressured with difficulties of mammoth ethnic minorities, insufficient agrarian reforms and gradual business improvement sustained through overseas capital.
A transparent, concise, brand new, authoritative background by way of one of many top historians within the country.
Give Me Liberty! is the top ebook available in the market since it works within the lecture room. A single-author e-book, supply Me Liberty! deals scholars a constant process, a unmarried narrative voice, and a coherent point of view during the textual content. Threaded during the chronological narrative is the subject of freedom in American historical past and the numerous conflicts over its altering meanings, its limits, and its accessibility to numerous social and fiscal teams all through American background. The 3rd variation areas American heritage extra absolutely in a world context. The pedagogy is additionally improved within the 3rd version, with a Visions of Freedom function in every one bankruptcy and extra wide checks!
Complete the entries in the following table two ways: (a) to make an even function and (b) to make an odd function: 1 , what is f (x)? x2 + 1 1 (b) If h(x) = x 2 − 1 and h(l(x)) = 4 − 1, what is l(x)? x 1 1 (c) If u(x) = and y(u(x)) = , what is y(x)? 1−x 1−x (a) If g(x) = x 2 and f ( g(x)) = y = f (x) 11. If f (0) = 2, can f be an odd function? What if f (0) is undefined? Explain your answers. 12. Determine graphically whether each of the following four functions is even, odd, or neither. 1 f +g 7.
Write your answers in interval notation (or, if the solution is a discrete set of points, a list of those points). x =0 x−2 x 3 − 5x 2 + 6x < 0 x >0 x−2 x 3 − 5x 2 + 6x = 0 Concepts 0. Problem Zero: Read the section and make your own summary of the material. 1. True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample. (a) True or False: Functions are the same as equations. (b) True or False: The domain of every function is a subset of R. | 677.169 | 1 |
Electronic Proceedings of the Twenty-fourth Annual International Conference on Technology in Collegiate Mathematics
Orlando, Florida, March 22-25, 2012
Paper S112Connecting Geometry, Measurement, and Algebra using GeoGebra for the Elementary Grades
Joseph M. Furner
Carol A. Marinas
Geometry, measurement, and algebra are important concepts to master. By using technology for teaching math, GeoGebra examples will create connections from geometry, to measurement, and algebra. Through the mathematical and pedagogical power of GeoGebra, the learner will use this user-friendly software to make meaningful connections for K-6 students. | 677.169 | 1 |
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Whether you're a teacher or a student, easily access our math lessons hosted from our very fast server. Math Gol a.k.a Math Life is also offering an eye-catcher quiz for each lesson. Of course you can also get our math worksheets either in open format or multiple-choice type. These resources are always for FREE of use.
also offers worksheets made and ran by LaTeX, a document preparation system and document markup language widely used in mathematics and other scientific endeavors. These worksheets are available for most of our lessons with no monetary obligations on your end.
Plus this website uses a responsive theme, which means it adapts to the device on which it's displayed. So you don't have to worry if this site looks great when using iPhones, other smartphones, iPads, and tablets. Even the quizzes and mathematical equations and symbols found here are running beautifully on all devices.
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Our math lessons are designed for ease of use to help you understand the basic and advanced levels.
Finding the best math lessons elsewhere can be confusing. So, we asked knowledgeable and experienced teachers and professors to help us designed lesson plans to achieve better learnings in mathematics and statistics.
But if you think our lessons do not fit to your standards, then you can email and inform us of your ways and guidelines to improve the writeups of this website. After all, we are all learners and educators.
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Whether using iPhone, iPad, tablet, or other smartphone, access our quizzes or practice tests anywhere, and anytime and be amazed of our elegant environment.
Thanks to G. Michael Guy, an Assistant Professor of Mathematics at Queensborough Community College, for providing such stunning plugin.
Download Worksheets Easily
Downloading worksheets hosted at Google Docs is easier when you have them publicly shared. That is why we've hosted our documents at the popular document hosting site.
If you are looking for printable math worksheets in pre-algebra, algebra, trigonometry, geometry, calculus, and statistics, probably in multiple-choice type, we recommend you bookmark this site and look no further.
If you have a suggestion or request to make a worksheet for a specific topic, then email us at no cost for you but if you may donate for the maintenance of this site, then you are welcome to do so. | 677.169 | 1 |
Communicating
Mathematics
with Maple
and LaTeX
June 15-July 3,
1998
This three week workshop concentrated on training 26 Central Kentucky High
School and Middle School science and math teachers in the use of LaTeX, the mathematical
wordprocessing language universally used in the scientific community for
disseminating information, and MapleV5, an interactive programming language
widely used to investigate and solve problems of a mathematical nature.
Here is a
visual
roll of the participants.
Maple
HandbookVisual
Problem Solving Monday
Maple basics. The todo for today is two Maple worksheets and three
txt files. Here is the zip
file containing the files. Download, unzip, and load into Maple.
Tuesday
Visual Problem solving with Maple Today we look at topics
in visual problem solving. Here is a
worksheet to start. Save it to d:\chisel\tmpdir and load into
Maple.
Wednesday Making up Quizzes
and Exams, keeping grades with Maple. Here is the zipfile.
Thursday
Exporting worksheets to LaTeX and HTLM More Visual problem solving.
Here is a zip
file.
Friday Building books
of worksheets. The Lottery. Here is the zip.
Week 3 -- Building books with
LaTeX and Maple
Making books with
Maple Monday
Getting hardware right -- Ken Kubota. Ramp experiments --
Bill Hill. A todo on using your unix accounts (ftp, telnet, elm).
zip Tuesday More
todo on using your unix account (posting stuff to your web page).
Exporting books of worksheets to LaTeX. Here is the zip.
Here is a zip
of the Koblitz I text in worksheet form.
Wednesday A little bit of Perl and
postscript. Here's a zip
Here's a nice Maple worksheet on colors
exported to html. Here's the actual worksheet. colors.mws Thursday Planning
and Projects for future workshops. Working with video capture. Friday
Issues of assessment and evaluation -- Joan Mazurpowerpoint
slides Communicating Mathematics:color
postscript.zipfile
of the book of worksheets. | 677.169 | 1 |
Product details
AUTHOR
SUMMARY
This algebra based text is a thorough yet approachable statistics guide for students. The new edition addresses the growing importance of developing students' critical thinking and statistical literacy skills with the introduction of new features and exercises.Brase, Charles Henry is the author of 'Understandable Statistics (Hardcover)' with ISBN 9780618949922 and ISBN 06189499 | 677.169 | 1 |
8 1 Study Guide And Intervention Answers 134084
glencoe mcgraw hill geometry worksheet answers photos
8 1 Study Guide And Intervention Answers 134084 involve some pictures that related one another. Find out the most recent pictures of 8 1 Study Guide And Intervention Answers 134084 here, so you can get the picture here simply. 8 1 Study Guide And Intervention Answers 134084 picture posted ang submitted by Admin that preserved in our collection. 8 1 Study Guide And Intervention Answers 134084 have an image from the other. 8 1 Study Guide And Intervention Answers 134084 It also will feature a picture of a sort that could be observed in the gallery of 8 1 Study Guide And Intervention Answers 134084. The collection that consisting of chosen picture and the best amongst others. These are so many great picture list that could become your ideas and informational purpose of8 1 Study Guide And Intervention Answers 134084 design ideas on your own collections. hopefully you are enjoy and lastly go through the gallery below the8 1 Study Guide And Intervention Answers 134084 picture. We offer image 8 1 Study Guide And Intervention Answers 134084 is similar obtainable. The assortment of images 8 1 Study Guide And Intervention Answers 134084 outside home, to be able to see immediately, you may use the category navigation or maybe it is using a arbitrary post of 8 1 Study Guide And Intervention Answers 134084. We hope you enjoy and find one of our best assortment of pictures and get influenced to enhance your residence. If the hyperlink is shattered or the image not entirely on8 1 Study Guide And Intervention Answers 134084you can call us to get pictures that look for We offer image8 1 Study Guide And Intervention Answers 134084 is similar, because our website concentrate | 677.169 | 1 |
Greetings College Algebra students! Here you will find a variety of information concerning your course. Feel free to bookmark this page as a future resource.
Course Description
This course is designed as preparation for higher level mathematics courses. Topics include the study of linear, quadratic, polynomial, rational, radical absolute value, logarithmic,
and exponential functions, relations and inequalities; graphs, basic characteristics, and operations on functions; real and complex zeros of functions; graphing techniques; systems
of equations and matrices. This is material that will provide a firm foundation for a variety of future courses as well as teach you critical thinking and processing skills. Our purpose is to help
make you successful in all degree fields!
The use of mathematical software and calculators is required. See course syllabus for more details. Non-STEM (Science-Technology-Engineering-Mathematics)
majors should enroll in MATH 1301, and Business majors should enroll in MATH 1315. Credit may be received for only one of MATH 1301, MATH 1302, or MATH 1315.
While the policy does not prohibit you from using an alternate calculator on homework and quizzes, the Math LRC highly recommends using on a regular basis the same calculator you will be utilizing on exams so as to increase your familiarity with its function. | 677.169 | 1 |
IB Math SL Questions & Answers
IB Math SL Flashcards
IB Math SL Advice
IB Math SL Advice
Showing 1 to 3 of 3
I would recommend this course because it provides a strong overview of many math topics that will be needed for college level math. This course also helps teach the student how to use a calculator to solve complicated math problems.
Course highlights:
The highlights of this course would definitely be learning how to input various things into the calculator and then seeing the right answer pop up on the screen. Another highlight would definitely have to be going into the IB test and coming out with extreme confidence in myself, knowing that I gave myself a very strong chance to get a 4+ on the test to help get my diploma. I learned different problem solving strategies and how to carry out basic math skills.
Hours per week:
6-8 hours
Advice for students:
You need a strong work ethic and a definite "want to learn" attitude when it comes to this course. You need to be strong in math and have a good foundation of previous algebra skills in order to have a chance at being successful. Learn how to do the math correctly the first time and after that its like riding a bike, you will never forget how to do it.
This was a great class that I feel like covered all the basic math categories. The class also taught me how to use a calculator properly.
Course highlights:
The highlights of this course were the problem solving techniques that I learned from the variety of math categories that I learned from. I learned vectors, probability, calculus, integrals, derivitives, and algebra.
Hours per week:
6-8 hours
Advice for students:
Make sure that you review the topics on a weekly basis that way things don't get forgotten.
Course Term:Spring 2016
Professor:Mrs. Vela
Course Tags:Many Small AssignmentsParticipation CountsFinal Paper
Feb 05, 2016
| Would highly recommend.
Not too easy. Not too difficult.
Course Overview:
This course is still challenging but still is very much manageable. It teaches necessary skills while not pushing over the edge.
Course highlights:
The highlights of this course was the big internal assessment project we had to do. For this project you pick a topic and a research question to conduct. It taught me the application of math to real everyday life. | 677.169 | 1 |
Math for Computer Science
This Text Provides the essential mathematics needed to study computing. The authors are aware that many student do not have the same mathematical background common 5 years ago and this book has been written to accommodate these changes.Many exercises are provided with detailed answers and difficult concepts are thoroughly illustrated to help learning. Chapters are designed to be read in isolation with interdependence between chapters minimalised.
"synopsis" may belong to another edition of this title.
From the Back Cover:
This book provides the essential mathematics needed to study computing, all under one cover. Aware that many readers do not have the same mathematical background common 5 years ago, this book has been written to accomodate these changes. Many exercises are provided with fully detailed answers and all difficult concepts are thoroughly illustrated to help learning.Compact and concise, the book fully explains the fundamentals of mathematics in an easy to read style. Difficult but crucial areas of the subject are developed by example and counter example. Chapters are designed to be read in isolation and interdependence between chapters in minimalised. | 677.169 | 1 |
Algebra and geometry
ExploreLearning Gizmos: Math & Science Simulations
Algebraic Reasoning Find the value of each object in the puzzle by looking for mathematical relationships.List of all mathematical symbols and signs - meaning and examples.
Math Worksheets - Full List - Super Teacher Worksheets
This is the reason I created the Standards based progress monitoring.Progress monitoring will allow you to document student growth and make sure that the interventions that you administer are working.
The Trigonometric Identities are equations that are true for all right-angled triangles.Need help with your Basic Math and Pre-Algebra homework and tests.Note: you can see the nice graphs made by sine, cosine and tangent.Study.com has engaging online math courses in pre-algebra, algebra, geometry, statistics, calculus, and more.Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum.All problems have been created such that no calculator is necessary.
Math Guided Textbook Solutions and Answers | Chegg.com
Note that you do not have to be a student at WTAMU to use any of these online tutorials.
Mathematics Archives - Topics in Mathematics - Algebra
Trigonometry Index Sine, Cosine and Tangent Unit Circle Algebra Index.And when the angle is less than zero, just add full rotations.Because the radius is 1, we can directly measure sine, cosine and tangent.
KEYWORDS: Tutorial, Inequalities, Absolute Values and Exponents, Fractional and Negative Exponents.Learn the basics of algebra for free—focused on common mathematical relationships, such as linear relationships.
Free Math Worksheets, Problems and Practice | AdaptedMind
Guided textbook solutions created by Chegg experts Learn from step-by-step solutions for over 22,000 ISBNs in Math, Science, Engineering, Business and more.Index for Algebra Math terminology from Algebra I, Algebra II, Basic Algebra, Intermediate Algebra, and College Algebra.
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
Geometry - Algebra.Com
Learn Math Online | Award-Winning Math Course | Math
Comprehensive math vocabulary lists are based on the Common Core State Math Standards and organized by K-12 grade level.Pre-Algebra, Algebra I, Algebra II, Geometry: homework help by free math tutors, solvers, lessons.Questions like these are common in engineering, computer animation and more. | 677.169 | 1 |
Is Vector Calculus useful for pure math?Pure math covers a lot of ground. There are areas where vector calculus is important (various branches of analyis), while there are others (algebraic areas) where it may not be.
Yes you should take it. You never know what you'll get into in grad school. For example I had always imagined I'd avoid analysis completely, until the school I was admitted to required an analysis qualifier. Good thing I forced myself through two semesters of analysis already. Yes vector calc might be very important, or you might not use it so much. But you should be prepared :) | 677.169 | 1 |
Mathematical Model of the Growth of Trees
Absract At different stages of life, the growth rate of a tree is not the same. This presentation is to: build a mathematical model according to the regular pattern which has been observed and then solve the problem and optimize the established model. Problem Proposition
A newly planted tree grows slowly, but gradually the tree grows tall and will grow at a faster speed. But when it grows to a certain height, the growth rate will gradually become stable and then slowly go down. This patter is universal. Problem Analysis
If we assume that the growth rate of a tree is proportional with its current height, it obviously does not meet the two ends, particularly the latter part of the growth process, because the tree won't grow faster and faster boundlessly But if we assume that the growth rate of the tree is proportional to the difference between the maximum height and the current height, it is obviously not in conformity with the middle section of the growth process. We made a compromise assuming that the growth rate is proportional with both its current height and difference between the maximum height and the current height. Assumptions
Assume that there is a maximum height of a tree can grow to, when this height is reached the tree will stop growing higher. Assume that the growth rate of a tree is only related to its current height and the difference between the maximum height and its current height, its not influenced by other environmental factors. Symbol Descriptors
Assume the maximum height of the tree is H (m) and at time t (year) the height is h(m). The proportional coefficient of tree growth rate and the current height and the difference between the maximum height and its current height is k. Model building and solving
According to the analysis of the problem and the assumptions made above, we obtain the following equation:
Where the proportional constant k >0 ....
YOU MAY ALSO FIND THESE DOCUMENTS HELPFUL
...MathematicalModels
Contents
Definition of MathematicalModel Types of Variables The Mathematical Modeling Cycle Classification of Models
2
Definitions of MathematicalModelMathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. It is a process that attempts to match observation with symbolic statement. A mathematicalmodelmodel Modeling Cycle
Simplify Real World Problem
Interpret
MathematicalModel
Program
Conclusions Simulate
Computer Software
5
The...
...Mathematicalmodel
A mathematicalmodel is a description of a system using mathematical language. The process of developing a mathematicalmodel is termed mathematical modelling (also writtenmodeling). Mathematicalmodels are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science,artificial intelligence), but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analystsand economists use mathematicalmodels most extensively.
Mathematicalmodels can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures.
Examples of mathematicalmodels
Population Growth. A simple (though approximate) model of population growth is the Malthusian growthmodel. A slightly more realistic and largely used population growthmodel is the logistic...
...Nolan's Model
Stages of GrowthModel (SGM)
A summary of the structure of Nolan's SGM (Stages of GrowthModel), a general theoretical model which describes the IT growth stages that can occur in an organisation.
Overview
Richard L. Nolan developed the theoretical Stages of growthmodel (SGM) during the 1970s. This is a general model, which describes the role of information technology (IT), and how it grows within an organisation.
A first draft of the model was made in 1973, consisting of only four stages. Two stages were added in 1979 to make it a six-stage model. There were two articles describing the stages, which were first published in the Harvard Business Review.
The structure of the final, six-stage model is depicted in the diagram below:
[pic]
Figure 1: Diagram showing the SGM continuum for growth/maturity
The diagram above shows six stages, and the model suggests that:
• Stage 1: Evolution of IT in organisations begins in an initiation stage.
• Stage 2: This is followed by expeditious spreading of IT in a contagion stage.
• Stage 3: After that, a need for control arises.
• Stage 4: Next, integration of diverse technological solutions evolves.
• Stage 5: Administration/management of data is necessitated,...
...What is Gordon GrowthModel,
"This model is use to determine the fundamental value of stock, it determines the value of stock based on sequence or series of dividends that matured at a constant rate , and the dividend per share is payable in a year"
Stock Value (P) = D / (k – G)--------------Equation 1 Where D= Expected dividend per share one year from now G= Growth rate in dividends k= required rate of return for equity investor
This model is useful to find the value of stock, with following assumption should be taken into account while calculating value of stock, which are: 1. That dividends remains to grow continuously on a constant rate 2. The growth rate should remain less than the required return on equity
Relationship between monetary policy and stock market
Monetary policy is a state owned measure which is an an important determinant of stock prices , lowering of increase in interest rate couzld be use by fedration to influence stock prices. it is very useful to find the"value of stock". Monetary policy effetcs stock prices in two ways:
1.
When in certain circumstances when the federations or the controller of monetray policty lowers interests rates, the return on bonds or securities (which is also considered as an alternative assest to stocks) decreses, this results that the investors who have invested ,are ready or accept to receive a lower required rate of...
...Solow model - how well it holds in the real world?
