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Beginning Pre-Calculus for Game Developers(Books & other media combined)
Synopsis
Successful game programming requires at least a rudimentary understanding of central math topics. While most books neglect the point-by-point details that are necessary to truly hone these skills, Beginning Pre-Calculus for Game Developers tackles each task head on, using easy-to-understand, hands-on exercises. You will conquer the basics of these essential math topics and will then learn how to specifically apply each skill to the field of game programming. Whether you are searching for an entertaining, engaging way to improve your math skills or you wish to develop the background skills necessary to boost your game programming, Beginning Pre-Calculus for Game Developers serves as the step-by-step guide that will help you tackle pre-calculus with confidence.
John P. Flynt, Ph.D., works in the software development industry, has taught at colleges and universities, and has authored courses and curricula for several college-level game development programs. His academic background includes work in information technology, the social sciences, and the humanities. Among his works are In the Mind of a Game, Simulation and Event Modeling for Game Developers (with co-author Ben Vinson), and Software Engineering for Game Developers. John lives in the foothills near Boulder, Colorado. Boris Meltreger graduated from a top mathematics and physics high school in Russia. He went on to earn an advanced degree in optical engineering. After completing a dissertation on acoustics and optics, Boris took up work for the Russian government developing optical computers. He has been the recipient of engineering awards for his work and has owned his own engineering company. Boris has in recent years performed pioneering work in the development of optical technologies for medical applications and currently works as a software engineer. Boris lives in Aurora, Colorado | 677.169 | 1 |
Mathematics and the Laws of Nature, Revised Edition
Mathematical methods are useful in understanding nature. Though many people accept this view without question, it is usually an act of faith. History demonstrates that nature's most fundamental and important… (See Below for Full Description)
Details
Mathematical methods are useful in understanding nature. Though many people accept this view without question, it is usually an act of faith. History demonstrates that nature's most fundamental and important patterns are neither easy to recognize nor easy to harness for the common good. The development of the concepts and methods necessary to deduce new knowledge of nature from already established results—and the development of methods to separate correct results from incorrect ones—remains a work-in-progress. Attempts to create these methods are documented in the earliest written records, and efforts to refine these methods and develop new ones continue to this day.
the conservation of momentum, the conservation of mass, and the conservation of energy. Chapters have been updated and revised to reflect recent information, including the mathematical pioneers who introduced new ideas about what it meant to solve an equation and the influential efforts of the mathematicians of the former Soviet Union. | 677.169 | 1 |
For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."
ZENTRALBLATT MATH
Review by G.Roepstorff, University of Aachen, Germany
"... Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics student in the middle of his training, it will certainly prove to be extremely useful."
THE PHYSICIST
Review by Paul Davies, Orion Productions, Adelaide, Australia
"I am pleased to have so many topics collected in a single volume. All the tricks are there of course, but supported by sufficient rigour and substantiation to make the dedicated mathematical physicist sigh with delight."
EMS [EUROPEAN MATHEMATICAL SOCIETY] NEWSLETTER
"This book is a condensed exposition of the mathematics that is met in most parts of physics. The presentation attains a very good balance between the formal introduction of concepts, theorems and proofs on one hand, and the applied approach on the other, with many examples, fully or partially solved problems, and historical remarks. An impressive amount of mathematics is covered. ... This book can be warmly recommended as a basic source for the study of mathematics for advanced undergraduates or beginning graduate students in physics and applied mathematics, and also as a reference book for all working mathematicians and physicists."
I migliori risultati di ricerca su AbeBooks
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Doing Math with Python shows you how to use Python to delve into high school—
Python can land you a lucrative job in numerous companies and dramatically increase your salary and earning potential. As you navigate these chapters, you will become quite adept in your journey to master the Python. | 677.169 | 1 |
Introduction to Mathcad 15
ISBN-10: 0136025137
ISBN-13: 9780136025139 MathCAD 15, 3/e is ideal for Freshman or Introductory courses in Engineering and Computer Science. Introduces MathCAD's basic mathematical and data analysis functions (e.g., trigonometric, regression, and interpolation functions) using easy-to-follow examples, then applies the functions to examples drawn from emerging or rapidly developing fields in engineering. ESourcePrentice Hall's Engineering Sourceprovides a complete, flexible introductory engineering and computing program. ESource allows professors to fully customize their textbooks through the ESource website. Professors are not only able to pick and choose modules, but also sections of modules, incorporate their own materials, and re-paginate and re-index the complete project. prenhall.com/esource | 677.169 | 1 |
Workshop 06
Tuesday, May 5: 3:45 PM – 4:45 PM
Workshop Description: Mathematics in Design – An Investigation using GeoGebra
Discovering mathematics in a realistic setting reveals relationships to other disciplines and can lead to powerful learning. Explore a technology tool with visualization and dynamic capabilities that support investigation and challenge thinking. This session introduces features and the basic functionality of GeoGebra, dynamic mathematics software that supports teaching and learning. A GeoGebra-in-action segment explores the relationship between seat ht. (m.) and time (sec.) during a ride on a ferris wheel. A given data set is graphed; visual patterns, observed; and a function that models the data set is discovered. The roles played by parameters of the function become evident.