Prepared by:-
Amol Rattan (75013)
Introduction
Prior to Solow Model, Harrod Domar model had shown how the savings rate could play a crucial role in determining the Long run rate of Growth. Solow model however proved a result that was contrary to what Harrod Domar model had predicted.
It showed that savings has only level effect on income and the growth rate of income depends upon the rate of efficiency or technical progress in the country.
Solow Model relies on certain assumptions
1. There are constant returns to Scale(CRS)
2. The production function is standard neoclassical production function with diminishing returns to factor
3. The markets are perfectly competitive
4. Households save at a constant savings rate 's'
Equilibrium in Solow Model is defined as the steady state level of capital where the economy grows at a constant rate. By assuming that the two factors of production are capital and labour per efficiency unit, it can be shown that savings only affects the level of per capita income. It is only the rate of growth of efficiency which determines the rate of growth of per capita output.
For production function: Y= KαL1-α
Steady state values are:...
...Macroeconomics Essay: "Countries grow at different rates because they accumulate capital at different rates." Is this true?
The Neoclassical growthmodel is a framework which we can use to attempt to explain how economic growth behaves. It much simplified model which attempts to explain long run economic growth by looking at capital accumulation, population growth and increases in technical progress. We will use the neoclassical model to explain how countries grow, by using the fundamental equation kdot= sf (k) – (n+g+d) k, where k dot is the differential of k with respect to t. The equation shows us how for countries not in the steady state how capital accumulation affects growth and that eventually all countries converge to the steady state. Then once a country has reached its steady state it will be shown that capital accumulation no longer affects economic growth.
Looking at the fundamental equation of the neoclassical growthmodel kdot= sf (k) – (n+g+d) k. It is from this equation that we can see if a country invests more than the break even investment, then kdot increases, i.e. they accumulate capital, and if a country invests less than the break even investment then kdot decreases. The equations shows that all countries will converge to a steady state when investment per effective worker is equal to the...
...Augmented Solow GrowthModel
The augmented Solow model was proposed by Mankiw, Rower and Weil (MRW) in their treatise "A Contribution to the empirics of Economic Growth". To better explain the variation in living standards across regions, they propose a model that adds human capital accounting for the fact that labor across different economies can possess different levels of education.
To test thismodel, a proxy variable in the form of human capital accumulation is added as an explanatory variable in the cross-country regression. MRW find that human capital accumulation is directly correlated with savings and population growth and the inclusion of human capital lowers the impact of savings and population. MRW claim that by testing the data, they find that this model accounts for 80% of the cross country income variance [cross–section regression of the 1985 level of output per worker
for 98 countries producing an R² of 0.78 ]
The model also predicts that poor countries are likely to have higher returns to human capital. The incorporation of human capital has the ability to tweak the theoretical modeling and the empirical analysis of economic growth. The theoretical impact will be based on the restructuring of growth process ideology. MRW quote Lucas (1988) stating that although there exist decreasing returns to... | 677.169 | 1 |
Course info
Algebra I will study numbers and the axioms of Algebra. Emphasis will be placed upon working with real numbers, variables, solving equations, inequalities, working with polynomials, factoring polynomials and problem solving. | 677.169 | 1 |
Online material.
If you follow one of these links and do not see any graphs,
you need to download Flash Player. Click to download the free player from the Macromedia site here:
Download Flash Player 7.
Do you need to check how to compute a derivative? The webpage for automatic
computing of derivatives can be found here.
Then follow the 'derivatives' link.
Do you need to check how to compute a derivative ?
The webpage for automatic computing of derivatives
(which I mentioned in class) can be found
HERE.
Then follow the 'derivatives' link.
Introduction
GOALS OF THIS COURSE: Math 131 is a calculus
course primarily intended for students in the life or social sciences, such as
Biology, Pharmacy, and Economics. It is different (but not easier) than the
four-credit calculus course, Math 141, designed for students who intend
to take more advanced math, such as engineering, computer science,
and mathemactics
majors. The main emphasis will on the practical interpretation of calculus in
numerical, graphical, and algebraic terms, although important theoretical
concepts will also be covered. The main topics of the course are functions,
differentiation, integration and applications.
EXPECTATIONS: We expect that you will give this
course 7-9 hours a week of your undivided attention, in addition to your class
time. This is an approximate figure of course, but don't assume that
you can spend less time than this and still get a grade you'll like. We also
expect that you will ATTEND YOUR CLASS.
Exams and Evaluation
There will be three evening exams given during the semester
outside of class.
Their dates will be posted on the central web page
and announced in class as soon as available.
All sections will take these exams.
The final exam will be scheduled at a common time for all sections.
The exams will reflect the variety of the homework problems.
Do not expect to be asked merely to solve homework problems with
the numbers changed. The best way to prepare for the exams,
and to develop confidence in your ability to solve problems,
is to work on the homework problems as suggested.
GRADING: Your grade will be determined out of a
possible of 600 points:
three common exams, 100 points for each exam
final exam 200 points
homework, quizes, or classwork 100 points | 677.169 | 1 |
Symmetry, Shape, and Space: An Introduction to Mathematics Through Geometry
Symmetry, Shape, and Space uses the visual nature of
geometry to involve students in discovering mathematics. The
text allows students to study and analyze patterns for themselves,
which in turn teaches creativity, as well as analytical and
visualization skills. Varied content, activities, and
examples lead students into an investigative process and provide
the experience of doing and discovering mathematics as
mathematicians do. Exercises requiring students to express their
ideas in writing and to create drawings or physical models make
math a hands-on experience. Assuming no mathematics beyond
the high school level, Symmetry, Shape, and Space is the
perfect introduction to mathematics in the liberal arts course of
study, and it is designed so that each chapter is independent of
the others, allowing great flexibility | 677.169 | 1 |
advanced QuickStudy guide is designed for students who are already familiar with Algebra 1. This 6-page guide is laminated and hole-punched for easy use. Covered topics include real number lines, graphing and lines, types of functions, sequences and series, conic sections, problems and solutions and much more! | 677.169 | 1 |
Radicals, Algebra Review Pages
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this file type before downloading and/or purchasing.
480 KB|19 pages
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Product Description
This 19 page section includes beginning of the year review pages I call Starting Blocks #1 and Starting Blocks #2. They provide a good review of basic math and allow a teacher to see where gaps or weaknesses may exist as the year is beginning. Also included are worksheets reviewing critical material called Cornerstone Algebra and Building Blocks. I like to use Building Blocks prior to solving equations and Cornerstone after solving equations.
In addition, notes (teacher copy and interactive student copy) and worksheets are included which cover simplifying, adding, and subtracting radicals. I teach radicals at the end of the year and assess this knowledge on the 2nd Semester Final Exam. | 677.169 | 1 |
SUB: MATHEMATICS
MODULE-2A
MODULE-2A
Functions of single variable, Limit, continuity and differentiability,
Mean value theorems.
Function: For sets A and B, a function A to B, defined by f: A
which assigns to every element x
, a unique element f(x)
, is a
SUB: MATHEMATICS
MODULE-3A
MODULE-3A
Evaluation of definite and improper integrals
_
Consider the infinite region S that lies under the curve
to the right of the line
above the x- axis, and
. You might think that, since S is infinite in extend, its area m
SUB: MATHEMATICS
MODULE-8A
MODULE-8A
Cauchys and Eulers equations, Initial and boundary value problems
An equation of the form
is called cauchys homogeneous linear equation.
Where X is a function of
Such equations can be reduced to linear differential equ
SUB: MATHEMATICS
MODULE-1C
MODULE-1C
Linear Algebra: Matrix algebra, system of linear equations, Eigen values and eigen vectors.
_
1.
The rank of the matrix A= [
a) One
b) Two
c) Three
d) None of the above
] is
Ans:
The rank of a matrix is order of highes
SUB: MATHEMATICS
MODULE-7A
MODULE-7A
Higher order linear differential equations with constant coefficients
These are the form
Where
are constants
In symbols form (
I.
)
To find the complementary function
Write the auxiliary equation (A.E)
and
Solve it for
SUB: MATHEMATICS
MODULE-6A
MODULE-6A
Differential equations: First order equations (linear and nonlinear)
A differential equation is an equation which involves differential co-efficient or
differentials.
The order of a differential equation is the order o
SUB: MATHEMATICS
MODULE-4A
MODULE-4A
Partial derivatives, Total derivative, Maxima and minima
Functions of two or more variables: A symbol z which has a definite value for every pair
of values of x and y is called a function of two independent variables x
SUB: MATHEMATICS
MODULE-7B
MODULE-7B
Higher order linear differential equations with constant coefficients.
_
5. The complete solution for the ordinary
1. A function n(x) satisfied the
differential equation
where L is a constant. The boundary
conditions a
Ashley is about to take the final exam for her general biology class. Shes spent many
long hours studying, and feels a little tired. On her way to class, she stops by the
student center to grab a large cup of coffee. She hopes that the caffeine in the cof
Profitability
EBIT margin: EBIT/sales
Virgins EBIT margin of 3.5% is higher than Qantas. It may be driven by higher sales or lower expenses.
Liquidity
Current ratio=current assets/current liabilities
Current ratio of Virgin is 0.6 which is slightly lower
SECULAR COUNTRY-FREEDOM OF RELIGION
INTRO
It is quite impossible not to be astonished by India.Nowhere on earth does
humanity presentItself in such creative burst of cultures and religion,races
and tongues.Every aspect of the country present itself on a
m
Chapter 16
Inventory Management
16-1
16-1
INVENTORY MANAGEMENT
Objectives
Techniques
Solved Problems
16-2
16-2
Inventory
Inventory refers to the stockpile of the products a firm
would sell in future in the normal course of business
operations and the comp | 677.169 | 1 |
Elementary Linear Algebra
Hardcover | June 23, 2008
Pricing and Purchase Info
about
Elementary Linear Algebra, First Canadian Edition, features a computational emphasis and contains just the right mix of theory and worked examples. The authors provide students with easy-to-read explanations, examples, proofs and procedures and also stress that linear algebra has many interesting and important applications, both in the sciences and the arts.The book mixes the theory and practice of linear algebra seamlessly, with a variety of interesting and topical applications such as music and fractals throughout, including one section that deals with using Fourier transforms to uncover the secrets behind the opening chords of a song! | 677.169 | 1 |
Showing 1 to 30 of 188
Project
This project introduces the idea of a mathematical
group. Since the properties that define a group are
familiar to your students, this can be an accessible
project even though it resembles an introduction
to abstract algebra. If you want to discus
4
Go
Test
For a chapter test, go to
Web Code: bfa-0453
nline
PHSchool.com
Assessment Resources
Multiple Choice
Open Response
1. Which matrix is the row-reduced echelon form
of the following matrix?
6. Solve the following system using Gaussian
Elimination.
Investigation Overview
This investigation continues the extension of the real
numbers into the complex numbers much as the
story continued historically. Mathematicians up until
the 19th century did not accept complex numbers
as having any actual usefulnes
Mathematical Reflections
5B
EXERCISES 68 At the start of the investigation,
you may have assigned these as Questions 13 for
students to think and write about.
In this investigation, you graphed exponential functions.
You wrote rules for exponential functi
Investigation Overview
In this investigation, students begin by solving
systems of two equations in two unknowns. They
review the solution techniques of substitution and
elimination that they learned in CME Project
Algebra 1. Then they extend this work to
Chapter 5
Exponential and
Logarithmic Functions
In this chapter, students extend the definition
of exponents to include rational and real-valued
exponents. They make this extension in a way that
preserves the laws of exponents. Along the way
they review p
Mathematical Reflections
5A
EXERCISES 68 At the start of the investigation,
you may have assigned these as Questions 13 for
students to think and write about.
In this investigation, you evaluated and simplied
exponents. You developed the laws of exponents
Investigation Overview
This investigation is an introduction to the power
of using matrix multiplication to model all sorts of
multivariate phenomena in a way that is conceptually
and notationally simple.
Basically, whenever you have a linear system with
Project
Project: Using Mathematical Habits
More Matrix Operations
In this chapter, you looked at several applications
of matrix algebra, including Gaussian Elimination,
matrix addition, and matrix multiplication. There
are several other operations on matr
Developing Students
Mathematical Habits
Key mathematical habits in this chapter include:
EXTENSION By making strategic choices that
preserve the laws of exponents, students extend the
set of numbers that can be used as exponents to
include all real number
2.3
Lesson Overview
Algebra With Functions
GOALS
Compose functions.
The basic rules of algebra tell you how the operations of addition and
multiplication behave. Addition and multiplication are operations that
combine numbers. In this lesson, you will le
4.13
Lesson Overview
Probability Models
GOAL
Analyze sequences of repeated probabilities.
Consider all those bugs from the Lesson 4.12 Maintain Your Skills exercises.
They all were moving around among the three corners of a triangle, named
T, L, and R. T
Chapter 4
Linear Algebra
This chapter introduces matrices both as shorthand
(to record all the information in a system of linear
equations) and as mathematical objects in their
own right. Students learn to translate between
systems of linear equations and
Project Overview
This project explores the functional equation that
exponential functions satisfy: f(x 1 y) = f(x) ? f(y).
Students start with a very small set of assumptions
about this function and try to build an understanding
of how any function that s
Mathematical Reflections
6B
EXERCISES 68 At the start of the investigation,
you may have assigned these as Questions 13 for
students to think and write about.
In this investigation, you learned to write any
composition of translations and dilations as an
Investigation Overview
Throughout this chapter, students have studied
exponential functions. In the last lesson of
Investigation 5B, students proved that exponential
functions are one-to-one, so they must have
inverses. In this investigation, students stu
8.1
Lesson Overview
Getting Started
GOAL
Warm up to the ideas of the investigation.
The values of trigonometric functions are related to the coordinates of
points on a circle with radius 1 centered at the origin.
Olivia watches Paul walk around a circle.
Developing Students
Mathematical Habits
Key mathematical habits in this chapter include:
VISUALIZATION Students visualize graphs as
transformations of the basic graphs, seeing them
as translations, scalings, and reflections or as
compositions of these tra
3C
Mathematical Reflections
In this investigation, you found relationships between
magnitudes and arguments of factors and products.
You also graphed the solutions to equations in the form
x n 2 1 5 0. These exercises will help you summarize what
you have
Investigation Overview
Matrices are much more than tables. They have a
mathematical life of their own. They can be added,
subtracted, multiplied, and multiplied by scalars
(real numbers). The algebra of matrices is similar
to the algebra of numbers studen
Investigation Overview
This investigation reintroduces the laws of exponents
as defined for positive integer exponents. It asks
students to use those laws as the basis for deciding
how to extend the definition to zero, negative,
and rational exponents. As
Chapter 6
Graphs and
Transformations
In this chapter, students extend the graphing skills
they learned in CME Project Algebra 1 and Geometry
to include more kinds of graphs. They also learn to
recognize transformations of these graphs and to
connect trans
Lesson Overview
1.10 Getting Started
GOAL
Warm up to the ideas of the investigation.
You can use a table to help you rewrite a recursive denition for a function
as a closed-form denition.
For Exercises 15, make a table of the function values for inputs b
6.3
Lesson Overview
Translating Graphs
GOAL
Recall the lumping method of factoring from Chapter 2. You can also
use the lumping technique to help you graph equations.
Minds in Action
episode 24
Sasha and Derman are trying to graph the equation y = (x 2 3)
Developing Students
Mathematical Habits
These key habits are developed in this chapter.
EXTENSION Students see the decisions made in
deciding how to calculate with complex numbers as
an extension from the real numbers in such a way
as to preserve the basi
Mathematical Reflections
4A
EXERCISES 68 At the start of the investigation,
you may have assigned these as Questions 13 for
students to think and write about.
In this investigation, you learned how to solve a system
of three equations in three unknowns. Y | 677.169 | 1 |
Calculus: Antiderivatives and Indefinite Integration
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this file type before downloading and/or purchasing.
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Product Description
This is a ten-lesson unit on Integrals for students enrolled in AP Calculus AB or BC, Calculus Honors, or College Calculus. Every lesson includes
✎ A set of Guided Student Notes
✎ A daily homework assignment
✎ Four forms of a daily homework quiz or exit ticket
✎ Teachers also have the benefit of a fully-editable SmartBoard® Lesson for presentation and discussion.
You Interact, edit, or create online at Smart Notebook Express.
Lesson Objective:
Students will understand the definition of antiderivatives and find the indefinite integral of polynomials and transcendental functions. Students will also solve basic differential equations for initial conditions. | 677.169 | 1 |
Book & Toy | August 17, 2014
Pricing and Purchase Info
$214.31
Earn 1072 plum® points
Quantity:
In stock online
Ships free on orders over $25
Not available in stores
about
John Squires and Karen Wyrick have drawn upon their successes in the classroom and the lab as inspiration for MyMathLab® for Developmental Mathematics: Basic Mathematics, Introductory Algebra, and Intermediate Algebra, Second Edition. This MyMathLab eCourse provides students with a guided learning path through content that is organized into small, manageable mini-modules. This course structure includes pre-made tutorials and assessments for every topic, giving instructors an eCourse that can be easily customized for a variety of learning environments. With this revision, the authors have added Applications material, expanded the breadth of Intermediate Algebra content, and developed Interactive Examples to provide an even more interactive and engaging student experienceAbout The Author
John Squires has been teaching math for more than 20 years. He was the architect of the nationally acclaimed "Do the Math" program at Cleveland State Community College and is now head of the math department at Chattanooga State Community College, where he is implementing course redesign throughout the department. John is the 2010 Cro... | 677.169 | 1 |
ISBN 13: 9780072903492
Fundamentals of Linear State Space Systems: Instructor's Manual
This book addresses two primary deficiencies in the linear systems textbook market: a lack of development of state space methods from the basic principles and a lack of pedagogical focus. The book uses the geometric intuition provided by vector space analysis to develop in a very sequential manner all the essential topics in linear state system theory that a senior or beginning graduate student should know. It does this in an ordered, readable manner, with examples drawn from several areas of engineering. Because it derives state space methods from linear algebra and vector spaces and ties all the topics together with diverse applications, this book is suitable for students from any engineering discipline, not just those with control systems backgrounds and interests. It begins with the mathematical preliminaries of vectors and spaces, then emphasizes the geometric properties of linear operators. It is from this foundation that the studies of stability, controllability and observability, realizations, state feedback, observers, and Kalman filters are derived. There is a direct and simple path from one topic to the next. The book includes both discrete- and continuous-time systems, introducing them in parallel and emphasizing each in appropriate context. Time-varying systems are discussed from generality and completeness, but the emphasis is on time-invariant systems, and only in time-domain; there is no treatment of matrix fraction descriptions or polynomial matrices. Tips for using MATLAB are included in the form of margin notes, which are placed wherever topics with applicable MATLAB commands are introduced. These notes direct the reader to an appendix, where a MATLAB command reference explains command usage. However, an instructor or student who is not interested in MATLAB usage can easily skip these references without interrupting the flow of text | 677.169 | 1 |
Mathematics is the means of looking at the patterns that make up our world and the intricate and beautiful ways in which they are constructed and realised.