Workshop Presenter: Judy Chandler
Judy has 22 years experience teaching middle & high school level mathematics. She holds a BA in mathematics from Colby College and a M.Ed in curriculum & instruction specializing in educational technology. An educational technology consultant, Judy currently serves as a MLTI Mathematics Mentor and an adjunct instructor at Husson University. | 677.169 | 1 |
Unit 1: Algebraic and Graphical Manipulations
▼
Overview
This unit focuses on the properties and graphs of important functions that are used to solve real world problems. Students learn to analyze graphs for areas of increase and decrease and end behavior and use this information to make predictions for real world data. Additionally, students review skills needed to work with functions (such as the properties of exponents and simplifying radicals) and are introduced to piecewise functions and their uses. | 677.169 | 1 |
Mathematics
In school, work, and life students will meet new challenges and need to utilize and implement creative, flexible, and adaptable mathematical skills. Math at CSG meets each student at their level and develops her skills to create a problem-solving disposition that includes confidence, willingness, and the ability to engage in the communication process. In each course, students engage in reasoning, journaling and weekly presentation practices as they grow and develop in their mathematical thought processes.
Scientists use mathematics as a language to communicate how different systems work. Students have multi-disciplinary opportunities in the Coastal Marine Ecosystems course to demonstrate understanding of and apply mathematical concepts through data collection, manipulation, and analysis.
Students may select Algebra II, Geometry, or Pre-Calculus, depending on their individual needs and the requirements of their sending school. | 677.169 | 1 |
1. The role of linear equation systems in applied sciences
- 2. General characteristics of systems of linear equations - 3. Compatibility
of linear equations - 4. The homogeneous system of linear equations - 5.
The number of solutions for a system in n equations and m unknowns - 6.
Compatibility relations and the general solution of a system of linear
equations - 7. Least squares solution of systems of linear equations -
Exercises
1. Linear mappings from one three dimensional space into
another - 2. Linear mappings of three dimensional space without full rank
- 3. Linear mappings from one three dimensional space into a plane or line
- 4. Linear mappings from a plane or line into a three dimensional space | 677.169 | 1 |
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
Discrete Math: earn better grades and discover great careers
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
Are you a Math, Computer Science or Computer Engineering student or maybe a proffesional who needs to successed in Discrete Mathemathics?
Do you need to develope your mathematical skills and learn with practice?
Are you already studying Discrete Math Subject but need a better resource and online teacher to study and get better grades?
Do you need to increase your GPA but have little time to study?
This is a great place to learn Discrete Mathematics! Enroll Now!
In this course you will learn about mathematical logic, mathematical proofs, set theory, functions, relations, graph theory, number theory as well as combinations and permutations.
Each chapter of the course can be taken inpedenently if required, and each chapter covers all of the listed topics in details so you will learn everything that is necessary and in the order that most suits you as a student. As students usually come to this course for specific topic(s) and exercises, here is the comprehensive list of what you will learn from each chater of this course:
All lectures are in high quality - 1080p and the powerpoint presentations are downloadable. (you can use them when you will need and they can save you time by revisiting the learned material as well). All the concepts and definitions are explained in the videos and each topic is ending with a set of examples as well as a small theory quiz (optional). We will go through each step to solve the given examples in each lesson as well as practice them at the end of the all 7 chapters. In case of difficulties, you can post a question and get help from the instructors!
This course will be useful toanyone studying discrete math and any related subject, such as linear algebra, calculus, economics, statistics, cryptography, finance, actuarial science, data structures, data science or algorithms. And if you are a computer science student and you were searching for mathematics for computer science course than you will definitely need to go through this course! This is also a great course for computer and math related majors, because they usually require a solid knowledge in doscrete math.
The instructorsof this course have both completed discrete mathematics in there computer engineering sophomore year and got the A+ (4.0) grade which has lead to the idea of creating this full and comprehensive course. We have seen how our university students in fields such as computer science, computer engineering and electrical engineering were struggling to study the material and worried about passing their exams. And if you are tired of learning everything on your own with university or from professors while going to the lectures everyday, you can now get this course for as little as two cups of coffee and this small investment will rapidly effect your life, career and especially your GPA! So make the right decision today and enroll in this course now!
In addition,to all of these, this course gives you 100% satisfaction or Money-Back Guarantee for 30 days so you have nothing to lose. The course can be watched on all devices and at the end you are even getting a certificate for course complition that you can put on your resume, linkedin, show your co-workers and/or classmates and professors.
After enrolling in this course you will feel 100% confident and will master your skills in Discrete Math. You will have all necessary materials to revisit and videos with lifetime access that you can watch even on your phone, laptop or TV screen. You will learn how to solve the problems in discrete math step-by-step and even know all the theory and concepts that are necessary for your success in this subject. Feel free to look at the free materials that are provided to you on this page. All the powerpoint presentations are downloadable so that you will be able to simply skim through them in 20 minutes if you will need to repeat some material or prepare for your class.
3 LANGUAGES that I can easily communicate in: English, Russian and Georgian.
AMERICAN EDUACATION from San Diego State University (Georgia campus) Here are some datails about my studies: Student in Computer Engineering , Named to the Dean's listseveral times, full scholarship, received grant.
19 DIPLOMAS / CERTIFICATES both from olympiads and courses: Math, Physics, Russian, English, German olympiads, School diplomas and Programming. RANKED in TOP1-8% in the highschool and national exams, Highschool: Chemistry, Biology, Geography, Math. National :Math, English, General skills.
TOP100 STUDENTS in 3 subjects according to national olympiads: Math (9th grade), Russian Language (9th grade) and Informatics (10th grade).