Mathematics contributes to the school curriculum by developing pupils' abilities to calculate; to reason logically, algebraically, and geometrically; to solve problems and to handle data. Mathematics is important for pupils in many other areas of study, particularly Science and Technology. It is also important in everyday living, in many forms of employment and in public decision-making.
As a subject in its own right, Mathematics presents frequent opportunities for creativity and can stimulate moments of pleasure and wonder when a problem is solved for the first time, or a more elegant solution to a problem is discovered, or when hidden connections suddenly manifest.
It enables pupils to build a secure framework of mathematical reasoning, which they can use and apply with confidence. The power of mathematical reasoning lies in its use of precise and concise forms of language, symbolism and representation to reveal and explore general relationships. These mathematical forms are widely used for modelling situations; a trend accelerated by computational technologies.
We aim to allow each girl to reach her own individual and mathematical potential and to develop a confident and positive attitude toward the subject.
We want each girl to develop a firm foundation of knowledge and skills to enable the use of mathematics in other disciplines, and in further study, and we hope that each student learns to appreciate the uses of mathematics outside of the classroom. Above all, we aim to instill an enjoyment for the subject.
Girls in Years 7 & 8 cover Foundation Level IGCSE and all girls sit Higher Level by the end of Year 11. Some girls will also be prepared for Further Pure IGCSE in Year 11. About half of the Sixth Form opt to study Advanced Level Mathematics in Year 12 and one class is also prepared for Further Mathematics A Level. We have enjoyed consistently outstanding examination results with many girls choosing to study Mathematics and Mathematics-related courses at university. | 677.169 | 1 |
About this title:
Synopsis: The style and structure of Concepts in Abstract Algebra are designed to help students learn the core concepts and associated techniques in algebra deeply and well. Providing a fuller and richer account of material than time allows in a lecture, this text presents interesting examples of sufficient complexity so that students can see the concepts and results used in a nontrivial setting. Charles Lanski gives students the opportunity to practice by offering many exercises that require the use and synthesis of the techniques and results. Both readable and mathematically interesting, the text also helps students learn the art of constructing mathematical arguments. Overall, students discover how mathematics proceeds and how to use techniques that mathematicians actually employ.
About the Author:
Charles Lanski is Professor of Mathematics at the University of Southern California.
Book Description American Mathematical Society. Hardcover. Book Condition: Good. 053442323X Item in good condition and has highlighting/writing on text. Used texts may not contain supplemental materials such as CD's, info-trac etc. Bookseller Inventory # Z053442323XZ3
Book Description American Mathematical Society. Hardcover. Book Condition: Very Good. 053442323X Item in very good condition and at a great price! Textbooks may not include supplemental items i.e. CDs, access codes etc. Bookseller Inventory # Z053442323XZ2
Book Description American Mathematical Society60835
Book Description American Mathematical Society. Hardcover. Book Condition: Very Good. 053442323X Very Good Condition. Has some wear. Five star seller - Buy with confidence!. Bookseller Inventory # Z053442323XZ2
Book Description American Mathematical Society2323X-2-4 | 677.169 | 1 |
Excursions in Modern Mathematics: With Mini-Excursions
Browse related Subjects ...
Read More-world applications of modern mathematics. The excursions are organized into four independent parts: 1) The Mathematics of Social Choice, 2) Management Science, 3) Growth and Symmetry, and 4) Statistics. Each part consists of four chapters plus a mini-excursion (new feature in 6/e). The book is written in an informal, very readable style, with pedagogical features that make the material both interesting and clear. The presentation is centered on an assortment of real-world examples and applications specifically chosen to illustrate the usefulness, relevance, and beauty of liberal arts | 677.169 | 1 |
How should I go up stages in mathematics?
I'm a student of a university in Japan. I'm enrolled in correspondance course. I'm a philosophy of science major.
I need to study mathematics and physics basically.I think I need to study maths and physics or other subjects in English. I can barely understand them in Japanese because Japanese textbooks use too many difficult "kanji" to translate academic words and they don't have so clear description.
When I checked some words with English dictionary for learners, I found that it is very clear and simple description. So, I thought ,perhaps, it is a good way to study these subjects in English.
How do you think about my idea?
Next question is a more concrete.
I found a old book written in English about mathematics in a local library in a university. It deals with pre-algebra. Is it a correct type of mathematics to start to learn mathematics? Or if not, would you recommend some books for beginners? And would you advise me how I should go up stages of matrhematics step by step?
I don't know how pupils and students from other country study mathematics or other subjects. So, I don't know which types of mathematics they begin to learn maths.
Once I've got a good information from this site which recommend some books, but I found that I had enough money to buy it.
At present,my purpose is to achieve A level in Cambridge International Examinations.
I'm looking forward to hearing from you.
It depends on when your mathematics instruction stopped in secondary school in Japan. For example, if you only received instruction in arithmetic, it might be a good idea to start with a refresher in arithmetic (especially if it has been some time since your last class) before going on to study more advanced topics.
It is also a little unclear when you say you need to study 'mathematics'. In English, mathematics includes many topics, from arithmetic to algebra, trigonometry, calculus, etc. Most of the math curricula in the US proceed from arithmetic to algebra to geometry to trigonometry to advanced algebra to calculus at the secondary level. In college, depending on the subject major, some of these topics can be repeated before studying more advanced topics in calculus or other branches of mathematics.
Thank you for replying. Your advice is accurate. To tell the truth, I don't know how mathematics branches are expand. So, I don't know each name of categories in mathematics well. In Japan, it is not taught well, I think. For example, one textbook contains several types of mathematics in Japanese high school. It doesn't systematic. If you could, would you recommend some books for self-learning arithmatic and algebra? I also want to know the meaning of pre-algrebra. In the text book I mentioned before, several kind of mathematics are contained. I hope that I could find best way to learn basic mathematics. I'm looking forward to hearing from you. Thank you. | 677.169 | 1 |
Showing 1 to 2 of 2
Elizabeth Jara
Mrs. Bratt
Int Math 1/Period 3
13 October 2016
The Math Hero
One-day Joey, a student in middle struggled to pay attention to a lesson being taught by
his teacher. His classmates were being loud and disruptive but he was too quiet to speak u
2007 AP" CALCULUS AB FREE-RESPONSE QUESTIONS
CALCULUS AB K E Y
SECTION II, Part A
Time—45 minutes
Number of problems—3
A graphing calculator is required for some problems or parts of problems.
20
1+x
1. Let R be the region in the first and second quadran
AP Calculus Advice
Showing 1 to 3 of 4
Going into college, I feel that it is crucial to have prior knowledge of Calculus, since most likely, every student will have to take a Calculus class in their college career.
Course highlights:
Being able to work in small groups to help each other out on difficult problems really helped to learn the material more thoroughly, considering that the instructor was fast paced. Repetition in certain topics like antiderivatives really helped to memorize the concepts as well.
Hours per week:
6-8 hours
Advice for students:
Do the homework that is assigned in class! It's not necessary to complete the entire assignment problem since no one has all the time in the world, but completing areas that you're having trouble with is crucial.
Course Term:Fall 2016
Professor:Mr. Adams
Course Tags:Math-heavyMany Small AssignmentsParticipation Counts
Jan 15, 2017
| Would highly recommend.
This class was tough.
Course Overview:
He teaches the subject in a great way, and is always there to help when you don't understand the class. This class will apply math to some things you really do see in life, and it allows you to really push yourself.
Course highlights:
I really learned a lot of math and techniques toward how to do it. I also learned my limits on when I can keep pushing and when I need to stop for the night and ask for help, which is one thing I always struggled with. It's okay to ask for help, if you don't get it someone else probably doesn't get it either.
Hours per week:
9-11 hours
Advice for students:
Take the teachers help when they offer it. Really pay attention in class don't think you know the basics that's enough, because it's not, and you'll realize that on the test.
Course Term:Fall 2016
Professor:Mr. Adams
Course Tags:Math-heavyMany Small AssignmentsCompetitive Classmates
May 01, 2016
| Would recommend.
This class was tough.
Course Overview:
I would recommend this class for students interested in the applications of university level mathematics.
Course highlights:
The course covers pre Calculus, Statistics, and Trig in depth. The course offers an application and introduction into the necessities of higher level mathematics.
Hours per week:
9-11 hours
Advice for students:
To prepare for this class, you should take at least Algebra II and Honors Geometry or higher level math courses. Additionally, you should be prepared to study math notes daily. | 677.169 | 1 |
Breadcrumbs
Numeracy
This book offers a fresh and easy approach to learning mathematics. This book is the first text designed for mathematic students at a beginners level. This includes the simple practice of number, multiplication, division... [Product Details...]
This book is intended as a textbook for those with a basic understanding of Vedic mathematics. Topics covered include the four rules of number, fractions and decimals, simplifying and solving in algebra | 677.169 | 1 |
branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus). Two mathematicians, Isaac Newton of England and Gottfried Wilhelm Leibniz of Germany, share credit for having independently developed the calculus in the 17th century. Calculus is now the basic entry point for anyone wishing to study physics, chemistry, biology, economics, finance, or actuarial science. Calculus makes it possible to solve problems as diverse as tracking the position of a space shuttle or predicting the pressure building up behind a dam as the water rises. Computers have become a valuable tool for solving calculus problems that were once considered impossibly difficult. Calculating curves and areas under curves The roots of calculus lie in some of the oldest geometry problems on record. The Egyptian Rhind papyrus (c. 1650 bce) gives rules for finding the area of a... | 677.169 | 1 |
Made Easy Math
About the Course
First 2 days trial class . All topic of Math and Science covered .
Topics Covered
Math
Trigonometry Algebra Computational statistics Determinants Probability distributions Probability Time and Work Problem on Train Number System with short tricks Volume and Surface Area Percentage Profit and loss Boat and Stream Partnership Average Discount Square and Square Root Age Related Problem etc
Science
Physics Chemistry Biology
Who should attend
Upto 6th to 10 Class Student
Pre-requisites
their Books and Copy
What you need to bring
Nothing
Key Takeaways
The ability to solve math in few Seconds
Content
Reviews
There are no Reviews yet.
Questions and Comments
Thousands of experts Tutors, Trainers & other Professionals are available to answer your questions | 677.169 | 1 |
Newcastle Sixth Form College
Mathematics
A Level
-
A Levels
Start Date
5th September 2017
Course Duration
2 years
Type
Full time
Venue
Newcastle Sixth Form College
Course Overview
Maths and Further Maths are exciting and challenging subjects, aiming to develop your understanding of maths and mathematical processes in a way that promotes confidence and fosters enjoyment. You will extend your maths skills and techniques and be able to recognise how a real-life situation may be represented mathematically.
Exam Board Information
Edexcel
Progression and Career Opportunities
Maths graduates have one of the highest rates of graduate employment after university and studying Maths will provide you with valuable skills and a firm base for life-long learning.
A Level Maths and Further Maths are highly regarded within higher education; the Russell Group of leading UK universities considers both A Level Maths and Further Maths as facilitating subjects and previous students have gone on to study a variety of subjects ranging from economics to medicine. | 677.169 | 1 |
TuxMathScrabble
Original Python Branch 2001-2014
TuxMathScrabble
TuxMathScrabble challenges young people to construct compound equations and consider multiple abstract possibilities.
This archive contains the original Python version.
The latest version runs in your browser and lives HERE. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
If trudging through your textbook to study and complete homework assignments has become a frustrating grind, then get ready for a smooth ride to higher test scores and outstanding grades with The Princeton Review's High School Math III Review.
We tell it to you straight, thoroughly explaining the important topics you'll need to understand to prepare for quizzes and tests, complete homework assignments effectively, and earn higher grades. We've carefully examined math textbooks just like yours to make sure that this book includes all the material essential to a thorough review. In this guide, we cover:
And since practicing your test-taking skills is just as important to getting good grades as knowing the material, we include two practice exams that feature the types of questions and problems that appear on in-class tests.
About the Author
David S. Kahn studied Applied Mathematics and Physics at the University of Wisconsin and has taught courses in calculus, precalculus, algebra, trigonometry, and geometry at the college and high-school level. He has taught Princeton Review couses for the SAT I, SAT II, GRE, GMAT, and the LSAT, as well as trained other teachers in the same. | 677.169 | 1 |
Whether you're new to fractions, decimals, and percentages or just brushing up on those topics, CliffsQuickReview Basic Math and Pre-Algebra can help. This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such as
Factors and prime numbers
Integers, exponents, and scientific notation
Measurements, the metric system, and graphs
Variables and algebraic equations
CliffsQuickReview Basic Math and Pre-Algebra acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review — you decide what works best with your needs. Here are just a few ways you can search for topics:
Use the free Pocket Guide full of essential information
Get a glimpse of what you'll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapter
Use the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to know
Test your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource Center
Basic Math and Pre-Algebra (Cliffs Quick Review) by Jerry Bobrow Ph.D. today - and if you are for any reason not happy, you have 30 days to return it. Please contact us at 1-877-205-6402 if you have any questions.
More About Jerry Bobrow Ph.D.
Jerry Bobrow, PhD, is an award-winning teacher and educator. He is a national authority in the field of test preparation. As executive directory of Bobrow Test Preparation Services, Dr. Bobrow has been administering the test preparation programs for most California State Universities for the past 27 years. Dr. Bobrow has authored more than 30 national best-selling test preparation books including Cliffs Preparation Guides for the GRE, GMAT, MSAT, SAT I, CBEST, NTE, ACT, and PPST. Each year he personally lectures to thousands of students on preparing for these important exams.
If you want to teach a second grader some basic math in half a year, this is a right book. We don't need three to five years to teach basic math. So skip the lengthy (and maybe even distracting) textbooks. Use this concise book as a guideline. This is achievable for bright kids. Maybe this is an unconventioal use of the book.
PASSED MY TEST! Feb 19, 2008
I just pasted my math test. Partially because of this book however not only because of this book.
For those who haven't seen Math since 6th grade Dec 27, 2007
This book is awesome. I had to take a standardized test to graduate from University. The book covers all of those little math skills and tricks that you haven't seen since middle school. I passed with flying colors. If you're not a math whiz like me, please buy this. It makes life and tests much easier.
Review of Basic Math Oct 15, 2007
This book is excellent, full of good examples for review and also as a good reference for basic math concepts. It is much better than the similarly entitled book from Master Math.
As so often happens, if not used,... forgotten!! This book refreshed my memory of high school basic math and Pre-Algebra. As I am now in an industry that utilizes math on a day by day, project by project basis, I've found this book to instrumental in my ability to succeed in my | 677.169 | 1 |
ALGEBRA! Perhaps the most feared subject by homeschooling moms in general.
Fear NOT, for behold–Here are algebra homeschool curriculum options with features to help your learning abled kid learn algebra.
These algebra homeschool curriculum are selected for their visual and/or hands-on methods for teaching high school students and are commonly used in homeschooling. Some sites are provided for their "FUN" math enrichment, allowing students to explore, play, and enhance their understanding of algebraic concepts. Other sites are complete algebra courses for high school level homeschooling.
Brief Aside for Fearful Parents
Before we talk about algebra homeschool curriculum for your high school student, I wanted to talk to you briefly about your options. If you are apprehensive about teaching your child high school algebra because you don't remember much from algebra or you doubt your own abilities, you might want to consider a refresher course for yourself. If you plan to teach your child directly, it could save you time to have a review first. For review, Parents Learn Algebra is designed specifically for parents. I have not personally used the Parents Learn Algebra program, so let me know if it is helpful for you or not. 😉 ALSO, the Practical Algebra, Self-Teaching Guide is a very well-liked option. 😉
Resources to Use as or in Addition to Your Algebra Homeschool Curriculum
Many of the algebra homeschool curriculum below include math teaching videos. Your high schooler may be able to learn the algebra more easily through the audio-visual teaching. Sometimes a student gets "stuck," and the explanation being used doesn't make sense, so some of the resources can be really helpful.
When my guys got stuck with their algebra homeschool curriculum and I wasn't sure how to explain the concepts to them we used Purple Math's and Khan Academy's free teaching videos online. It is fairly easy to locate videos that teach whatever math concept your child is having trouble understanding through one of these resources or via YouTube videos. We sometimes used one or the other, and sometimes both!
High School Algebra Homeschool Curriculum Choices:
Hands-on Equations is a great multi-sensory program that helps kids conceptualize and understand equations. Since equations are at the very heart of Algebra, Hands-On Equations is an excellent program to use as you transition from division and fractions into equations. While we have pre-calculus programs, one of the biggest math conception jumps actually occurs with the transition from simple computation into application and reasoning using equations. Therefore, I think of Hands-On Equations as a "pre-Algebra" program that will benefit any child who is struggling to make the transition from elementary-middle school math into high school math.
**Coolmath Algebra – hundreds of really easy to follow lessons and examples that can help your child be successful in learning algebra.
**Math-U-See – A great homeschool curriculum at the elementary levels, but somewhat less rigorous at the upper math levels. The explanatory DVDs and Videos are great. The texts are plain. The printing is all black and white, uncluttered, and very straightforward. This algebra homeschool curriculum may be the best of the lot for those wanting simple presentation where the child does not require visual graphics to understand the content. If you need in depth explanation or visual diagrams, you will likely find the program falls short of your needs.
Catchup Math – If your child is struggling with high school math, this math and algebra homeschool curriculum is a mastery-based program that will review basic concepts with your child as needed, and progress through mastery of high school-level math. "Catchup Math covers Grade 6 Math up through Geometry, Algebra 2 and College Developmental Math, drilling down to elementary school topics as needed." This program is a good overall math program, but is especially good for kids who are struggling with Algebra. Because the program goes back and reviews basic concepts as needed, it can help fill in the learning gaps for your child as he works on Algebra. The main thing to be aware of is that the program includes both Algebra 1 and 2 as well as Geometry, so it isn't "just" an Algebra program. Be sure to check out the free trial before buying to see if the program suits your child.
**A Beka Academy DVD Program – This algebra homeschool curriculum is provided at a college preparatory level and is my favorite of the Algebra I & II video-based programs. It has a lot of neat elements, like having the DVD instructor show the word "parenthesis" when she introduces parenthesis. This helps a 2e child see how the word is spelled, hear what it sounds like, and to see what parenthesis look like at the time of introduction. The book is colorful, with many visual drawings & diagrams to demonstrate concepts, and presented in a clear, concise manner. I did not, however, care for the Pre-Algebra (as of May 2005), as the text was black-and-white with few visual aids. While the program is pricey, I think it will be worth the money for any college-bound student needing to learn Algebra. The only downfall of Abeka's teaching DVDs is using a real classroom setting.. Sometimes the showing of other students can be a distraction to the viewer. This is particularly true when a student in the video works a problem incorrectly. This can be confusing to a child who is watching the DVD even though the errors are corrected by the teacher. Therefore, you'll want to consider how much of a problem this may be for your learning abled kid before selecting this algebra homeschool curriculum.