I am Mikheil Chkheidze from Georgia. I have graduated from U.S. high school when I was an exchange student in 2010-2011. With top scores and experience, I received full grant and now, I am majoring in Computer Engineering at San Diego State University. My passion is software development and online learning systems. | 677.169 | 1 |
Most Mathematics courses have prerequisites that are listed as part of the course description. You can meet the prerequisite by taking the designated class or by achieving a certain score on the math placement test. If it is unclear that you have met the prerequisite for the class in which you wish to enroll you might be blocked by the system. For more information about how prerequisites work please visit us at the college website: www. canadacollege.edu/registration/index.php
To inquire about placement tests and the assessment process please visit us here: www. canadacollege.edu/assessment/index.php
You may also contact the Cañada College Counseling Office (located in Building 9, Room 139) at (650) 306-3452 for assistance.
Description: This is the third course in a 4 part series covering elementary and intermediate algebra and is a continuation of MATH 112. Topics include a review of equations, absolute value, lines and graphs, functions, rational exponents, radical expressions and equations, and complex numbers. Students who complete this course with a C or better should enroll in MATH 123. innerst@smccd.edu. | 677.169 | 1 |
NUMERICAL METHODS, Fourth Edition emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Readers learn why the numerical methods work, what kinds of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are the same as those covered in the authors' top-selling Numerical Analysis text, but this text provides an overview for students who need to know the methods without having to perform the analysis. This concise approach still includes mathematical justifications, but only when they are necessary to understand the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the reader that the method is reasonable both mathematically and computationally.
Editorial Reviews
About the Author
J. Douglas Faires is a Professor of Mathematics at Youngstown State University. His research interests include analysis, numerical analysis, and mathematics history. Dr. Faires has won many awards, including Outstanding College-University Teacher of Mathematics, Ohio Section of MAA (1996) and Youngstown State University, Distinguished Professor for Teaching (1995-1996).Top customer reviews
This book is horrible. The whole point of a text book is for someone to be able to learn the material that it presents and this book fails at this. It uses terminology that you can follow, but this same terminology is far more complex than it needs to be. Also, all of the examples in this book skip far to many steps, which makes it incredibly hard to learn from the examples. For instance, this book has an example for the Neville algorithm, but it only describes how to do the first part. To make matters worse, this book is way to expensive for a student.
The existing reviews were somewhat off-putting when I started preparing for the postgrad course that uses this book. I am now halfway through the semester (and the book) and I must say I actually like the book.
While we have not, and will not, cover every single method in the book, my experience so far is that the methods are actually explained quite clearly. Sometimes things can get a little confusing (e.g. the way indices are used to explain Romberg integration confused me a lot), and sometimes you will need to read a section multiple times before things become clear. But I put that down to the method itself, not the book. So far the examples in the book have helped me a lot to make sense of the methods presented and subsequently code things up in MATLAB myself. More examples is always better, but I have not seen a need for that (so far anyway).
Would I recommend the book for an undergrad course? Probably not, the book would need to include more step-by-step examples for that. Lastly, the electronic edition I am using actually looks great formatting wise. Not really important, but not unimportant either. The book is of course way, way too expensive.
Note: I am renting the electronic version through a different provider due to the cost. | 677.169 | 1 |
This unit introduces students to a range of mathematical techniques from algebra and calculus. Its focus is on the modern application of these ideas, with a particular emphasis on applications to problems in economics, business and finance, and provides a sound mathematical basis for further study in these areas. Topics include algebra relevant to basic financial mathematics, the development of the techniques of differentiation and integration with applications to constrained and unconstrained optimisation, including multivariable cases, and the development and application of a variety of useful approximation techniques. A key focus of the unit is the development of a clear understanding of the role that mathematics plays in modern society, and the development of a sound grasp of how mathematics is used to provide sophisticated modelling of complex real problems.
While the mathematical content of this unit has considerable overlap with the mathematical content of MATH130, the flavour with which the material is presented is such that this unit is the appropriate choice for economics, business and finance students, while students who wish to pursue study in science will be better served by studying MATH130ignments
Due: see iLearn
Weighting: 30%
Three assignments, each having a weight of 10%.
This Assessment Task relates to the following Learning Outcomes:Post tute
Due: See iLearn
Weighting: 20%
Complete post-tute assessment on a weekly basis.
This Assessment Task relates to the following Learning Outcomes:
Demonstrate a well-developed knowledge of the principles, concepts and techniques of mathematics as they apply to finance, economics, and the sciences.
Hughes-Hallett and Gleason; Calculus: single and multivariable, 4th edition
Additional Notes
Numeracy Centre notes on introductory concepts and techniques that are assumed knowledge for MATH123. These notes also cover some of the material in MATH123. Students who have not studied maths for several years, or who did HSC General Mathematics often find these notes helpful.In order to complete the group work video assessment task, students will need access to a device capable of recording video and audio, such as a smartphone or computer with a webcam. Students who do not have access to such devices will be assisted in joining a group that does.
Difficulties with your home computer or internet connection do not constitute a reasonable excuse for lateness of, or failure to submit, assessment tasks.