**Addison-Wesley Algebra – Hornsby, Lial, & McGinnis – An excellent option that won't cost you an arm and a leg, this algebra homeschool curriculum is provided at a college preparatory level. Some of the college level texts have horrible reviews, but the Beginning Algebra and other High School level courses have excellent reviews. The teaching DVD set is available for less than fifty dollars. Even though the textbook itself is pricey, the low price of the DVDs make this an affordable option for those seeking a "traditional" text book with thorough explanations and teaching DVDs. You'll pay about half as much for the text, solutions, and teaching DVDs for Lial's mathematics than you will for Chalkdust or Abeka. In comparison, the DVDs are equal in quality, but the text is slightly less appealing, visually speaking. The print is small and there is a lot of text packed on each page. There are a reasonable number of visual diagrams and other visual elements. Lial Introductory Algebra Video Sample Or see Margaret Lial's Algebra Books Listed
**Saxon Math and D.I.V.E. DVDs – Many children benefit from the detailed step-by-step algebra homeschool curriculum that Saxon offers. This math program builds upon itself with plenty of repetitive practice, cementing the concepts cognitively. The Algebra texts are plain. Little in the way of visual content is provided. While the program provides in-depth explanations and spiral teaching of concepts, the lack of visuals may be an issue for highly visual learners. Buy through ChristianBook.com Saxon Math on Amazon.com
Uncle Dan's Algebra – Dan sent me home-copied DVDs of his algebra homeschool curriculum to view, as well as a link to his downloadable workbook. If you are looking for a low-cost, complete, Algebra solution, "Uncle Dan's Algebra" may suit your needs. The program costs a fraction of the price of many other programs with teaching videos and text. This program uses incremental steps that are well explained by Dan in the videos. His slow speech provides ample processing time for kids who process information slowly, particularly those with auditory processing issues. Instructions are specific on the videos, leaving no doubt about when to stop the tape to work problems. The (Workbook and Solution Key) texts are "print-it-yourself" documents on CD and are straightforward and uncluttered, providing practice problems, quizzes, and tests. Dan will send anyone a FREE copy of the Algebra Workbook file via email attachment. You get video lessons that are as good as any. It's a good package for the money, but nothing fancy at all. "Uncle Dan's Algebra" is definitely "Homespun", not a commercially published program in that there is no fancy packaging or DVD labels, etc. Dan copies the DVD's himself, labels them, and ships them, keeping the price low. It's a one-man operation. Dan will answer your questions about his algebra homeschool curriculum by e-mail, making him one of the more reachable producers of such a package.
Switched On Schoolhouse Math – We switched to the S.O.S. Math programs after difficulty with careless errors in a large number of traditional text-based problems. S.O.S. provides immediate feedback by giving a "correct" or "try again" response to the student in the interactive problems. S.O.S. is a visual software program which provides the instant feedback that is often essential for children with learning disabilities. Additonally, the S.O.S. algebra homeschool curriculum provides visual and auditory reinforcement through teaching text, text-to-speech features, and teaching video clips. The S.O.S. programs are available for all grades up through Pre-Algebra (8th), Algebra I (9th), Algebra II (11th), Geometry(10th), and Pre-Calculus (12th) in High School | 677.169 | 1 |
Download and read online Spectrum Geometry in PDF and EPUB With the help of Spectrum Geometry(R) for grades 6 to 8, children develop problem-solving math skills they can build on. This standards-based workbook focuses on middle school geometry concepts like points, lines, rays, angles, triangles, polygons, circles, perimeter, area, and more. --Middle school is known for its challengesÑlet Spectrum(R) ease some stress. Developed by education experts, the Spectrum Middle School Math series strengthens the important home-to-school connection and prepares children for math success. Filled with easy instructions and rigorous practice, Spectrum Geometry helps children soar in a standards-based classroom!
Download and read online The Social Work Skills Workbook in PDF and EPUB THE SOCIAL WORK SKILLS WORKBOOK, Eighth Edition, enables students to develop proficiency in professionalism and the essential social work skills. Each skill supports one or more of the 43 knowledge and value statements and the 31 practice behaviors that elaborate the core competencies in the 2015 EPAS of the CSWE. The skills also align with nationally standardized licensing exams. The text includes expository content grounded in contemporary research, assessment tools and processes, and strong experiential components that help students get a realistic sense of the field. Case examples, summaries, and skill-building exercises cultivate students' professionalism and expertise as confident, ethical, and effective helpers. Current social issues are evident throughout. The book can be used as a main text in social work skills labs, a resource for field or internship courses, or a supplement to social work methods and practice courses. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Download and read online Geometry Homework Practice Workbook in PDF and EPUB The Homework Practice Workbook contains two worksheets for every lesson in the Student Edition. This workbook helps students: Practice the skills of the lesson, Use their skills to solve word problems.
Download and read online Geometry in PDF and EPUB The theorems and principles of basic geometry are clearly presented in this workbook, along with examples and exercises for practice. All concepts are explained in an easy-to-understand fashion to help students grasp geometry and form a solid foundation for advanced learning in mathematics. Each page introduces a new concept, along with a puzzle or riddle which reveals a fun fact. Thought-provoking exercises encourage students to enjoy working the pages while gaining valuable practice in geometry.
Download and read online Algebra Essentials Practice Workbook with Answers Linear and Quadratic Equations Cross Multiplying and Systems of Equations in PDF and EPUB This Algebra Essentials Practice Workbook with Answers provides ample practice for developing fluency in very fundamental algebra skills - in particular, how to solve standard equations for one or more unknowns. These algebra 1 practice exercises are relevant for students of all levels - from grade 7 thru college algebra. With no pictures, this workbook is geared strictly toward learning the material and developing fluency through practice. This workbook is conveniently divided up into seven chapters so that students can focus on one algebraic method at a time. Skills include solving linear equations with a single unknown (with a separate chapter dedicated toward fractional coefficients), factoring quadratic equations, using the quadratic formula, cross multiplying, and solving systems of linear equations. Not intended to serve as a comprehensive review of algebra, this workbook is instead geared toward the most essential algebra skills. Each section begins with a few pages of instructions for how to solve the equations followed by a few examples. These examples should serve as a useful guide until students are able to solve the problems independently. Answers to exercises are tabulated at the back of the book. This helps students develop confidence and ensures that students practice correct techniques, rather than practice making mistakes. The copyright notice permits parents/teachers who purchase one copy or borrow one copy from a library to make photocopies for their own children/students only. This is very convenient for parents/teachers who have multiple children/students or if a child/student needs additional practice.Download and read online Geometry Study Guide and Intervention Workbook in PDF and EPUB Study Guide and Intervention/Practice Workbook provides vocabulary, key concepts, additional worked out examples and exercises to help students who need additional instruction or who have been absent. | 677.169 | 1 |
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MathematicsMathematics (G100): The rigorous analysis of quantities, magnitudes, forms and their relationships, using symbolic logic and language, both in its own right and as applied to other disciplines. | 677.169 | 1 |
1. Linear transformations
Linear transformations are the bread and butter of Linear Algebra. You have
already encountered them in Geometry I. Roughly speaking a linear transformation
is a mapping between two vector spaces that preserves the linear structu
1
0.1
Determinants
Let A = (aij ) be a 22 matrix. Recall that the determinant of A was dened
by
a
a
det(A) = 11 12 = a11 a22 a21 a12 .
(1)
a21 a22
Notation 0.1.1. For any n n matrix A, let Aij denote the submatrix
formed by deleting the i-th row and the j
MTH5112 Linear Algebra I 2011
Coursework 9
(Late Coursework or Coursework put in the wrong box will NOT be marked.)
Hand in your solution of the starred exercises by 4.30pm, Thursday 8 December 2011.
Put it in the Red Linear Algebra I Collection Box in th
MTH5112 Linear Algebra I 2011
Coursework 8
Hand in your solution of the starred exercises by 4.30pm, Thursday 1 December 2011.
Put it in the Red Linear Algebra I Collection Box in the (Mathematical Sciences) basement.
(Late Coursework or Coursework put in
MTH5112 Linear Algebra I 2011
Coursework 7
Hand in your solution of the starred exercises by 4.30pm, Thursday 24 November 2011.
Put it in the Red Linear Algebra I Collection Box in the (Mathematical Sciences) basement.
(Late Coursework or Coursework put i
MTH5112 Linear Algebra I 2011
Coursework 6
Hand in your solution of the starred exercises by 4.30pm, November 17 November 2011.
Put it in the Red Linear Algebra I Collection Box in the (Mathematical Sciences) basement.
(Late Coursework or Coursework put i
MTH5112 Linear Algebra I 2011
Coursework 4 Solutions
Exercise 1. A is invertible i det A = 0.
Since the determinant of a matrix equals the determinant of its transpose, we have A I is
invertible i det(A I) = 0 i det(A I)T ) = 0 i det(AT I) = 0 i AT I is i
MTH5112 Linear Algebra I 2011
Coursework 5
Hand in your solution of the starred exercises by 4.30pm, Thursday 3 November 2011.
Put it in the Red Linear Algebra I Collection Box in the (Mathematical Sciences) basement.
(Late Coursework or Coursework put in
MTH5112 Linear Algebra I 2011
Coursework 4
Hand in your solution of the starred exercises by 4.30pm, Thursday 27 October 2011.
Put it in the Red Linear Algebra I Collection Box in the (Mathematical Sciences) basement.
(Late Coursework or Coursework put in
MTH5112 Linear Algebra I 2011
Coursework 3
Hand in your solution of the starred exercises by 4.30pm, Thursday 20 October 2011.
Put it in the Red Linear Algebra I Collection Box in the (Mathematical Sciences) basement.
(Late Coursework or Coursework put in
MTH5112 Linear Algebra I 2011
Coursework 2
Hand in your solution of the starred exercises by 4.30pm, Thursday 13 October 2011.
Put it in the Red Linear Algebra I Collection Box in the (Mathematical Sciences) basement.
Write your name and student number on
B. Sc. Examination by course unit 2011
MTH5112
Linear Algebra I
Duration: 2 hours
Date and time: 26 May 2011,
2.30pm
Apart from this page, you are not permitted to read the contents of
this question paper until instructed to do so by an invigilator.
You s
MTH5112 Linear Algebra I 2011
Coursework 1
Hand in your solution of the starred exercise by 4:30pm, Thursday 6 October 2011.
Put it in the Red Linear Algebra I Collection Box in the (Mathematical Sciences) basement.
Write your name and student number on y
MTH5112 Linear Algebra I 20122013
Coursework 11 Solutions
Exercise 1.
(a) First we show that N (A) N (AT A). In order to see this suppose that x N (A), that is,
Ax = 0.Then AT Ax = AT 0 = 0, that is, x N (AT A).
Next we show that N (AT A) N (A). In order | 677.169 | 1 |
Math Dr. Richard Newcomb, Head of Department
School mathematics should engage students in real mathematics. This view is at the center of the teaching and learning of mathematics at Cistercian. Every departmental course at Cistercian seeks to engage our students in both formal and informal modes of mathematical reasoning. The journey from arithmetic to calculus begins with Cistercian's Middle School mathematics curriculum. The focus here is first on developing the students' understanding of rational arithmetic and basic geometry. The second two years of the Middle School are considered together as serving the purpose of introducing algebra into the treatment of both arithmetic and geometry.
Mathematics in the Upper School begins with Euclid's geometry. Students need to learn geometry, not only because it is indispensable for all of applied mathematics, engineering, architecture, physics, and calculus, but even more importantly because it has simply speaking set the standard that any piece of reasoning must meet to be called a branch of mathematics. Forms VI and VII are a continuation of the earlier forms but the weaving of geometry and algebra is now more complete. Cistercian's mathematics curriculum culminates in Form VIII with a yearlong calculus course taught at the college level with a selection of material which also allows willing students to take the Advanced Placement exams in calculus.
At the same time, topics from discrete mathematics such as counting and probability are important and are included in each required course. Moreover, students wishing to delve deeper into these topics can take advantage of various mathematics electives in the Upper School as well as join Cistercian's Math Club or one of our many math teams | 677.169 | 1 |
Mathematics
* Students will be required to take a placement test in addition to teacher recommendation to determine which Algebra class they are eligible to take as a freshman.
APPLIED ALGEBRA, COURSE A
Full Year Course-2 credits
Grade Level: 9-12
Prerequisite: none
This is the first course in the 2-yr. Applied Algebra Series. Completion of Applied Algebra Courses A & B is equivalent to Algebra I. Topics of study include Patterns, Integers, Functions, Equations & Inequalities
APPLIED ALGEBRA, COURSE B
Full Year Course-2 credits
Grade Level: 9-12
Prerequisite: Applied Algebra, Course A
This is the second course in the 2-yr. Applied Algebra series. Completion of Applied Algebra Courses A & B is equivalent to Algebra I. Topics of study include Matrices, Exponents, Transformations, Polynomials & Factoring.
LIFE SKILLS MATH
Full Year Course-2 credits
Grade Level: 10-12, elective
Prerequisite: Algebra I or Applied Math
This course will introduce students to math situations to be used as a skill for life. Topics covered include loans, checking and savings, grocery shopping, travel, income, and entertainment.
ALGEBRA I
Full Year Course-2 credits
Grade Level: 9-12, elective
Prerequisite: none
This class is about practical solutions to problems not always solvable by everyday arithmetic. Students planning on attending college or vocational school after graduation should plan on taking this class. Topics of study include integers, order of operations, relations, and factoring.
GEOMETRY
Full Year Course-2 credits
Grade Level: 9-12, elective
Prerequisite: Algebra I or Applied Algebra A & B
Geometry is the study of points, lines, and planes in two and three dimensional figures. Topics of study include deductive and inductive reasoning, proportion, similarity, congruence, perimeters, area, volume, and proof.
ALGEBRA II
Full Year Course-2 credits
Grade Level: 10-12, elective
Prerequisite: Algebra I or Applied Algebra A & B
Algebra II is a continuation of the skills learned in Algebra I. Topics of study include an in-depth study of linear equations and inequalities, quadratic equations, solving systems of equations, graphing, operations with rational and irrational exponents and the complex number system.
COLLEGE ALGEBRA (ICN course)
Semester Course-1 credit
Grade Level: 11 & 12 elective (TAG)
Prerequisite: consent of administration
This course is designed to strengthen and expand the algebra skills required for further mathematical study. This course may also be used as a terminal course in mathematics for non-mathematics majors. The emphasis will be on using algebraic manipulation, graphing and functional concepts to investigate and solve real-life applications. The properties of real numbers, exponents and radicals will be used to develop problem solving strategies. A background in intermediate algebra is required. Graphing calculators will be used.
TRIGONOMETRY/PRE-CALCULUS
Full Year Course-2 credits
Grade Level: 11-12, elective
Prerequisite: Algebra II and Geometry
Trigonometry is the study of triangles. This is a semester course. Topics include trigonometric and circular functions; their inverses and graphs; relations among the parts of a triangle; trigonometric identities; and solutions of right and oblique triangles.
Pre-Calculus is also a semester course. Topics include a review of the structure of the real number system and the complex: polynomial; logarithmic, exponential and rational functions; inverses and graphs; vector; sequences and series. This course is for the college bound student | 677.169 | 1 |
Trigonometry: How trigonometry works
Who else wants to be able to understand trigonometry? This is an area of mathematics that can be confusing to students yet with a guiding hand it is easy to understand. Students who use this book will find it virtually impossible not to understand.The book utilises the Studymates approach of an overview per chapter and then material is broken down into bitesize chunks in the same way the BBC do it with their series for GCSE students. This is what makes this book special and an important addition to the ever growing and popular Studymates series.
Top customer reviews
The great strength of this book is that it conducts the user in a friendly, clear and accessible way through the whole continuum of trigonometry, from first pre-GCSE principles to full use in A2. So it can be used by those coming with a hazy notion of trig as something to do with rather suspect ladders leaning dodgily against walls of indeterminate height, through to those grappling with the use of identities and harmonic form! Everything necessary for GCSE and A level is covered.
As well as the essential clarity of the book, I particularly liked the suggestions for some simple practical activities (e.g., manipulating the angles and dimensions of your room, or finding sine wave patterns in sunset times). The support for more demanding areas of A level is strong and reasoned. The diagrams at first seemed to me rather simple, but then I realised that "uncluttered" was the word I was looking for – no bad thing.
This is a little book which I think should enable student, parent, or adult learner to take control and gain a clearer understanding of trigonometry.
This book is a clear, step-by-step guide to trigonometry, starting right at the beginning and working up to A2 content. Each principle is introduced with a full explanation allowing the reader to understand where the trig rules and formulae come from, and why they work. Practical examples and practise questions pepper the book throughout, enabling the student to get to the grips with each new piece of content before progressing to complex problems. I would recommend this book for anyone who wants a strong grasp of trigonometry.
The book starts with the basic concepts of trigonometry and gradually works up to more advanced concepts, and thanks to it, my knowledge of trigonometry has increased. There are many worked examples and practical questions, and I've found the questions interesting and achievable. The author's use of English is clear and straightforward, which is important for solving maths problems. I give this book five stars. | 677.169 | 1 |
YOU MAY ALSO FIND THESE DOCUMENTS HELPFUL
...Calculus
I. What is Calculus?
Calculus is the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences.
a. Differential Calculus - concerned with the determination, properties, and application of derivatives and differentials.
b. Integral Calculus - concerned with the determination, properties, and application of integrals.
II. Brief History of Calculus
Calculus was created by Isaac Newton, a British scientist, as well as Gottfried Leibniz, a self-taught German mathematician, in the 17th century. It has been long disputed who should take credit for inventing calculus first, but both independently made discoveries that led to what we know now as calculus. Newton discovered the inverse relationship between the derivative (slope of a curve) and the integral (the area beneath it), which deemed him as the creator of calculus. Thereafter, calculus was actively used to solve the major scientific dilemmas of the time, such as:
a. calculating the slope of the tangent line to a curve at any point along its length
b. determining the velocity and acceleration of an object given a function describing its position, and designing such a position function given the object's velocity or acceleration
c. calculating arc lengths and the volume and surface area of solids
d. calculating the relative and absolute extrema of objects, especially projectiles... | 677.169 | 1 |
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$84 History of Mathematics: An Introduction, Seventh Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools.
Elegantly written in David Burton's imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics' greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Seventh Edition a valuable resource that teachers and students will want as part of a permanent library.
Table of Contents
Preface
Early Number Systems and Symbols
Primitive Counting
A Sense of Number
Notches as Tally Marks
The Peruvian Quipus: Knots as Numbers
Number Recording of the Egyptians and Greeks
The History of Herodotus
Hieroglyphic Representation of Numbers
Egyptian Hieratic Numeration
The Greek Alphabetic Numeral System
Number Recording of the Babylonians
Babylonian Cuneiform Script
Deciphering Cuneiform: Grotefend and Rawlinson
The Babylonian Positional Number System
Writing in Ancient China
Mathematics in Early Civilizations
The Rhind Papyrus
Egyptian Mathematical Papyri
A Key to Deciphering: The Rosetta Stone
Egyptian Arithmetic
Early Egyptian Multiplication
The Unit Fraction Table
Representing Rational Numbers
Four Problems from the Rhind Papyrus
The Method of False Position
A Curious Problem
Egyptian Mathematics as Applied Arithmetic
Egyptian Geometry
Approximating the Area of a Circle
The Volume of a Truncated Pyramid
Speculations About the Great Pyramid
Babylonian Mathematics
A Tablet of Reciprocals
The Babylonian Treatment of Quadratic Equations
Two Characteristic Babylonian Problems
Plimpton
A Tablet Concerning Number Triples
Babylonian Use of the Pythagorean Theorem
The Cairo Mathematical Papyrus
The Beginnings of Greek Mathematics
The Geometric Discoveries of Thales
Greece and the Aegean Area
The Dawn of Demonstrative Geometry: Thales of Miletos
Measurements Using Geometry
Pythagorean Mathematics
Pythagoras and His Followers
Nichomachus' Introductio Arithmeticae
The Theory of Figurative Numbers
Zeno's Paradox
The Pythagorean Problem
Geometric Proofs of the Pythagorean Theorem
Early Solutions of the Pythagorean Equation
The Crisis of Incommensurable Quantities
Theon's Side and Diagonal Numbers
Eudoxus of Cnidos
Three Construction Problems of Antiquity
Hippocrates and the Quadrature of the Circle
The Duplication of the Cube
The Trisection of an Angle
The Quadratrix of Hippias
Rise of the Sophists
Hippias of Elis
The Grove of Academia: Plato's Academy
The Alexandrian School: Euclid
Euclid and the Elements
A Center of Learning: The Museum
Euclid's Life and Writings
Euclidean Geometry
Euclid's Foundation for Geometry
Book I of the Elements
Euclid's Proof of the Pythagorean Theorem
Book II on Geometric Algebra
Construction of the Regular Pentagon
Euclid's Number Theory
Euclidean Divisibility Properties
The Algorithm of Euclid
The Fundamental Theorem of Arithmetic
An Infinity of Primes
Eratosthenes, the Wise Man of Alexandria
The Sieve of Eratosthenes
Measurement of the Earth
The Almagest of Claudius Ptolemy
Ptolemy's Geographical Dictionary
Archimedes
The Ancient World's Genius
Estimating the Value of p
The Sand-Reckoner
Quadrature of a Parabolic Segment
Apollonius of Perga: The Conics
The Twilight of Greek Mathematics: Diophantus
The Decline of Alexandrian Mathematics
The Waning of the Golden Age
The Spread of Christianity
Constantinople, A Refuge for Greek Learning
The Arithmetica
Diophantus's Number Theory
Problems from the Arithmetica
Diophantine Equations in Greece, India, and China
The Cattle Problem of Archimedes
Early Mathematics in India
The Chinese Hundred Fowls Problem
The Later Commentators
The Mathematical Collection of Pappus
Hypatia, the First Woman Mathematician
Roman Mathematics: Boethius and Cassiodorus
Mathematics in the Near and Far East
The Algebra of al-Khowârizmî
Abû Kamil and Thâbit ibn Qurra
Omar Khayyam
The Astronomers al-Tusi and al-Karashi
The Ancient Chinese Nine Chapters
Later Chinese Mathematical Works
The First Awakening: Fibonacci
The Decline and Revival of Learning
The Carolingian Pre-Renaissance
Transmission of Arabic Learning to the West
The Pioneer Translators: Gerard and Adelard
The Liber Abaci and Liber Quadratorum
The Hindu-Arabic Numerals
Fibonacci's Liver Quadratorum
The Works of Jordanus de Nemore
The Fibonacci Sequence
The Liber Abaci's Rabbit Problem
Some Properties of Fibonacci Numbers
Fibonacci and the Pythagorean Problem
Pythagorean Number Triples
Fibonacci's Tournament Problem
The Renaissance of Mathematics: Cardan and Tartaglia
Europe in the Fourteenth and Fifteenth Centuries
The Italian Renaissance
Artificial Writing: The Invention of Printing
Founding of the Great Universities
A Thirst for Classical Learning
The Battle of the Scholars
Restoring the Algebraic Tradition: Robert Recorde
The Italian Algebraists: Pacioli, del Ferro and Tartaglia
Cardan, A Scoundrel Mathematician
Cardan's Ars Magna
Cardan's Solution of the Cubic Equation
Bombelli and Imaginary Roots of the Cubic
Ferrari's Solution of the Quartic Equation
The Resolvant Cubic
The Story of the Quintic Equation: Ruffini, Abel and Galois
The Mechanical World: Descartes and Newton
The Dawn of Modern Mathematics
The Seventeenth Century Spread of Knowledge
Galileo's Telescopic Observations
The Beginning of Modern Notation: Francois Vièta
The Decimal Fractions of Simon Steven
Napier's Invention of Logarithms
The Astronomical Discoveries of Brahe and Kepler
Descartes: The Discours de la Méthod
The Writings of Descartes
Inventing Cartesian Geometry
The Algebraic Aspect of La Géometrie
Descartes' Principia Philosophia
Perspective Geometry: Desargues and Poncelet
Newton: The Principia Mathematica
The Textbooks of Oughtred and Harriot
Wallis' Arithmetica Infinitorum
The Lucasian Professorship: Barrow and Newton
Newton's Golden Years
The Laws of Motion
Later Years: Appointment to the Mint
Gottfried Leibniz: The Calculus Controversy
The Early Work of Leibniz
Leibniz's Creation of the Calculus
Newton's Fluxional Calculus
The Dispute over Priority
Maria Agnesi and Emilie du Châtelet
The Development of Probability Theory: Pascal, Bernoulli, and Laplace
The Origins of Probability Theory
Graunt's Bills of Mortality
Games of Chance: Dice and Cards
The Precocity of the Young Pascal
Pascal and the Cycloid
De Méré's Problem of Points
Pascal's Arithmetic Triangle
The Traité du Triangle Arithmétique
Mathematical Induction
Francesco Maurolico's Use of Induction
The Bernoullis and Laplace
Christiaan Huygens's Pamphlet on Probability
The Bernoulli Brothers: John and James
De Moivre's Doctrine of Chances
The Mathematics of Celestial Phenomena: Laplace
Mary Fairfax Somerville
Laplace's Research on Probability Theory
Daniel Bernoulli, Poisson, and Chebyshev
The Revival of Number Theory: Fermat, Euler, and Gauss
Martin Mersenne and the Search for Perfect Numbers
Scientific Societies
Marin Mersenne's Mathematical Gathering
Numbers, Perfect and Not So Perfect
From Fermat to Euler
Fermat's Arithmetica
The Famous Last Theorem of Fermat
The Eighteenth-Century Enlightenment
Maclaurin's Treatise on Fluxions
Euler's Life and Contributions
The Prince of Mathematicians: Carl Friedrich Gauss
The Period of the French Revolution: Lagrange, Monge, and Carnot
Gauss's Disquisitiones Arithmeticae
The Legacy of Gauss: Congruence Theory
Dirichlet and Jacobi
Nineteenth-Century Contributions: Lobachevsky to Hilbert
Attempts to Prove the Parallel Postulate
The Efforts of Proclus, Playfair, and Wallis
Saccheri Quadrilaterals
The Accomplishments of Legendre
Legendre's Eléments de géometrie
The Founders of Non-Euclidean Geometry
Gauss's Attempt at a New Geometry
The Struggle of John Bolyai
Creation of Non-Euclidean Geometry: Lobachevsky
Models of the New Geometry: Riemann, Beltrami, and Klein
Grace Chisholm Young
The Age of Rigor
D'Alembert and Cauchy on Limits
Fourier's Series
The Father of Modern Analysis, Weierstrass
Sonya Kovalevsky
The Axiomatic Movement: Pasch and Hilbert
Arithmetic Generalized
Babbage and the Analytical Engine
Peacock's Treatise on Algebra
The Representations of Complex Numbers
Hamilton's Discovery of Quaternions
Matrix Algebra: Cayley and Sylvester
Boole's Algebra of Logic
Transition to the Twenthieth Century: Cantor and Kronecker
The Emergence of American Mathematics
Ascendency of the German Universities
American Mathematics Takes Root: 1800-1900
The Twentieth Century Consolidation
Counting the Infinite
The Last Universalist: Poincaré
Cantor's Theory of Infinite Sets
Kronecker's View of Set Theory
Countable and Uncountable Sets
Transcendental Numbers
The Continuum Hypothesis
The Paradoxes of Set Theory
The Early Paradoxes
Zermelo and the Axiom of Choice
The Logistic School: Frege, Peano and Russell
Hilbert's Formalistic Approach
Brouwer's Intuitionism
Extensions and Generalizations: Hardy, Hausdorff, and Noether
Hardy and Ramanujan
The Tripos Examination
The Rejuvenation of English Mathematics
A Unique Collaboration: Hardy and Littlewood
India's Prodigy, Ramanujan
The Beginnings of Point-Set Topology
Frechet's Metric Spaces
The Neighborhood Spaces of Hausdorff
Banach and Normed Linear Spaces
Some Twentieth-Century Developments
Emmy Noether's Theory of Rings
Von Neumann and the Computer
Women in Modern Mathematics
A Few Recent Advances
General Bibliography
Additional Reading
The Greek Alphabet
Solutions to Selected Problems
Index
Table of Contents provided by Publisher. All Rights Reserved.
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Customer Reviews
The History of MathematicsAugust 7, 2011
by Jacki Leach
The minute I got this textbook I fell in love with it and I was reading it every day. The problems at the end of the chapters are so cool. I would recommend this textbook for a course any day in the history and development of mathematics for those who have had some experience with mathematical proofs. Burton did a wonderful job on this book History of Mathematics: An Introduction: 5 out of 5 stars based on 1 user reviews. | 677.169 | 1 |
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Quartic Regions
Students explore the concept of quartic regions. In this quartic regions lesson plan, students find the area under a curve using their Ti-89 calculator. Students find definite integrals of two curves. Students determine the points of inflection of a function. | 677.169 | 1 |
Syllabus: The main topics for the quarter will be ring theory
and field theory. Note that, in coordination with this year's 150B, this
deviates from the usual department syllabus. The ring theory is roughly
weeks 6-10 of the
150B department
syllabus, while the field theory is roughly weeks 5-10 of the
150C department
syllabus.
TA: Nathaniel Gallup
Discussion: R 7:10-8:00, Cruess 107
TA Office Hours: M 3:10-4:00, R 4:10-5:00, MSB 3217
Grading: 30% homework, 25% midterm, 45% final exam
Homework: Assigned weekly, due each Friday in class
Welcome to Math 150C: Algebra
Algebra is a core branch of mathematics. It is important in and of itself,
and also to a wide range of other fields, including number theory,
algebraic geometry, and algebraic topology. In addition, it has
applications ranging from cryptography to crystallography. We will
spend the first half of the quarter on the theory of rings, including
factorization and modules. In the second half of the quarter, we will
discuss fields and field extensions, with applications to topics such
as ruler and compass constructions.
Unique factorization domains:
this is a presentation of the material from Artin's Section 12.3, rephrased
for polynomials over general unique factorization domains (rather than just
over the integers).
Review of definitions for midterm:
A summary of all the definitions you will be expected to know for the
midterm, as well as some of the basic results relating the definitions
to one another.
Splitting fields: this is the
presentation of splitting fields as given in lecture.
Finite fields: this is the
presentation of finite fields as given in lecture.
Galois theory: this is the
presentation of Galois theory as given in lecture. It will be updated
further as more is covered.
Problem sets
Problem sets will be posted here each Friday, due the following Friday
in class. You are encouraged to collaborate with other students, as
long as you make sure you understand your answers and they are in your own
words. You are not, under any circumstances, allowed to get answers to
problems from any outside sources.
A selection of problems will be graded from each problem set, and some
points will be assigned based on the number of problems completed. To
minimize resulting randomness of scores, your lowest problem set score
will be dropped when calculating your grade.
Problem set #0, "due" 4/3: do Exercises 1.6 (a), 2.1, 3.2,
and 4.1 of Chapter 11. Also do Exercises 3.3 and 3.4 if you didn't do them
last quarter.
Note: these are suggested review problems for last
quarter's material, and are not actually to be turned in.
Problem set #1, due 4/10: do Exercises 11.1.3, 11.3.5(b)
(take as the definition of α being a multiple root that f
is a multiple of (x-α)2), 11.3.9, 11.3.11 (prove
or disprove each direction separately), 11.4.2, 11.5.3 and 11.5.5.
Grading: 10 points for 11.3.5(b), 10 points for 11.5.3, 10
points for completeness of remaining problems.
Problem set #7, due 5/22: do Exercises 16.3.1, 16.3.2,
16.3.3, 15.M.4, 15.7.1, 15.7.10 (hint: show that if F has
pr elements, then the Frobenius map sending each element
to its pth power is surjective).
Grading: 10 points for 16.3.2, 10 points for 15.7.10, 10
points for completeness of remaining problems.
Problem set #8, due 5/29: do Exercises 15.7.5, 15.7.7,
15.7.9, 15.M.1, 16.4.1 (the first part of (a) was already done in class),
16.6.2, and 16.7.1.
Grading: 6 points for 15.7.7, 8 points for 16.4.1, 8
points for 16.7.1, and 8 points for completeness of remaining problems.
Problem set #9, due 6/5 (you may turn in the assignment in
the reader box marked for the class on the first floor of MSB): do
Exercises 16.5.1 (you should assume these automorphisms keep C
fixed, otherwise they are not uniquely determined by Artin's description),
16.5.3, 16.6.3, 16.7.2, 16.7.6 and 16.7.8.
Grading: 10 points for 16.5.1, 10 points for 16.7.6,
and 10 points for completeness of remaining problems.
Exams
There will be one in-class midterm exam, on Wednesday, May 6. It
will cover all material up through and including the lecture on May 1,
corresponding to the first five problem sets.
The final exam is scheduled for Monday, June 8 6:00-8:00 PM.
Anonymous Feedback
If you have any feedback on the course, regarding lecture, discussion
section, homework, or any other topic, you can provide it anonymously
with the below form. | 677.169 | 1 |
Expanded explanations of both linear and nonlinear systems as well as new problem sets at the end of each chapter
Illustrative examples in all the chapters
An introduction and analysis of new stability concepts
An expanded chapter on neural networks, analyzing advances that have occurred in that field since the first edition
Although more mainstream than its predecessor, this revision maintains the rigorous mathematical approach of the first edition, providing fast, efficient development of the material.
Linear Systems Theory enables its reader to develop his or her capabilities for modeling dynamic phenomena, examining their properties, and applying them to real-life situations.
Synopsis
"Linear Systems Theory", second edition is a comprehensive text that presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms, and more. Intended to be more mainstream than its predecessor, this revision does maintains the rigorous mathematical approach of the first edition. Many of the longer case studies will be replaced with numerical examples drawn mainly from electrical and mechanical engineering applications. Expanded explanations of both linear and nonlinear systems and new problem sets at the end of each chapter are included in the Second Edition. The chapter on neural networks has been expanded to include the many advances that have occurred in that system since the publication of the previous edition. -- Presents new examples and problems featuring EE/ME applications -- Is self-contained for reference use -- Suitable for cross-disciplined courses in systems theory -- Focuses on computer-oriented techniques | 677.169 | 1 |
***Includes Practice Test Questions***Get
A detailed overview of the ILTS Mathematics (115) Exam
A guide to processes and applications
An in-depth look at number sense and measurements
A full study of algebraic patters, symbols, functions, and models
An analysis of geometric methods
A breakdown of probability and statistics
Comprehensive practice questions with detailed answer explanations
It's filled with the critical information you'll need in order to do well on the test: the concepts, procedures, principles, and vocabulary that the Illinois State Board of Education (ISBE) expects you to have mastered before sitting for the exam. The Processes and Applications section covers:
These sections are full of specific and detailed information that will be key to passing the ILTS Mathematics ILTS Mathematics Exam. Each answer is explained in depth, in order to make the principles and reasoning behind it crystal clear. | 677.169 | 1 |
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Product Description
These are guided notes for a lesson on determining if a relation is a function or not. Skills covered are: identifying a relation as a function from ordered pairs, tables, and graphs. Introduces the concept of writing and solving function notation.
The notes include key vocabulary, examples, and illustrations.
I have included a teacher key to show you what to fill in the blanks as your students follow along. I have also included specific things I said to make sure the students understood.
To use these notes, I simply projected them onto my whiteboard, gave the students their blank copies, and had them follow along and write what I wrote. This works great when you do not have loads of time, or students do not have the attention span, to take lengthy notes and it helps to still leave time for working independently!
I provide the Word version of these notes so that you may edit them to your liking but you could also save as a PDF and use an interactive board to annotate (I can send you a PDF if needed).
I have several others I am working on getting teacher keys for. Let me know if you're searching for a particular topic/lesson! | 677.169 | 1 |
Autograph is an excellent tool for investigation, and mathematics is at its strongest and most appealing when students can embark upon such journeys of self-discovery.
The ten activities are designed to allow students to fully utilise Autograph's power to explore, investigate and ultimately understand concepts at a depth which the normal classroom setting would not allow.
Autograph Activities: Teacher Demonstrations for 16-19
The fifteen teacher demonstrations will allow you dynamically to introduce, review, extend or illustrate important topics or concepts in ways not previously possible. They are intended for use on an interactive whiteboard or by means of a digital projector.
The demonstrations are presented in an easy to follow, step-by-step manner, complete with full colour screenshots, suggested questions and prompts, thus allowing even a first time user to feel confident enough to deliver them.
Topics covered include: Introducing Volumes of Revolution; Discovering the Chain Rule; and Things to Watch Out For when Integrating.
This book will unlock the wonders of Autograph, and one thing is for sure: you will never teach these topics in the same way again.