Unit Schedule
WEEK
BEGINNING
CALCULUS
ALGEBRA
TASK DUE
1
31/7/2017
Graphs
Order of operations, decimals, Fractions, real numbers
2
7/8/2017
The XY plane
Expansions and Factorisation
3
14/8/2017
Derivatives
Powers, Linear equations
4
21/8/2017
Marginals, Tangents and Normals
Linear and Quadratic equations
5
28/8/2017
Maxima and Minima
Linear and Quadratic equations
6
4/9/2017
Optimization
Exponential and logarithmic functions
7
11/9/2017
Integration
Exponential and logarithmic functions
8
2/10/2017
Exponentials, Logs, and Lagrange Multipliers
Inequalities, absolute value
9
9/10/2017
Lagrange Multipliers
Progressions: arithmetic and geometric
10
16/10/2017
Newton's Method
Applications of GPs to finance
11
23/10/2017
Numerical Integration
Matrices
12
30/10/2017
Differential Equations
Matrices and Linear Equations
13
6/11/2017
Revision RevisionAssignments
There will be three assignments in this unit. Assignment questions will be made available on iLearn after the material your considers task
Group work video
Learning and teaching activity be | 677.169 | 1 |
Linear Algebra
Linear algebra is essential to economic analysis because linear models offer the simplest representations of many real-world systems: supply and demand, national income, firm production, employment, IS-LM, investment and so on. A linear system can be solved efficiently by exploiting properties that are particular to a linear space. More generally, the language and concepts of linear algebra are widespread across many disciplines. In this module you will learn the basic tools of linear algebra, with an emphasis on their applications in economics.
Topics covered
Systems of linear equations
Vectors and matrices
Linear independence
Elementary matrix operations
Matrix inversion
Determinants
Quadratic forms
Optimisation
Economic applications
Learning
20 one-hour lectures
9 one-hour tutorials
Assessment
Coursework (20%)
Final exam, 2 hours (80%)
Contact us
The University of Leicester,
University Road,
Leicester,
LE1 7RH,
United Kingdom | 677.169 | 1 |
Rebuild a Damaged Runway Using Applied Practical Math
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Students will assume the role of an airport manager that is responsible for repairing a damaged runway. Using applied practical math concepts, they will use math formulas for the area and volume of a rectangle to assist in calculating costs to reconstruct the damaged runway. They will calculate the amount of concrete needed for the repairs and establish the cost of completing the project.
Additional scenarios based upon real world events are provided for students to choose, research and apply to the repair project. | 677.169 | 1 |
A Level Mathematics for Edexcel: Core C3/C4
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New. 2010. Paperback. This series covers the latest 2008 curriculum changes and also takes a completely fresh look at presenting the challenges of A Level. It specifically targets average students, with tactics designed to offer real chance of success to more students, as well as providing morestretch and challenge material. Num Pages: 352 pages. BIC Classification: 4KL; PB. Category: (UA) A / AS level. Dimension: 256 x 197 x 19. Weight in Grams: 660 | 677.169 | 1 |
Graphing Calculator MathlabPRO 4.12.147 Patched Apk
It allows the students to both watch and learn how the calculations are made and how to find the final answer. Second, the graphing ability is absolutely stunning! Not only does the calculator beautifully display the graphs, but it automatically generates the x- and y- values and displays them as well. | 677.169 | 1 |
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Students match logarithmic and exponential equations with their corresponding solutions in this matching activity. Answer key included. File is a Word document that you can revise if you need to. I used it with CPM Integrated Math 3 chapter 5 section 5.2.2 to give my students a little more practice in groups of 4. It can also be used as an interactive way to review logarithm and exponential equations in pre-calculus. | 677.169 | 1 |
When it's time to look for a new calculator, some specific issues regarding the style and engineering of these electronic devices come into play. The calculator used to be a relatively simple buy, but it's not a one-size-fits-all solution anymore. Some students or other users need calculators for an increasingly complex array of higher math functions, and choosing the right calculator is critical for a variety of educational or vocational projects. Some simple steps will help to determine calculator needs for a specific user.
Steps
1
Look at academic requirements. When selecting a calculator for a course or exam, it's important to consider what features and functions will be needed for the task at hand. For courses, take a look at the syllabus or other instructive documentation. Special tests like the SAT may also have lists of requirements for a test, including whether the test taker is allowed to have a calculator at all.
If the syllabus does not have the required information, contact the teacher, department or test center and ask about exactly what is needed for a math class or test.
2
Evaluate vocational needs. Some businesses require highly-specialized calculators. For instance, unlike many retails shops where a basic calculator or adding machine may provide for measuring revenues and expenses in cash flows, a lending or housing business may rely on a very different calculator with loan amortization functions.
Be knowledgeable on math needs in your industry. For mortgage calculators and other similar gear, having the right calculator for output is not going to be effective unless the user also knows how to explain amortization to the untrained customer. Build a good loan office setup with a combination of good tools and competent knowledge, and make sure that calculators have the right output function to make the underlying structure of amortized loans clear to a wide spectrum of individuals.
3
Consider the interface. For some projects that require graphing, having a visual graphing function on a calculator may be very important. For other more basic needs, no graphing is necessary. With graphing calculators, it's helpful for the graphs in the interface to be clearly labeled and scalable.
4
Make note of functional setups. Some calculators run off regular household batteries, where others may have lithium ion batteries or a solar power source.
Factor in output needs. Some businesses may have requirements for keeping track of calculations on paper, either for tax purposes or for other more general accounting methods. In these cases, a simple math calculator with a paper feed may be the most useful solution.
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Price calculators according to budget requirements. If cost is a factor, a buyer may be able to get more functionality and features for less money by purchasing an off-brand device or taking advantage of sale offers from distributors. | 677.169 | 1 |
Mathematics for Science 2
Mathematics is the language of much of science and is an integral part of your degree. In this module, the topics will become increasingly advanced and have been chosen to relate to more than one scientific discipline. | 677.169 | 1 |
A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises. more...