£25, by C N Barton
Bundle of 5 Sets of both volumes of Autograph Activities. 5 x Teacher Demonstrations Books and 5 x Student Investigations books. All full colour throughout and including CD-ROMs of activities and investigations. | 677.169 | 1 |
ISBN-13: 9780321643728
Edition: 13aeussler, Paul, and Wood establish a strong algebraic foundation that sets this text apart from other applied mathematics texts, paving the way for readers to solve real-world problems that use calculus. Emphasis on developing algebraic skills is extended to the exercisesincluding both drill problems and applications. The authors work through examples and explanations with a blend of rigor and accessibility. In addition, they have refined the flow, transitions, organization, and portioning of the content over many editions to optimize learning for readers. The table of contents covers a wide range of topics efficiently, enabling readers to gain a diverse understanding. ALGEBRA; Review of Algebra; Applications and More Algebra; Functions and Graphs; Lines, Parabolas, and Systems; Exponential and Logarithmic Functions; FINITE MATHEMATICS; Mathematics of Finance; Matrix Algebra; Linear Programming; Introduction to Probability and Statistics; Additional Topics in Probability; CALCULUS; Limits and Continuity; Differentiation; Additional Differentiation Topics; Curve Sketching; Integration; Methods and Applications of Integration; Continuous Random Variables; Multivariable Calculus For all readers interested in introductory mathematical | 677.169 | 1 |
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Description
This dynamic and accessible approach fully covers the Cambridge IGCSE Mathematics syllabus at Extended Level, and supports the strongest achievement in exams. Providing a sequential and logical teaching path through the full syllabus, it thoroughly addresses all four curriculum areas with clear pictures and diagrams - supporting EAL learners. Using an active approach to learning, it includes plenty of worked examples and graduated exercises, with answers, to steadily build learners' confidence. A CD loaded with conceptual support for every part of the book further cements understanding. A Teacher Resource Kit is also available, providing ideas, lesson plans and support.
Author Biography
Sue Pemberton Sue has taught mathematics for over thirty years and has worked as an examiner since 2003. She is also involved in professional development and has conducted training workshops in various countries across the world. She is particularly interested in raising standards in mathematics by promoting more active learning in the classroom. | 677.169 | 1 |
I. Assessment of Student Learning Outcomes
2. Goal Statements and Student Learning Outcomes
[General Content] Graduates are proficient in performing basic operations on fundamental mathematical objects and have a working knowledge of the mathematical ideas and theories behind these operations.
(S15). As far as possible, we used assessment items similar to those in Year 3 of our assessment plan. Math 260 courses were taught by two instructors who contributed to developing the instruments and agreed to make them common to their respective exams. All instructors also contributed to constructing rubrics that we applied to determine performance at the Exemplary, Proficient, Acceptable, and Unacceptable levels.
In appendix A we collect assessment items, rubrics, raw scores and sorted data for all class assessments. Student work is available upon request. When possible, we used the rubrics of Year 3 as a guide, updating as needed. Rubrics for new items follow the same general style with descriptions of performance at the Exemplary, Proficient, Acceptable, and Unacceptable levels.
6. Assessment Results
Student Learning Outcome
Where sample is from
(sample size)
Measure
%
Exemplary
+
Proficient by item
GC2-I
MATH 350 (5)
Embedded Test 1 Problem 1
88
GC2-I
MATH 350 (5)
Embedded Test 1 Problem 2
59
GC2-I
MATH 350 (37)
Embedded Test 2 Problem 1
55
GC2-I
MATH 350 (39)
Embedded Test 3 Problem 1
74
GC2-P
MATH 350 (5)
Embedded Test 1 Problem 3
64
GC2-P
MATH 350 (37)
Embedded Test 2 Problem 2
18
GC2-P
MATH 350 (39)
Embedded Test 3 Problem 2
34
GC2-M
MATH 350 (5)
Embedded Test 1 Problem 4
12
GC2-M
MATH 350 (37)
Embedded Test 2 Problem 3
55
GC2-M
MATH 350 (39)
Embedded Test 3 Problem 3
18
PS-M
MATH 260 (8)
Embedded Test 1 Problem 1
88
PS-M
MATH 260 (8)
Embedded Test 2 Problem 1
88
PS-M
MATH 260 (8)
Embedded Test 2 Problem 2
88
Tech-P
MATH 230 (13)
Embedded Test 1 Problem 2
42
Tech-P
MATH 230 (12)
Embedded Final Exam Problem 2
80
Tech-P
MATH 230 (13)
Embedded Test 1 Problem 3
36
Tech-M
MATH 230 (13)
Embedded Test 1 Problem 4
16
Tech-M
MATH 230 (12)
Embedded Final Exam Problem 3
18
PS-M
MATH 351 (13)
Embedded Test 1 Problem 3
36
PS-M
MATH 351 (14)
Embedded Test 2 Problem 4
0
PS-M
MATH 351 (14 )
Embedded Test 3 Problem 4
50
GC2-I
MATH 305 (23)
Embedded Test 1 Problem 13
50
GC2-P
MATH 305 (21)
Embedded Final Exam Problem 1
43
GC2-M
MATH 305 (22)
Embedded Test 1 Problem 4
43
Analysis / Interpretation of Results
Fall, 2014 Assessment
Math 350: Math 350 is the first course in a three semester sequence required for statistics majors. It is required for statistics majors and many math majors take it as an elective. Engineer students also often take this class to fulfil a math requirement for their major.
Test 1 Problem 1: This problem involves solving a probability problem using Bayes' Theorem. The following steps were evaluated:
whether they used the correct formula
whether they calculated the correct conditional distribution
whether they had the correct final answer
Most students were able to solve this problem. 88% of the students got full points for this problem while only 12% missed this question.
Test 1 Problem 2: This question involved finding conditional probability for disjoint events. For this problem students generally got full credit or no credit, therefore, they were scored simply on whether or not they got it correct.
59% of the students got this correct and 41% did not get this correct.
Test 1 Problem 3: This question involved finding the union of 2 events when the events are independent. The students were scored on the following criteria:
whether or not they recognized that the events were independent
whether or not they used the correct formula
whether or not they calculated the intersection correctly
64% of the students got this answer completely correct while the remainder had at least one mistake. About 14% lost all points on this question.
Test 1 Problem 4: This problem was a counting probability problem. They were graded on the following criteria:
whether or not they used permutations or combinations
whether they got the denominator correct or incorrect
whether they got the numerator correct
whether they used the correct formula
These sorts of problems are generally harder for students. Only 12% got this problem completely correct while 29% got either the denominator or numerator incorrect. 7% of students did not receive get anything correct.
Test 2 Problem 1: This problem involved using the properties of a probability distribution in order to solve for an unknown. The criteria used to grade this problem were:
whether or not they recognized if it was a discrete variable
whether they set up the equation correctly
whether they solved for the unknown correctly
55% of the students had no mistakes on this question while about 41% had at least one major mistake.
Test 2 Problem 2: This problem was a counting problem using binomial distribution. They were graded on the following criteria:
whether they recognized that it is a binomial problem
whether or not they used the correct combinatoric formula
whether or not they multiplied by 2 since there were 2 scenarios
Only 18% of students received full credit for this problem. 21% had only a small error while 61% of students had at least one major error.
Test 2 Problem 3: This problem involved finding a probability given a joint distribution. The criteria that was used to grade this problem was as follows:
setting up the integration correctly
integrating correctly
whether the bounds of the integration were correct
55% got this answer completely correct, 18% were acceptable and 26% had at least 2 major errors.
Test 3 Problem 1-This problem involved calculating a probability given a moment generating function. The criteria used to grade this problem are as follows:
whether or not they recognized it as a Poisson
whether they got the parameter correct for a Poisson
whether they computed the probability correctly
74% got this answer correct and 21% made at least one major error.
Test 3 Problem 2-This question involved calculating a probability using the normal distribution. There were 3 parts to this question. Criteria for grading this question were as follows:
Did they use the correct formula
Did they know to use the results of the Central Limit Theorem
Did they use the binomial formula correctly in the third part
Did they use the normal distribution table correctly
Only 34% of students got this question completely correct. 47% did used the wrong distribution or formula and 13% had 3 or more major errors.
Test 3 Problem 3: This problem involved determining the moment generating function from a uniform distribution. The criteria for grading this problem were as follows:
Whether or not they set up the integration correctly
Whether the bounds of the integration were correct
Whether they integrated correctly
Only 18% got full credit for this question and 56% had so little correct that they received no credit. 25% received partial credit for this question.
Raw data for our analysis is available in Appendix A (M350). Copies of students' work are available upon request.
MATH 260: The Math 260 course is required for Applied Mathematics, General Mathematics, and Statistics, majors, and also taken by some Mathematics Education majors. It is also a required course for most Engineering majors. Two instructors who taught three sections of the course in Fall 2014 together prepared problems common to their two tests for assessment.
Problem 1. This is a problem dealing with calculations within the population model. Students were expected to demonstrate their ability to solve a differential equation, and interpret the meaning of its solution. The following steps were evaluated:
- Setting up correct differential equation for population growth
- Correct solution of this equation
- Correct use of data for finding a rate of growth
- Correct expression for determining a population at any time t
- Correct evaluation of time, and the world population in 2020
Most students were able to handle well this problem: 50% of the majors scored at the Exemplary and 37.5% at the Proficient level.
Raw data for our analysis is available in Appendix M260. Copies of students' work are available in Appendix M260_tests.
Problem 2. This is a problem for finding the general solution of a linear second-order non-homogeneous differential equation. Students were expected to demonstrate their ability to find a general solution of a linear homogeneous differential equation with constant coefficients, and construct a special solution to a given non-homogeneous equation.
Most students were able to solve this differential equation correctly: 75% of the majors scored at the Exemplary and 12.5% at the Proficient level.
Problem 3. Students were offered to find the form of the general solution of a linear second-order non-homogeneous differential equation. Students were expected to obtain the correct form of the solution using the method of undetermined coefficients without having to evaluate these coefficients. One of the complications of the problem was the interference between the homogeneous solutions and the right hand side of the equation.
Most students were able to solve this differential problem correctly: 37.5 % of the majors scored at the Exemplary and 50.0 % at the Proficient level.
Raw data for our analysis is available in Appendix A (M260). Copies of students' work are available upon request.
MATH 230. This course is an introduction to computational Mathematics. It is a required course for Math Education majors and recommended for Applied Mathematics majors, as a prerequisite for the required course Math 461: Numerical Analysis. The course provides basic knowledge of the computer algebraic software Mathematica, and prepares students to use computer to solve mathematical problems.
PROGRESSING LEVEL
Problem 1 (Question 2: Midterm Exam Fall 2014)
Application of the theory of numbers. Create a list of 100 random two-digit positive integers that are not prime numbers. b. Among them give the list of all distinct integers that are squares.
Results: Most students were able to solve this problem correctly: 42% of the majors scored at the Exemplary and 33% at Acceptable level.
Problem 2 (Question 2 -Final Exam Fall 2014)
Application of Calculus II – Area between two curves. Students needed to compute the area between two given curves up two 4 digits after the decimal point.
Results: Most students were able to solve this problem correctly: 80% of the majors scored at the Exemplary and 20% at Acceptable level.
Problem 3 (Question 3 – MidTerm Exam)
Application of Calculus I and II: Zeros of a function and area under a curve. Approximate the area under a given curve up to 2 digits after the decimal point:
Results: Most students were able to solve this problem correctly: 36% of the majors scored at the Exemplary and 45% at Acceptable level.
MASTERY LEVEL
Plot 10 random points inside a given square, and find the two points that are the furthest away from each other. Draw the line segment connecting those two points.
Results: More than half of students were able to solve this problem correctly: 16% of the majors scored at the Exemplary and 42% at Acceptable level.
Problem 2 (Question 3 - Final Exam)
Writing a program that calculates all the solutions (real and complex) of the quadratic equation. Consider all different cases, and give examples for illustration
Results: More than half of students were able to solve this problem correctly: 18% of the majors scored at the Exemplary and 36% at Acceptable level.
Problem 3 (Question 4. Final Exam)
Writing a program that reproduce given picture. This question required a knowledge on the geometry of circles and trigonometry in addition to programming. (Write a program that draws on a light background five concentric circles of different color, and add colored layers of small disks of equal radius next to each other).
Results: Only 27% of students were able to solve this problem correctly: 18% of the majors scored at the Exemplary and 9% at Acceptable level.
Raw data for our analysis is available in Appendix A (M230). Copies of students' work are available upon request.
Spring, 2015 Assessment
MATH 305: Math 305 is requires for all students taking the mathematics major with the Mathematics Education option, and some Statistics option students also take the course. Two students enrolled in the course in Spring 2015 were senior Computer Science majors, and their department chair had allowed this course instead of Math 350 to meet graduation requirements without schedule conflict.
Midterm 1 problem:
This is a problem dealing with the relationship between standard deviation and percentile. Students were evaluated on both their ability to determine a percentile knowing a score (part a) and to determine the score knowing the percentile (part b). Students were evaluated on correct use of the equation correct interpretation of z-scores. 50% of students solved this problem at an Exemplary level and 27% solved it at an Acceptable level.
Midterm 1 Results:
Midterm 2 problem:
Overview: This problem focuses on binomial distribution, specifically programming to find it, interpreting the outcome, and analyzing its use in context. 77% of students were able to solve this problem: 41% at the Exemplary level and 36% at the Acceptable level.
Midterm 2 Results:
Example problem from Final Exam:
Overview: This problem deals with comparing data sets from two different groups using beginner and advanced methods while incorporating checks on single-variable analysis tools. Students are checked on: naming null and alternative hypothesis, comparing box plots, finding outliers, two-sample t-tests, and understanding and interpreting p-values and alphas and their significance. 42.5% of students could successfully complete this problem at the Exemplary level (43%) or Acceptable level (9.5%), with another 24% able to compute solutions but not interpret them.
Final Exam Results
Raw data for our analysis is available in Appendix A (M305). Copies of students' work are available upon request.
MATH 351. Math 351 is the second semester of a 3 semester series that is required for statistics majors and minors. In addition, a few math majors take this class as an elective. It is a calculus based statistics course.
Test 1 Problem 3: This problem had students determine which estimator is most efficient by finding the variances of 2 estimators. The criteria used to grade this problem is as follows:
Whether they correctly found the variances of each estimator
Whether they were able to justify correctly which estimator was more efficient
Whether they were able to identify the correct distribution of the pdf
36% of the students in this class received a near perfect score on this problem. Almost half of the students had a number of major mistakes.
Test 2 Problem 4: This problem involved finding a probability after identifying the correct distribution. The following criteria were used to grade this problem:
Whether they correctly identified the chi-‐square distribution
Whether they correctly manipulated the equation to use the chi-‐square distribution
Whether they correctly solved the probability using the chi-‐square distribution
Although any students were on the right track for this problem, no student got it completely correct. 23.1% of the students correctly recognized the distribution but failed to find the probability correctly. About 54% of students used a different distribution to solve the problem.
Test 3 Problem 4: This problem dealt with using Bayesian methods to derive a posterior distribution when the data follow an exponential distribution and the parameter is a gamma distribution. The criteria that was used to grade this problem is as follows:
Identify that Bayesian statistics was necessary to derive the posterior distribution
Set up the conditional distribution correctly
Integrate the denominator correctly
Correctly identify the posterior distribution
About 50% of the students were able to complete this difficult problem without any major errors and 36% of students had at least one major error.
Raw data for our analysis is available in Appendix A (M351). Copies of students' work are available upon request.
8. Planned Program Improvement Actions Resulting from Outcomes:
No program improvements are planned for Math 230, 260, 305, 350, or 351 as a result of the SLO assessment.
9. Planned Revision of Measures or Metrics:
For the most part, there are no planned revisions for the measures or metrics for any of our course assessments. | 677.169 | 1 |
Paperback | April 25, 2013
Pricing and Purchase Info
about
Every year, thousands of students declare mathematics as their major. Many are extremely intelligent and hardworking. However, even the best will encounter challenges, because upper-level mathematics involves not only independent study and learning from lectures, but also a fundamental shiftfrom calculation to proof. This shift is demanding but it need not be mysterious - research has revealed many insights into the mathematical thinking required, and this book translates these into practical advice for a student audience. It covers every aspect of studying as a mathematics major, from tackling abstractintellectual challenges to interacting with professors and making good use of study time. Part 1 discusses the nature of upper-level mathematics, and explains how students can adapt and extend their existing skills in order to develop good understanding. Part 2 covers study skills as these relate tomathematics, and suggests practical approaches to learning effectively while enjoying undergraduate life.As the first mathematics-specific study guide, this friendly, practical text is essential reading for any mathematics major.
About The Author
Lara Alcock is Senior Lecturer in the Mathematics Education Centre at Loughborough University, UK. An accomplished undergraduate and graduate mathematician at Warwick, her doctorate was in mathematics education before holding various academic posts including Assistant Professor of Mathematics
Education and Mathematics at Rutgers Univer...
"Making the transition from school-level to university-level mathematics is hard, in terms of the complexity of the subject matter, the rigour of thought, and the need to be able to study much more independently. This excellent and wide-ranging book engages with all these issues and more,giving a very helpful insight into what is coming for beginning undergraduates in mathematics or mathematics-related disciplines. I just wish this book had been available in my day!" --Geoff Tennant, Institute of Education, University of Reading, UK | 677.169 | 1 |
Fourier Series Of Periodic Functions. A tutorial on how to find the Fourier coefficients of a function and an interactive tutorial using an applet to explore, graphically, the same function and its Fourier series.
Quadratic Functions (general form). Quadratic functions and the properties of their graphs such as vertex and x and y intercepts are explored interactively using an applet.
Quadratic Functions(standard form). Quadratic functions in standard form f(x) = a(x - h) 2 + k and the properties of their graphs such as vertex and x and y intercepts are explored, interactively, using an applet.
Definition of the Absolute Value. The definition and properties of the absolute value function are explored interactively using an applet. The properties of basic equations and inequalities with absolute value are included.
Absolute Value Functions. Absolute value functions are explored, using an applet, by comparing the graphs of f(x) and h(x) = |f(x)|.
Exponential Functions. Exponential functions are explored, interactively, using an applet. The properties such as domain, range, horizontal asymptotes, x and y intercepts are also investigated. The conditions under which an exponential function increases or decreases are also investigated.
Find Exponential Function Given its Graph.It is a tutorial that complements the above tutorial on exponential functions. A graph is generated and you are supposed to find a possible formula for the exponential function corresponding to the given graph.
Logarithmic Functions. An interactive large screen applet is used to explore logarithmic functions and the properties of their graphs such domain, range, x and y intercepts and vertical asymptote.
Logistics Function. The logistics function is explored by changing its parameters and observing its graph.