Analysis is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. more... | 677.169 | 1 |
Physics 101 SE
Physics 101 SE is the perfect solution for physics students and teachers everywhere. Physics 101 SE is the premier physics calculation tool (rated 4.5 out of 5 mice by Macworld™) allowing you to focus on physics and not mathematical tedium. With its ability to instantly solve for almost any variable in over 150 of the most commonly used formulas organized within twenty-four sections, and the ability to solve for variables within most of those formulas you will quickly get through homework problems and assignments. Beyond formulas, the application offers advanced simulations of circuits, projectiles, rocketry, free body diagrams, and more.
Most Helpful Reviews
Very Useful -
I love this app. Works great and goes way beyond just 101 level physics.
Found helpful by 16 out of 16 people
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5/5
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Review by ToonMaker
A Very Impressive App -
This program far exceeded my expectations. If you are a physics student, you'll find that it contains many useful features, for a great price!
Found helpful by 8 out of 8 people
5/5
Version 8.0
Review by Quicksilver31337
A must have for any students! -
I cant say eneough about how useful this app is. I've been using it for a long time now and I recommend it to as many people as I can. If you are a highschool or college student who has to take any physics at all then you will really thank yourself for getting Physics 101. It has saved me more time than I can imagine.
Found helpful by 7 out of 7 people
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STUPENDEOUS! If I actually did work this would be the best app for me! maybe one day ;)
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When I got my first Mac it was for college and this was one of the first apps I installed. Great app and for the price is a definite must have! | 677.169 | 1 |
Visualizar/Abrir
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This work aimed to facilitate the study of the content of complex numbers for students in the 3rd year of High School, within a focus covering a geometric context, with the use of Geogebra software, combined with notebook student (SÃO PAULO, 2014). The main motivation of this study was to search for an innovative practice, aiming to improve the quality of the teaching-learning process, in relation to the content, since the numerous difficulties demonstrated by students. The theoretical research was based mainly on the theory of representation semiotics registers of Raymond Duval and analysis of curriculum documents for Middle School. Already the methodology was built based on the steps of the Didactics Engineering idealized by Michele Artigue. The production of information involved mathematical activities performed by 31 students of Higher Education of a Civil Engineering course and between 10 to 12 students (there was variation) of a 3rd year of High School; providing the basis for answering the following research issues: I What knowledge about complex numbers, students of Higher Education bring the baggage of high School? II - That prospect of construction of knowledge the notebook of the Student gives the learning of complex numbers? III - The Geogebra can add the construction of knowledge when articulated to the notebook of the Student, made available by the Department of the São Paulo State of Education? The instruments used to collect the amount of information produced by participants, in empirical step of our research were: questionnaire, written records of tasks (protocols) and images of mathematical activities carried out with the help of Geogebra. The results obtained in the analysis of the questionnaires showed that the knowledge of the students in higher education, as well as the students in the middle school, are negligible in relation to the need of those who follow their studies in the field of exact area. With respect to the results obtained from the implementation of tasks for high school students, using the software proved to be efficient for a geometrized viewing the content in relation to construction of its concepts, which allowed students a much better understanding across the studied content. | 677.169 | 1 |
Elementary algebra is the most basic form of algebra taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. While in arithmetic only numbers and their arithmetical operations occur, in algebra one also uses symbols (such as a, x, y) to denote numbers. 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 to talk about "unknown" numbers, the formulation of equations and the study of how to solve these (for instance "find a number x such that 3x + 2 = 10)
it allows to formulate functional relationships (such as "if you sell x tickets, then your profit will be 3x - 10 dollars")
These three are the main strands of elementary algebra, which should be distinguished from abstract algebra, a much more advanced topic only taught to college seniors.
In algebra, an "expression" may contain numbers, variables and arithmetical operations; examples are a + 3 and x2 - 3. An "equation" is the claim that two expressions are equal. Some equations are true for all values of the involved variables (such as a + (b + c) = (a + b) + c); these are also known as "identities". Other equations contain symbols for unknown values and we are then interested in finding those values for which the equation becomes true: x2 - 1 = 4. These are the "solutions" of the equation.
As in arithmetic, in algebra it is important to know precisely how mathematical expressions are to be interpreted. This is governed by the order of operations rules.
It is then necessary to be able to simplify algebraic expressions. For example, the expression
The central technique is add/subtract/multiply or divide both sides of the equation by the same number, and by repeating this process eventually arrive at the value of the unknown x. For the above example, if we subtract 3 from both sides, we obtain
Expressions or statement may contain many variables, from which you may or may not be able to deduce the values for some of the variables. For example:
(x - 1) × (x - 1) = y × 0
After some algebraic steps (not covered here), we can deduce that x = 1, however we cannot deduce what the value of y is. Try some values of x and y (which may lead to either true or false statements) to get a feel for this. | 677.169 | 1 |
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
Algebra and Trigonometry: Linear Functions
Understanding Linear Functions and the Different Mathematical Operations Related to Them computer connected to the Internet having a working browser.
Description
This course teaches you all the important underlying concepts in Linear functions in mathematics. The knowledge that you gain here can be further completed in our next courses towards a complete mastery of calculus.
This course covers the following topics:
Linear Functions
Modeling with Linear Functions
Fitting Linear Functions to Data (Statistics)
As described above, this course can also be taken in combination with our other courses in this course series. If you're interested in learning mathematics with us all the way up to calculus, please read our "Mathematics" page on "Greatitcourses" website (a Google search will get you there).
Who is the target audience?
Anyone who wants to build a strong foundation of mathematics for any reason.