Compare Exponential and Power Functions. Exponential and power functions are compared interactively, using an applet. The properties such as domain, range, x and y intercepts, intervals of increase and decrease of the graphs of the two types of functions are compared in this activity.
Rational Functions. Rational functions and the properties of their graphs such as domain, vertical and horizontal asymptotes, x and y intercepts are explored using an applet. The investigation of these functions is carried out by changing parameters included in the formula of the function.
Graphs of Hyperbolic Functions. The graphs and properties such as domain, range and asymptotes of the 6 hyperbolic functions: sinh(x), cosh(x), tanh(x), coth(x), sech(x) and csch(x) are explored using an applet.
One-To-One functions. Explore the concept of one-to-one function using an applet. Several functions are explored graphically using the horizontal line test.
Inverse Function Definition. The inverse function definition is explored using java applets. The conditions under which a function has an inverse are also explored.
Inverse Functions. A large window applet helps you explore the inverse of one to one functions graphically. The exploration is carried out by changing parameters included in the functions.
Explore graphs of functions. This is an educational software that helps you explore concepts and mathematical objects by changing constants included in the expression of a function. The idea is to introduce constants ( up to 10) a, b, c, d, f, g, h, i, j and k into expressions of functions and change them manually to see the effects graphically then explore.
Graph Transformations
Horizontal Shifting. An applet helps you explore the horizontal shift of the graph of a function.
Vertical Shifting. An applet that allows you to explore interactively the vertical shifting or translation of the graph of a function.
Horizontal Stretching and Compression. This applet helps you explore the changes that occur to the graph of a function when its independent variable x is multiplied by a positive constant a (horizontal stretching or compression).
Vertical Stretching and Compression. This applet helps you explore, interactively, and understand the stretching and compression of the graph of a function when this function is multiplied by a constant a.
Reflection of Graphs In x-axis. This is an applet to explore the reflection of graphs in the x-axis by comparing the graphs of f(x) (in blue) and h(x) = -f(x) (in red).
Reflection of Graphs In y-axis. This is an applet to explore the reflection of graphs in the y-axis by comparing the graphs of f(x)(in blue) and h(x) = f(-x) (in red).
Reflection Of Graphs Of Functions. This is an applet to explore the reflection of graphs in the y axis and x axes. Graphs of f(x), f(-x), -f(-x) and -f(x) are compared and discussed.
Equations of Lines and Slope
Slope of a Line. The slope of a straight line, parallel and perpendicular lines are all explored interactively using an applet.
Slope Intercept Form Of The Equation Of a Line. The slope intercept form of the equation of a line is explored interactively using an applet. The investigation is carried out by changing parameters m and b in the equation of a line given by y = mx + b.
Find Equation of a Line - applet. An applet that generates two lines. One in blue that you can control by changing parameters m (slope) and b (y-intercept). The second line is the red one and it is generated randomly. As an exercise, you need to find an equation to the red line of the slope intercept form y = mx + b.
Equation of a Circle. An applet to explore the equation of a circle and the properties of the circle. The equation used is the standard equation that has the form (x - h) 2 + (y - k) 2 = r 2.
Find Equation of Circle - applet. This is an applet that generates two graphs of circles. The equations of these cirles are of the form (x - h) 2 + (y - k) 2 = r 2. You can control the parameters of the blue circle by changing parameters h, k and r. The second circle is the red one and it is generated randomly. As an exercise, you need to find an equation to the red circle.
Equation of the Ellipse
Equation of an Ellipse. This is an applet to explore the properties of the ellipse given by the following equation (x - h) 2 / a 2 + (y - k) 2 / b 2 = 1.
Equation of the Hyperbola
Equation of Hyperbola. The equation and properties of a hyperbola are explored interactively using an applet. The equation used has the form x 2/a 2 - y 2/b 2 = 1 where a and b are positive real numbers.
Tangent Function. The tangent function f(x) = a*tan(bx+c)+d
and its properties such as graph, period, phase shift and asymptotes by changing the parameters a, b, c and d are explored interactively using an applet.
Secant Function. The secant function f(x) = a*sec(bx+c)+d and its properties such as period, phase shift, asymptotes domain and range are explored using an interactive applet by changing the parameters a, b, c and d.
Graphs of Basic Trigonometric Functions. The graphs and properties such as domain, range, vertical asymptotes of the 6 basic trigonometric functions: sin(x), cos(x), tan(x), cot(x), sec(x) and csc(x) are explored using an applet.
Trigonometric Equations and the Unit Circle. The solutions of the trigonometric equation sin(x) = a, where a is a real number are explopred using an applet. Both the graph of sin(x)and the unit circle are used to explore the solutions of this equation as a changes. | 677.169 | 1 |
CONTINUITY OF A FUNCTION
About the Course
Students will get idea about the continuous function first by definition and graph and then we will search the continuity at a point or an interval. The complete concept will be there.
Topics Covered
Basics of the function. Definition of continuity of a function at a point and in an interval How to find and elaborate the continuity of different functions like trigonometric, polynomial and etc. Different condition to get the idea of continuity of a function in an interval and at a point.
Who should attend
All interested students because this is the base chapter for the major topic CALCULUS in class XII
Pre-requisites
Student should aware about the definition of the function , domain and range of the funcion.
What you need to bring
Only their notebooks.
Key Takeaways
Students will be confident to diagnose about the continuity of any type of the function and it will assist them to solve the problems of APPLICATION OF DERIVATIVES.
Date and Time
About the Trainer
working with secondary and senior secondary students since last 13 yrs and since 12 yrs getting 100% pass percentage with both secondary and senior secondary with quality more than 75%. Also doing with the candidates preparing for Reasoning Mathematics, for SSC and different competitive examinations. | 677.169 | 1 |
Math literacy tanks even further
One of the professors here put together a quiz to give his Calc-I students on the first day of class. The intent was to find out not how well prepared the students were in terms of pre-calc material (the answer to that has been more than adequately established, to everyone's chagrin), but how well prepared they are on basic (mostly middle-school) algebra. The motivation for doing so is the increased pressure to improve the "success rate" of Calc-I, defined by the fraction of enrolling students that get a grade of C or higher, to at least 85%. A "successful teacher" is one who meets this criteria. Note that absolutely no effort is made to how well "successful students" of "successful teachers" fare in Calc-II or other courses compared to other students.
Here's the quiz.
1) Factor x^2 - x - 2 completely.
2) Same directions: x^4 - 16.
3) Multiply out: (x+4)^2.
4) Same directions: (X-1)(x+5).
5) Solve by any method: x^2 - 2x = -1.
6) Solve by any method: x(x-2)(x-3) = 0.
7) Simplify if possible. If not possible, write "not possible":
x+1
------
x+2
8) Simplify if possible. If not possible, write "not possible":
sqrt ( x^2 + y^2 )
9) What is cos(pi)?
10) What is sin(3pi/2)?
Note that on the quiz exponents were shown as exponents (not using the ^ operator), that sqrt() and pi used the standard symbols, and the fraction in #7 was printed as a fraction instead of the three line wannabe fraction used here.
The average score on this quiz was 50%.
Already this semester I have dealt with a junior comp sci major that literally did not know what an average was. He had to Google it (and still didn't grasp it). This was after having to Google what a millisecond was and having no idea what a gigahertz or megahertz was.
I worked with another junior that had to bring up the Windows calculator to find 12345 divided by 1000. Then had to use the Windows calculator again to find 12345 divided by 10000. Then again to find 12345 divided by 10. Then, you guessed it, again to divide by 100.
Well to be honest I cant do any of those equations being there is no defined value for X I can see but I can do the 12345 and related stuff in my head faster than most people can with a calculator.
Applied math that uses real numbers and real equations relating to real life problems is easy for me but anything that anyone claims to be math that uses the alphabet without defined values for the letters forget it I have zero time or interest in it. Never have never willNote that absolutely no effort is made to how well "successful students" of "successful teachers" fare in Calc-II or other courses compared to other students.
Click to expand...
Things you don't measure tend to get worse, and conversely I've seen things get better in industrial environments with no more action than merely starting to measure it. It's hard to convince the line workers that some parameter is important, if you don't even measure it.
I was extremely impressed with the U. of Chicago business school's approach to this. Every student fills out a survey on every class, covering things like hours per week spent on homework, quality of the teacher, usefulness of the material and so on. Maybe 30 metrics or so. And boy oh boy, I can tell you that a 5-star teacher is indeed superior to a 2-star teacher. A 2-star teacher at the U of C would be a star in many other locations but the 5-star ones are truly stellar.
My point is, the rating system gives a lot of timely feedback on how things are going with every subject and teacher. It's hard to make continuous improvements without that sort of attentionClick to expand...
Yep, algebra is foundational for calculus. My high school calc teacher was fond of saying that you can teach the principles of calculus to a third grader and many of them will understand the concepts just fine, but the algebra would kill them. I always figured he was exaggerating for effect, but I've actually had occasion to introduce some fifth and sixth graders to the concepts of calculus (particularly integral calculus) and they really did seem to have little trouble with them.
But without the algebra skills, it is nearly impossible to get much beyond the qualitative conceptual understanding and into the meat of the subject. So these kids are crippled before they even start -- and it only gets worse from here as they move on to more advanced material with increasingly poor preparation.Well ... duh!... I didn't mean 1000 stronger... but a 1000 times more hurtful! ... as if !... really dude, get your facts straight...But if we have to put up with grade-inflation, doesn't it stand to reason that wrestling has to contend with pain-inflation.
The U.S. school system is a complete mess and proficiency in reading, writing, math, and science is virtually nonexistent.
Unfortunately, anyone who proposes any serious reform is immediately dog piled by the social engineers who like the status quo. From my own experience, proponents of educational reform find themselves living in a "Twilight Zone" where workable ideas are ridiculed as either "Can't Do" or "There's nothing wrong with what we're doing and we should continue with the same (-IE- failed) policy".
Many have made the observation that the U.S. is headed down the same road to Hell that did in Roman Empire. | 677.169 | 1 |
Online Maths Resource- a Proven Method to Educate students
Online maths resource is probably one of the most sought-after educations programs and courseware to be used by students these days. Among all the subjects that are offered, maths is believed to be the toughest. However, with maths online programs students have been experiencing a fun and engrossing learning experience. There are several educations institutions, both private and government based that offers a range of maths tutorials and courses that can be downloaded. These tutorials include small courses based on different areas of mathematics and certification courses too.
There are some basic online maths programs that include the Basic Maths Review. This is supposedly a guide that benefits students of different age groups. It helps them in learning the subject and allows them to grasp methods and problem solving techniques. It also allows students in developing their understanding about the subject and the application of the subject in different spheres of life.
Maths Skill Test is an excellent online course that is designed for people who would want to improve their basic skills in mathematics. This course is accessible to all, and mainly for students who would want to learn basic fundamentals, such as addition, subtraction, division and multiplication.
Mathematical Problem Solving is an interesting online course in mathematics that is intended for students requiring some fundamental knowledge of mathematical solutions. Problems and its related issues like numbers, distance, money, percentage etc can be easily solved with this program.
Calculus Learning Programs are also very interesting and interactive. These online maths courses have helped many students in learning the basics of calculus and implementing the same in their daily life. Such courses usually revolve round the problem solving skills and related derivatives. It benefits students because these are interactive courses that allow a student to have in-depth understanding and knowledge of a subject.
The modern online maths courses emphasize more on the basic techniques of problem solving rather than getting into the details of operations. There are many affordable courses that teach different variations of maths and include everything like exponents, rations, radical signs, absolute value, fractions, decimals etc.
Yesteachme - About Author: YesTeachMe is No 1 Online Math Library with best Online Learning Programs . If you are looking for Science Online Learning resource then Visit NOW!! | 677.169 | 1 |
How can you explain to new students trying to enroll in college why math is the biggest hurdle to get over?Now, why it's harder for some than others, that is still...
Hi, jakande,
Now, why it's harder for some than others, that is still the $64,000 question for many. There is no one correct answer. For some, it is because they had poor math teachers in high school. It may be they will have some tough math teachers in college. For some, it is because they didn't work and study hard enough in high school to learn it. For some, it may be per the college policy. For instance, I know one high school student who was allowed to take a math class at a college his senior year in high school. When he was a junior in high school, he took Pre-Cal and got a C. When he got approval to take college classes, he was required to take a test on a computer for his math placement. He has a test anxiety, especially taking them on computers. So, he didn't do well on the test. So, for the college math class he took his senior year of high school, it was equivalent to his Algebra 1 class he had his freshman year. The college never did consider his transcript from high school, only his score on the computer placement test. I could have even seen requiring him to take Pre-Cal again in the college class. But, that was 2 levels "above" where he tested.
Given this information, jakande, I wish I could give you one or two items how you could explain to new students that math is the biggest hurdle to get over. What I would try is this, possibly, if it ever comes up.
A similar question math teachers get a lot is, "When will we ever need to use this in the real world?" What I ask back is, "Why do football players bench press weights?" I explain that nowhere in a football game is there a point where football players are asked to lay on their back and benchpress 300 pounds over their heads several times. "So, why benchpress?" All students have been able to answer, "Because it makes them stronger; it makes them better football players." I explain to the students, "That's what math is for the average person. In this class, we solve problems. In the real world, you will have problems to solve. Now, the technique may not be the same to solve the problems out in the real world that we solve in here. But, similar with football and bench press, it's been found that the ability to solve problems in this class is the same ability as solving problems in the real world. Math class to the real world is like bench press to a football player."
If we look at math as a language, a set of symbols that can be used to express relationships among elements of logic, we can see that, while the ordinary social experiences of a teenage (or highschool) student automatically build a verbal vocabulary, the same cannot be said of the mathematical language. After trigonometry and geometry, math learning becomes alienated from real-life experiences. Therefore, excellence in math skills is a good indicator of a student's ability to learn abstractions; the college applications often divide on this indicator: Is the highschool student mentally ready to tackle college-level learning? Those students with good math skills stand out for this reason. | 677.169 | 1 |
Introductory Differential Equations
ISBN
9780124172197
Edition
4 Rev ed
Publisher
ELSEVIER AUSTRALIA
Author(s)
Martha L. Abell
Publication Date
1 Jan 2014
Overview
This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, and Fourier Series. Differential Equations is a text that follows a traditional approach and is appropriate for a first course in ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. Some schools might prefer to move the Laplace transform material to the second course, which is why we have placed the chapter on Laplace transforms in its location in the text. Ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple would be recommended and/or required ancillaries. Because many students need a lot of pencil-and-paper practice to master the essential concepts, the exercise sets are particularly comprehensive with a wide range of exercises ranging from straightforward to challenging. Many different majors will require differential equations and applied mathematics, so there should be a lot of interest in an intro-level text like this. The accessible writing style will be good for non-math students, as well as for undergrad classes. * Provides the foundations to assist students in learning how to read and understand the subject, but also helps students in learning how to read technical material in more advanced texts as they progress through their studies.* Exercise sets are particularly comprehensive with a wide range of exercises ranging from straightforward to challenging.* Includes new applications and extended projects made relevant to "everyday life" through the use of examples in a broad range of contexts.* Accessible approach with applied examples and will be good for non-math students, as well as for undergrad classes. | 677.169 | 1 |
Improving Success of Students in Introductory Mathematics and Statistics Courses
By: David F. Brakke and Linda Cabe Helpern
We live in a world of enormous complexity and are surrounded by quantitative problems, awash in numbers and information. This era of "big data" came quickly upon us, forcing us to re-think how we prepare our students to think and reason analytically, for life before and after graduation.
James Madison University (JMU) is a large, public, selective, comprehensive university in Virginia. Our goal is to prepare educated and enlightened citizens who will lead productive and meaningful lives. We believe that we need to enhance quantitative literacy, and to do so in a context of ethical decision making. To that end, a decade ago, we reported in Peer Review on multiple approaches being used to improve quantitative skills at James Madison University (Brakke and Carothers 2004). In that article we addressed first-year advising, support, assessment, curricular changes, minors and majors, and interdisciplinarity. We have continued those efforts and recently expanded them to address specific courses.
Placement for Success and Not for Failure
We cannot overemphasize the importance of placement into mathematics courses while also recognizing the landscape has become more complicated since our article was published. We must start with placement for success, not for failure. Students are entering universities with a wide range of skills and degrees of preparation. We recognize the importance of strong algebra skills regardless of what more advanced topics students were introduced to through IB, AP, and other courses and base our placements mostly on algebra. We have carefully studied the success rates of students in a range of mathematics courses in relation to their SAT and mathematics placement scores. Where necessary we have developed new courses designed to prepare students to be successful and have worked hard to improve advising about mathematics courses.
In other cases, we have begun conversations between the mathematics and statistics faculty and programs relying heavily on them. Examples include an engineering program now beginning its seventh year, working with biological mathematics, mathematics and the physical sciences and data analytics. These conversations may occur across one or more departments and in some cases cross multiple colleges.
Rather than providing an update on all of the areas addressed by Brakke and Carothers (2004) or describe conversations in early stages, we want to report on outcomes for two specific projects that we hope will illustrate ways that focused efforts can achieve very positive results and improve student learning outcomes. In so doing, we will suggest ways to structure collaborative efforts that lead to cooperation, increased understanding across programs, and improved student success.
Increasing Student Success in Two Gateway Mathematics Courses
In 2009, as part of the strategic planning process required by the state and coordinated by the State Council of Higher Education in Virginia, JMU undertook a project to increase student success in the two gateway mathematics courses with the largest undergraduate enrollments. These were Math 205, Introductory Calculus I— the three-credit calculus course taken by many students in the College of Business as well as a variety of other majors—and Math 220, Elementary Statistics, which is required by a large number of majors. Over 20 percent of new first-year students take one of these two courses in their first semester. In 2009–2010, the year this project started, the total fall and spring enrollment across these two courses was 3,823 students. In the same year, JMU enrolled 3,952 new first-year students and 669 new transfer students. Even allowing for some retakes and some students taking both courses, it is clear that a very large percentage of our students take at least one of these courses in their first-year. Improving student success in these two courses, therefore, had the potential of having an impact on a very large number of JMU undergraduates, making it a powerful project for improving overall student success.
Investigating Causes for Student Failure
In the fall of 2009, two task forces, one for each course, were formed to investigate causes of student failure—defined as students completing the course with grades of D, F, or W (withdrawn)—and design possible strategies to increase success. Five years later, the very notable achievements of this project, and its general applicability to a number of undergraduate institutions, have led us to share project details. Before the project began, A, B, and C grades in Math 205 ranged from 62.3 to 71.7 percent and reached 83 percent in 2013–14. For Math 220, the percentages were from 70.8 to 76.0 percent prior to the project and reached 86 percent in 2013–14.