Anyone who wants to build a successful career in mathematics, engineering, science, etc.
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Learn how to use PTC® Mathcad Prime® 3.0, one of the world's leading tools for technical computing, in the context of engineering, science, and math applications. Quickly harness the power of PTC Mathcad Prime 3.0 to solve both simple and complex problems. Essential PTC® Mathcad Prime® 3.0 is perfect for college students, first-time users, and experienced Mathcad 15 users who are moving to PTC Mathcad Prime 3.0.
Updated from Maxfield's's tools while also demonstrating how users can eff ectively incorporate Microsoft® Excel spreadsheets into the software.
Learn the basics faster: Chapter 1 introduces many fundamentals of Mathcad, allowing the reader to begin using the program in less time.
Learn PTC Mathcad tools in context: Incorporates many applied examples and problems from a wide variety of disciplines.
Includes a link to PTC with instructions on how to purchase the PTC® Mathcad Prime® 3.0 Student Edition (The Student Edition software is intended for educational purposes only.)
"Sinopsis" puede pertenecer a otra edición de este libro.
About the Author:
Brent Maxfield is a Professional Structural Engineer in Utah and a Professional Civil Engineering in California. He graduated Magna Cum Laude from Brigham Young University with a degree in Civil Engineering and earned a Master of Engineering Management degree. He is active in professional associations, having served on the Board of Directors of the Structural Engineers Association of Utah and in the Structural Advisory Committee to the Utah Uniform Building Codes Commission. He has used Mathcad extensively for nearly 20 years. In Essential Mathcad, Maxfield shares his vast Mathcad experience and knowledge.
Descripción Elsevier Science & Technology Books 40545386 Academic Press Inc 2013-11-125196
Descripción Elsevier Science & Technology Books, 201469246N1 | 677.169 | 1 |
The 5 strands are:
Statistics and Probability
Geometry and Trigonometry
Number
Algebra
Functions
Aims of Project Maths
From the NCCA website the main aims of Project Maths are to:
To provide greater coherence and progression between the mathematics experiences of students in primary school and in the post-primary junior cycle, and between junior cycle and senior cycle mathematics make mathematics more relevant to the lives and experiences of students.
To provide an appropriate mathematics education to meet the needs of all learners give greater emphasis to the understanding of mathematical concepts and the application of mathematical knowledge and skill encourage more students to study higher level mathematics.
Mathematics is a wide-ranging subject with many fields and applications. Mathematics gets used everywhere, and everyone can find some use for it. For students it opens doors to careers. No longer just the language of science, mathematics contributes in direct and fundamental ways to business, finance, health and defence. Whether it's managing your monthly budget or a part of your job, mathematics has a place in everyone's life.
What do we Aim to Achieve?
Our aim is to make mathematics more understandable and relative to the pupil's everyday life and teach them how to understand mathematics. We hope to make mathematics more enjoyable for the pupils and give them confidence in problem solving and developing their mathematical thinking. We feel that this understanding of maths will give pupils the essential tools required for achieving good grades in both the junior and leaving certificate maths exam. The importance of mathematics in the pupil's lives has been recognised by many third level institutes and they are now awarding 25 extra points in the leaving cert for a pass in honours leaving cert. The initiative will both reward students for their efforts in studying the subject. Higher-level maths provides students with key skills needed in all business sectors and, in particular, the skills needed for the high-tech jobs Ireland is working to attract. | 677.169 | 1 |
Achieving the level of mathematical knowledge, strenghening mathematical skills and development of logical thinking.
Mastery of mathematical tools necessary to formulate and solve real problems.
Obtaining mathematical knowledge needed for applications in professional cources and other separate knowledge gathering by studying professional literature.
Course contents:
1.
Introduction (allowance 1/1)
a.
Set theory
b.
Propositional calculus
2.
Differential calculus (allowance 12/9)
a.
Function, basis concepts and properties
b.
Sequences
c.
Limit and continuity of function
d.
Derivative of function
e.
Applications of derivatives and curve sketching
3.
Integral calculus (allowance 10/7)
a.
Indefinite integral
b.
Definite integral and its applications
c.
Improper integral
4.
Linear algebra (allowance 12/7)
a.
Vectors. Linear dependence and independence of vectors. Vector space
b.
Matrices and determinants
c.
Systems of linear equations
5.
Polynomial approximation (allowance 7/4)
a.
Solution of algebraic equations
b.
Taylors polynomial, Lagranges interpolation formula
c.
Least square method
Learning outcomes and competences:
Generic competences:
-
ability to apply knowledge
-
ability to make decisions
-
ability to solve problems
-
ability to work independently
-
basic computing skills
Specific competences:
-
Student is able to describe properties of one variable function and analyze it. Furthermore, from graph derivate their properties.
-
Student is able with using limit and integration methods solve improper integral.
-
Student knows approximate function with least square method.
-
Student knows how to use operations with matrices and determinants for solving of systems of linear and matrix equations.
-
Student knows to use derivatives for finding of extreme function values, i.e. its minimums and maximums.
-
Student knows with use of definite integral calculate surface area and volume of rotate solids42 h
practice
28 h
Self-study
preparation for exam
40 h
preparation for regular assessment
10 h
preparation for regular testing
20 h
Total
140 h
Assessment methods:
The exam is written and consists of two parts: computer-based test and a written exam. To pass the exam, it is necessary to get at least 50% in each part. | 677.169 | 1 |
Logic and Representation brings together a collection of essays, written over a period of ten years, that apply formal logic and the notion of explicit representation of knowledge to a variety of problems in artificial intelligence, natural language semantics and the philosophy of mind and language.