One important aspect of the formation of the task forces is that they included faculty from the departments whose curricula build on the two mathematics courses under review. So, for example, the initial task force examining student success in Elementary Statistics included faculty from biology, health sciences, justice studies, and psychology, as well as a faculty leader from the general education program. This breadth of representation allowed the group to consider not only what students needed to be successful in the gateway mathematics class but also what they needed to retain to be successful in a subsequent class in their major. A similar approach was taken for the one-semester calculus course. Both task forces were promised modest support, but it was clear that JMU could not provide significant new funding. Initial recommendations of both faculty groups and ongoing work on this project fall into three broad areas: student preparation and placement, course augmentations, and alignment.
Student Preparation and Placement
One immediate finding related to Elementary Statistics was that both our math placement test and preparatory courses were more closely aligned with calculus than statistics. Faculty began working immediately on a new section of our existing math placement test that would focus on the preparation students would need to succeed in statistics and also developed a quantitative literacy course that both matches the student learning outcomes of our general education program and provides focused preparation for further study in statistics.
After analyzing data on the relationship between math placement scores and student success in Introductory Calculus, we found that DWF rates were significantly higher for students who did not follow placement advice and took a higher math class than was recommended by their first-year advisors, so the task force recommended much tighter enforcement of placement scores as first-year students registered for classes.
Course Augmentation
Mathematics faculty on both task forces also began work on supplemental materials that students could use to develop their skills. Over several summers, JMU has provided modest summer funding for mathematics and statistics faculty to develop homework questions and problem sets using WeBWorK, an open-source online homework system that is supported by the Mathematical Association of America and the National Science Foundation. Faculty believed the homework system would improve student learning and retention, and that it had the potential to reduce the workload on individual instructors because faculty are assigned to develop homework problems their colleagues could share. They have continued to build the test bank and increase the number of faculty using the homework system.
JMU had existing student support in supplemental instruction, as well as a comprehensive Science and Mathematics Learning Center providing tutoring and homework help for students in both courses. Even so, the group looking at statistics implemented more robust training for student tutors and both task force groups encouraged their colleagues to make greater use of the Supplemental Instruction program.
One of the most creative augmentation efforts has been the development of a one-credit "booster" course for students who do not place into Introductory Calculus, but whose scores fall into a range just below the cut-off point. The course is designed as a self-paced, primarily online supplement taken in the same semester as Introductory Calculus, allowing these students to avoid a three-credit full semester preparatory course. The benefits are many, including the fact that these students are able to move into calculus a semester earlier, and their success in calculus has improved.
Alignment
Both task force groups recognized divergence across sections of the same course as a problem. Faculty in the calculus group proposed to increase alignment through promoting the WeBWorK homework system and through fostering, in the words of their report, "an environment that promotes open discussion opportunities between faculty who teach Math 205." Both courses are also making use of peer study leaders.
Statistics faculty implemented a number of specific initiatives designed to improve alignment across sections. These included instituting a Math 220 coordinator in the department, having statistics faculty approve a core list of course content topics to be covered in all sections, and analyzing the grade variance for greater consistency in grading. Because each of these initiatives came from the statistics group and were not mandated, they were widely embraced. The course coordinator worked so well that the same model was adopted by the calculus group.
Another move undertaken across the department of mathematics and statistics was an effort to align faculty enthusiasm and commitment with their course schedules and teaching assignments. This move also more clearly defined the roles of faculty in teaching not only Math 205 and Math 220 but also other courses.
Results
The results to these combined efforts have been stunning. As one faculty member noted at the beginning of the process, JMU started with success rates that many departments around the country would be proud to match. The current success rates (grades of A, B, or C) of 83 percent in Introductory Calculus and over 85 percent in Elementary Statistics exceed the targets we set by a great deal, and represent an extraordinary achievement by a dedicated group of faculty. Equally notable is the scale at which this has been achieved—in 2013–14 there were ninety-eight sections enrolling over 3,800 students during the fall and spring semesters. While reporting the major gains in student success, we need to emphasize that there was no change in course content or rigor of the courses. One of the instructions to the task forces from the very start was that they not back away from content, but instead focus on ways students can be more successful.
Because the project to increase student success in these two math courses was undertaken as part of a state-level strategic planning process, it started with specific targets by which the improvement would be considered successful. Table 1 lists actual student performance in these courses beginning in 2000, and compares those results with the established targets and thresholds. In each course, large increases in student success followed the implementation of the improvement strategies described in this article.
Mathematics and statistics faculty are proud of the success of these efforts, and are continuing to seek ongoing improvement. For 2014-2015, they have expanded the use of the one-credit booster course and are considering the model for other more specialized introductory math courses. They continue to expand the problem sets used in WeBWorK. We may reach a point where the university's goal will be to maintain our level of student success in these courses rather than continued improvement in success rates, but we hope to see further progress in the near future.
Acknowledgments
We would like to acknowledge the leadership of our colleagues in the department of mathematics and statistics. The task force promoting student success in Math 205 was led by Debra Polignone Warne, professor of mathematics; the task force promoting success in Math 220 was led by Hasan Hamdan, professor of mathematics, and Kane Nashimoto, associate professor of mathematics. David Carothers, mathematics department head, has supported their efforts throughout the process. | 677.169 | 1 |
Courses are offered cooperatively by
Portland State University and Adventures In Education, Inc.
PSU Course Number
PSU Dept and Prefix
Quarter Grad Credits
Course Title and Description
Tuition
Grad Credit Fee
10134
CI 810
5
Topics in College Algebra and Graphing Technology Strengthen
understanding of mathematics and use technology as a means to
enhance the construct of mathematical knowledge. Research current
pedagogical approaches and implications of teaching mathematics with
handheld technology. Examine and critique lesson design units for
topics such as linear functions, quadratic, polynomial functions,
exponential and logarithmic functions; curve fitting; and matrices.
Design instructional units that foster development of analytical
skills and increase problem solving ability of all college algebra
students. Content is aligned with ISTE National Educational
Technology Standards.
Statistics and Technology Integration
Acquire skills and knowledge to teach and learn in the digital
age. Use modern technology as a means to improve the construct of
statistical knowledge. Analyze current mathematics education
research on pedagogical approaches to teaching and learning
statistics using handheld and spreadsheet technology. Examine and critique lesson design
units for topics such as descriptive statistics, probability
distributions, linear regression and hypothesis testing. Design
instructional units that foster development of analytical skills and
increase problem solving ability of all statistics students. Content
aligned with ISTE Standards.
Topics in Trigonometry and Graphing Technology
Deepen understanding of trigonometric concepts and use graphic technology as a means to
improve the construct of mathematical knowledge. Analyze current
mathematics education research on pedagogical and andragogical approaches
to teaching and learning with technology. Examine and critique lesson units for
topics such as basic and composite trig functions, trig identities,
polar graphs, and periodic modeling.
Design lessons that foster development of analytical
skills and increase problem solving ability of all
students. Content is aligned with ISTE National Educational
Technology Standards.
Topics in Analytic Geometry & Calculus and Graphing
Technology
Deepen understanding of analytic geometry and calculus concepts and use
graphic technology as a means to
improve the construct of mathematical knowledge. Analyze current
mathematics education research on the complex relationship between
technology, pedagogy and mathematical content within the framework
of TPACK. Emphasis is on recursive, piece-wise, and absolute value
functions, parametric equations, conics, rate of change, vector
forces, derivatives, and Riemann sum. Examine and critique existing lessons
to design effective learning environments and experiences for all
students. Content aligned with ISTE Standards.
Mathematical Modeling and Digital Learning
Apply algebraic concepts to develop mathematical models and deepen understanding of
mathematical content knowledge. Emphasis is on non-linear models,
supported by use of graphic technology, and effective communication
of quantitative concepts and results. Analyze current
mathematics education research on teaching and learning with ICT. Examine and critique
existing instructional units for
topics such as logarithmic, log-linear, exponential, hyperbolic,
power, periodic and parametric models and design effective learning
environments and experiences for all students. Content aligned with ISTE National Educational
Technology Standards.
Linear Regression Models and Modern Technology
Acquire skills and knowledge to teach and learn in the digital age.
Use graphic calculator and spreadsheet technology as a means to
improve the construct of mathematical knowledge. Analyze current
mathematics education research on ICT-Assisted PBL. Examine and critique lesson
design units for
topics such as linear, piece-wise linear, log-linear, multiple and
median-median regression, correlation and multicollinearity.
Develop new learning practices that foster development of analytical
skills and increase problem solving ability of all students. Content aligned with ISTE Standards.
Course Schedule:
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IMPORTANT: PSU limits enrollment to 8 quarter credits per term unless officially admitted to
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Courses are offered cooperatively by Adventures In Education, Inc. and
Portland State University, Continuing Education/Graduate School of Education
with the School of Extended Studies. | 677.169 | 1 |
Math 130, Math in the Social Sciences, Summer 2010
Math for the Social Sciences is a freshman level class taken by students in the humanities and social sciences. Topics covered in class included: voting theory, scheduling, Euler and Hamilton circuits, apportionment, and basic statistics. Class sessions consisted of lectures and hands-on group work. Students also completed a project in which they found occurrences of mathematics in their hobbies and daily lives56 4.5 4.56 4.43
Student Comments
"Cory did an outstanding job of teaching this class. She was thorough and patient. Thoughtful when answering questions. I enjoyed the class."
"She came into class excited to teach and was always willing to help or show me how to do something if I didn't understand."
"The class was really interesting. Cory was really helpful with any questions. I can also tell she really cares about teaching math because it made the class that much better. She was great about creating relevance and engaging attention."
"I liked the class, you're a great teacher."
"I like that you explain every step thoroughly. It lets me be sure I will understand the material. You are awesome!" | 677.169 | 1 |
This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities | 677.169 | 1 |
Algebra 2 Questions & Answers
Algebra 2 Flashcards
Algebra 2 Advice
Algebra 2 Advice
Showing 1 to 3 of 7
I would recommend this course because it prepares you for math classes that you will take in a college and shows you the basics of factoring,solving square roots,and all you need to know to be able to succeed in higher level classes.
Course highlights:
What I learned from this course is how to find a imaginary number in a equation and all the I's for example what x square, x to the 3rd and etc.. I also learned shortcuts for division to make it easier for anyone who doesn't like long division much.
Hours per week:
6-8 hours
Advice for students:
The advice I would give any student considering this class is that they should take notes even if the teacher doesn't tell you to because even though you think you know what is being taught or understand it, your brain could trick you while doing any test or quiz. I also recommend that you always go back to check your work when solving a problem because even with one wrong step you could get the whole problem wrong.
The reason why I would recommend this course is because It teaches the different aspects of algebra and it shows a series of a higher-level math that will help us students succeed in college and life. Because many students fail math classes and some of them graduate from high school unprepared for college or work.
Course highlights:
Able to be a master in Algebra is the key that will unlock the door before you, also will help you excel into any major or field your heart desires to, Mathematics is one of the first things we humans learn in life. Even as a baby we learn to count. from learning how to use building blocks, how to count and then move on to drawing objects and figures. All of these things are important preparation to doing algebra.
Hours per week:
0-2 hours
Advice for students:
Well first try attending your Algebra 2 classes regularly But, if you want to get the most out of class, you need to pay attention and take good notes. Write down the formulas your teacher goes over, as well as any information that he or she writes on the board, another good idea is make study groups and talk about the way you guys can solve an equation, and learn the different techniques. | 677.169 | 1 |
An introduction to the Xcas interface
Abstract:
This document describes the Xcas software, which combines
a computer algebra system, a dynamic geometry and a spreadsheet.
It will explain how to organize your worksheet. It does not
explain in details the functions and syntax of the Xcas
computer algebra system (see the relevant documentation). | 677.169 | 1 |
Pre AP Pre Calculus Syllabus Instructor: Cheryl Weixelman Industrial High School Welcome to Pre AP Pre Calculus! This course is a key component in your
mathematics foundation. As a result, it
is imperative that you be successful in this class.Your success in Pre AP Pre
Calculus depends on your willingness to be challenged and on how well you
develop the self discipline to complete your work, turn it in on time, and ask
questions when you do not understand. I
expect your best effort at all times. If
you do this, we will have a great year!
Most
homework will receive a numerical grade. Some, however, may receive a check grade. Check grades are a means of checking how much
effort that you put into an assignment. I will check to see that the majority of the problems have been
attempted, and provided that the assignment had been turned in promptly, the
student will receive a check. I will
also use check grades as a means of keeping track of which students have turned
in their progress reports, graphing calculator contracts, and other various
forms. I will do a textbook and graphing
calculator inspection each six weeks to insure that each student has the text
and calculator issued to him/her and will document this with a check. Check grades are assigned as follows:
√ indicates all problems were attempted and
assignment completed on time
- assignment partially completed or late
Ø indicates the assignment was missing or less
than half of the problems were
attempted
These
check grades will accumulate into 2 daily grades. At the end of the six weeks, a student will
have a 100 if there were no –'s or Ø's. Each – will count off 2 points and each Ø will count off 4 points.
Short
quizzes, in-class assignments, lab activities, and notebooks will also receive
numerical grades and count as daily grades. And, as mentioned earlier, most homework will also receive a numerical
daily grade.
Late Work Late work is highly discouraged! I will follow the district guidelines for late work. See your student handbook for details. If you
are going to miss school because of an extracurricular event, your homework is
due the day you get back.
If you are going to miss a test, prior arrangements should be made.
Classroom
Rules THESE RULES, ALONG WITH ALL SCHOOL RULES, WILL BE OBSERVED IN THE
CLASSROOM.
1. Be seated and ready to work when the
tardy bell rings and remain seated throughout the period unless given
permission to do otherwise.
2. Show respect for all school
personnel, self, and others. (No talking
back and no profane or abusive language.)
3. Bring all required supplies to
class. (Text, notebook, paper, pencil,
calculator, ruler, and whatever else I tell you).
4. Remain attentive and alert. (Class participation is expected at all
times!)
Because of the nature of an advanced
course, it is imperative that you "keep up" in this class. You are expected to do your own work and to
do it well. As stated earlier, your
success in Pre AP Pre Calculus depends on your willingness to be challenged and
on how well you develop the self discipline to complete your work, turn it in
on time, and ask questions when you do not understand. I expect your best effort at all times. If you do this, we will have a great year! | 677.169 | 1 |
Calculus
Browse related Subjects ...
Read More Chapter 10. Numerous examples throughout the text contain all the algebraic steps, with key steps highlighted in colour, needed to complete the solution. The examples are complimented by more than 7,000 section and chapter exercises featuring drill, application, calculator, show/prove/disprove, and challenge problems. Each problem set begins with Self-quiz questions to help students evaluate their understanding of basic ideas in the section. The development of calculus is outlined in extensive historical notes. Biographical sketches impart information on renowned mathematicians | 677.169 | 1 |
3.2.11 Special Functions
This is directly from "Special Functions" in the Mathematica Help
Browser
Mathematica includes all the common special functions of
mathematical physics found in standard handbooks. We will discuss
each of the various classes of fu
Extra Credit - Create your own problem to take advantage of
using:
1. FindRoot[ ]
2. Solve [ ] and DSolve[ ]
3. /.
Create examples for both 1 and for 2 while using 3 in both.
The example below uses 1 and 3.
Two equations and two unknowns (x1 and x2)
Here
MSE 310/ECE 340
Electrical Properties of Materials
Dept. of Materials Science & Engineering
Fall 2011/Bill Knowlton
Problem Set 4 Solutions
(Show all work for all problems)
1. In class, we considered the radial wave function of an electron in a hydrogen a
MSE 310/ECE 340
Electrical Properties of Materials
Dept. of Materials Science & Engineering
Fall 2011/Bill Knowlton
Problem Set 4
(Show all work for all problems)
1. In class, we considered the radial wave function of an electron in a hydrogen atom given
Dept. of Materials Science & Engineering
Fall 2011/Bill Knowlton
MSE 310/ECE 340
Electrical Properties of Materials
Problem Set 3
1. ABET PROBLEM: You are to determine the identity of three mystery (i.e., unknown) elements. The
only information you have a
MSE 310/ECE 340
Instructor: Bill Knowlton
Problem Set 0
Fall 2011
Solutions for Problem Set 0
2a. Create a data set of at least 4 sets of (x,y) data where x = electric field and y = voltage. For instance, at 0
volts, the electric field is 0 therefore we
MSE 310/ECE 340
Electrical Properties of Materials
Dept. of Materials Science & Engineering
Fall 2011/Bill Knowlton
Problem Set 0
1. Download the Band Diagram Program and open the file Au-Sio2-Au.bds. Keep this program on your computer
as we will be using
Boise State University
Department of Materials Science and Engineering
Fall 2011
Bill Knowlton
MSE 310/ECE 340: Electrical Properties of Materials
- Course Syllabus and Objectives - You are responsible for understanding what is expected of you as outlined
Bill Knowlton and Wan Kuang
ECE and MSE Departments
Boise State University
Linear Algebra and Matrix Algebra Module
Linear equations are very common in Engineering and science problems. This tutorial will teach you how to use Mathematica to solve such equ
Dept. of Materials Science & Engineering
Bill Knowlton
Extra Credit
Mathematical operators:
An operator is a symbol that tells you to do something to whatever follows the symbol.
Typically the operator will have a hat or caret symbol,^, over it. An exampl
Dept. of Materials Science and Engineering
Bill Knowlton
Extra Credit Assignment 2
Using the computers in MEC 408 (or your own software package of Mathematica), use
Mathematica to work through:
From Chapter 0 of the book A Mathematica Companion for Diffe
Dept. of Materials Science and Engineering
Bill Knowlton
Extra Credit Assignment 1
Using the computers in various computer labs throughout the university and COEN (e.g,
ET 239), use Mathematica to work through:
Mathematica Getting Started (Mathematica 7)
Dept. of Materials Science and Engineering
Bill Knowlton
Differential Equations Module Chapter 1
Using the computers in MEC 408 (or your own software package of Mathematica), use
Mathematica to work through:
From Chapter 1: An Introduction to Differentia
Dept. of Materials Science and Engineering
Bill Knowlton
Extra Credit for Advanced Mathematica Users
Note: These extra credit assignments are for students that have already finished the extra
credit assignments in this or other courses. In order to obtain
Dept. of Materials Science and Engineering
Bill Knowlton
Extra Credit Assignment 3
Using the computers in MEC 408 (or your own software package of Mathematica), use
Mathematica to work through:
From Chapter 0 of the book A Mathematica Companion for Diffe
Knowlton
Materials Science and Engineering
Boise State University
Text, Arrows and Legends - How to use them in you plots
Extra Credit: Use the example below to create
your own program
We will plotting the activity of component one and two as a function | 677.169 | 1 |
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