Teaching children involves more than knowing your subject and being able to maintain control of a class. Every child that comes into the classroom is unique. All have different home environments, ethnic backgrounds, abilities and learning styles. And every child develops a different relationship with the teacher.
A collection of 20 refereed research or review papers presented at a six-day seminar in Switzerland. The contributions focus on stochastic analysis, its applications to the engineering sciences, and stochastic methods in financial models, which was the subject of a minisymposium.
The MIT Encyclopedia of the Japanese Economy was the first English-language encyclopedia to cover all major aspects of Japan's postwar economy. The second edition has been fully revised and expanded, and includes previously unpublished data as well as coverage of recent developments in the economy.
The solution manual provides step-by-step solutions guiding the student through the reasoning behind each problem in the text. There is also a self-test at the end of each chapter, designed to assess the student's mastery of the material.
Combined in this dictionary are explicit definitions of more than 7,000 mathemathical terms, concepts and relationships – and multilingual indexes giving in alphabetical order their Russian, German, French and Spanish equivalents – covering a broad range of terms from the elementary to the most recent… | 677.169 | 1 |
Definitions, Postulates, and Theorems Explained
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Do your students have trouble understanding the difference between a definition and a theorem? This resource is geared towards geometry students to help them grasp the mathematical terminology used in formal proof.
My students were asking for a resource like this since we use these terms all the time and they had difficulty differentiating. It can be used as a handy resource to go along with lists of definitions, postulates, or theorems they have in their notes. | 677.169 | 1 |
Graph2Go - Graphing calculators are instrumental in teaching and learning mathematics. It is an environment that supports conceptual understanding of functions in general, and school algebra and real analysis in particular. Especially, it enhances connections between graphic and symbolic representations. A major objective of algebra teaching is equipping learners with tools to mathematize their perceptions. A multi-representational approach has the potential to shift the focus of solving even traditional problems from assigning and solving for an unknown to analyzing the various processes and relations among those processes. The integration of multiple representations of function creates opportunities for developing a wider range of solution methods to traditional problems. Zooming in on the use of the graphing calculator, researchers point on four patterns and modes of use: computational tool, data analysis tool, visualizing tool, and checking tool.
Dynamic transformations are a unique facility of Graph2Go.
Dynamic control involves the direct manipulation of an object or a representation of a mathematical object. As the driving input is the letter-symbolic one, the transformations are carried out on the numbers involved in the function's expression. Thus, by parameterizing an example we turn it into a family of functions. Research suggests that the kinesthetic relation between the user and the object on the screen can have an important role in developing a deeper understanding of the mathematical concept.
Basic features of Graph2Go:
* Graphs of single variable function expressions.
* Dynamic graphing of transformed expressions.
* Points of interest (maximum, minimum, inflection_ are marked and their numerical values are presented.
* Graph and expression of the derivative function.
* Graph, expression of the integral function's family.
* Area expressed by the integral of a given function.
* Zooming and rescaling options.
Graph2Go is a special purpose graphing calculator that operates for given sets of function expressions. The given families of function expressions and the tools that support easy changes of any given example have been designed for fast and easy use with the small keyboard.
Suggested Activities
Below is an interesting example that combines the use of visual thinking with an analytic task and has the potential to enhance procedural operations with conceptual understanding:
Prove or refute each of the following statements.
Explain and demonstrate your method and answer using Graph2Go, paper and pencil, or mental operations
* The derivative of a family of functions cannot be a single function.
* [k*f(x)]' is equal to k*[f(x)]'
* [k*(f(x)]' is equal to [f(kx)]'
If you study calculus with the support of graphing calculators, see the AP (Advanced Placement) calculus site for examples of calculus assessment problems (carried out with or without graphing tools).Quad2Go Quad2Go - Explorations with Quad2Go are especially appropriate for 11-12 year old students. Teaching geometry to students of this age focuses on the critical attributes of quadrilaterals and on the hierarchical relations among them. Learning means identifying critical attributes and non-critical attributes
Fit2Go Fit2Go supports exploration and modeling activities. It supports data collection by proposing a model that can appropriately describe the user's data. The tool highlights the numeric aspects of a phenomenon. Together, Sketch2Go and Fit2Go provide a comprehensive view of models and modeling
Sketch2Go Sketch2Go - encourages visual exploration of phenomena by providing qualitative indication of the ways in which the sketch drawn by the user changes. The sketch is a diagrammatic representation that attempts to help the viewer focus on the principles rather than on tedious details of the represented phenomenon. Phenomenon can refer to processes outside of mathematics (e
BrainBooster Train your brain with this simple maths and time it to beat your own record
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Tropical geometry is a combinatorial shadow of algebraic geometry, supplying new polyhedral instruments to compute invariants of algebraic forms. it truly is in line with tropical algebra, the place the sum of 2 numbers is their minimal and the product is their sum. This turns polynomials into piecewise-linear capabilities, and their 0 units into polyhedral complexes. those tropical types hold a stunning volume of data approximately their classical opposite numbers. Tropical geometry is a tender topic that has gone through a fast improvement because the starting of the twenty first century. whereas constructing itself as a space in its personal correct, deep connections were made to many branches of natural and utilized arithmetic. This ebook deals a self-contained advent to tropical geometry, appropriate as a direction textual content for starting graduate scholars. Proofs are supplied for the most effects, similar to the elemental Theorem and the constitution Theorem. a variety of examples and specific computations illustrate the most thoughts. all the six chapters concludes with difficulties that may aid the readers to perform their tropical talents, and to realize entry to the study literature.
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Ncert Solutions
Model Solutions
Explanatory Videos
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NCERT solutions are extremely useful for students as this segment includes detailed answers to the questions mentioned in NCERT textbooks. These solutions help students get the underlying concepts of each chapter (in respective subjects) and they can compare their answers with the same.
How will NCERT Solutions help you study better?
FREE online questions and model answers for all classes
Complete and customized answers for each question in consonance with NCERT textbooks
Extensively researched solutions created by subject matter experts
Answers have been framed in lucid and easy to understand language
Videos and animations to support the solutions of difficult questions in Mathematics
Answers enhanced with graphs and illustrations for better comprehension of concepts
Easy and quick access of chapter-wise questions and answers
Topics and concepts explained thoroughly with appropriate examples
Helpful for quick revisions during examination or tests
NCERT solutions are one of the biggest contributors in effective exam preparation for CBSE students. Why students prefer studying using these textbook solutions over other sources is due to the recurring instances of similar questions appearing in CBSE Board exam question papers. The questions and solutions are simplified, but clear all possible doubts easily for students is what makes teachers, tutors and parents recommend NCERT textbooks.
The NCERT solutions offered by us are arranged in an extremely efficient manner. Mirroring the order of chapters and topics in the textbooks, the answers give students the opportunity to explore the traditional or evident method of completing a question. The solutions are smart, which means that they reach the conclusion using the ideal method, and do not confuse students. The language is straightforward, saving students' time and effort taken in preparation.
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Meritnation.com is an online education portal that provides interactive study material for students of classes 1st to 12th for CBSE, ICSE, Maharashtra (MSBSHSE), Karnataka (KSEEB) Kerala (SCERT) and Tamil Nadu boards. Complete with elaborate live classes, multimedia tutorials, interactive exercises, practice tests and expert help, we endeavour to make school easy for students and help them score more. We also provide free NCERT solutions, subject-wise synopses and chapter-wise revision notes for classes 1st to 12th for a thorough understanding of concepts right from a basic to an advanced level of difficulty. Our products are carefully designed to ensure maximum learning through proven techniques such as conceptual videos, adaptive learning and collaborative learning methods.
In addition to curriculum aligned study material, Meritnation.com has an extensive personality development section that helps students identify and enhance their soft skills for a holistic development. We also offer online courses to help students prepare for important competitive exams such as JEE Mains and JEE Advanced, PMT/AIPMT/State PMTs, CPT, BBA, NDA and Hotel Management. | 677.169 | 1 |
arson's TRIGONOMETRY is known for delivering sound, consistently structured explanations and exercises of mathematical concepts Enhanced WebAssign® features fully integrated content from the text, with the addition of End-of-Section problems and Chapter Tests, as well as problem-specific videos, animations, and lecture videosFresh Chapter Openers highlight real-life problems that connect to the examples and exercises presented in the following chapter.
Innovative Summarize Features help students organize the lesson's key concepts into a concise summary, providing a valuable study tool at the end of each section.
Unprecedented How Do You See It? Exercises in every section present real-life problems that students solve by visual inspection using the concepts in the lesson.
Original Checkpoint Problems encourage immediate practice and check students' understanding of the concepts in the paired example.
New Series Companion Website features chapter projects, data tables, assessments, study tools, video solutions, and more to support students outside the text.
Enhanced Exercise Sets deliver more rigor, relevancy, and coverage than ever before and feature multi-step, real-life exercises to reinforce problem-solving skills and mastery of concepts.
Expanded Section Objectives offer students the opportunity to preview what will be presented in the upcoming section.
Enriched Remarks reinforce or expand on concepts helping students learn how to study mathematics, avoid common errors, address special cases, or show alternative or additional steps to a solution of an example.
Up-to-the-minute homework support through CalcChat.com, an independent website, provides students with free solutions to all odd-numbered problems in the text.
Features
Side-By-Side Examples help students see not only that a problem can be solved in more than one way but also how different methods--algebraically, graphically, and numerically--yield the same result. The side-by-side format also addresses many different learning styles.
Algebra Helps direct students to sections of the textbook where they can review algebra skills needed to master the current topic.
Technology Features offer suggestions for effectively using tools such as calculators, graphing calculators, and spreadsheet programs to deepen student understanding of concepts, ease lengthy calculations, and provide alternate solution methods for verifying answers obtained by hand with Instructor's Website
ISBN: 9781337278539
This time-saving manual contains solutions to all exercises from the text, including Chapter Review Exercises and Chapter Tests.
PowerPoint® with Image Library Slides on Instructor's Website
ISBN: 9781337278522
Microsoft® PowerPoint® slides and image library for the entire book, posted on the Instructor Companion Website, let you incorporate images from the book right into your lectures.
Cengage Learning Testing, powered by Cognero® Instant Access
ISBN: 9781337278515 This is available online via
Student Solutions Manual
ISBN: 9781337278485
This guide offers step-by-step solutions for all odd-numbered text exercises, Chapter and Cumulative Tests, and Practice Tests with solutions, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Annotated Instructor's Edition
ISBN: 9781337278478
FOR STUDENTS
Student Solutions Manual
ISBN: 9781337278485
This guide offers step-by-step solutions for all odd-numbered text exercises, Chapter and Cumulative Tests, and Practice Tests with solutions, giving you a way to check your answers. | 677.169 | 1 |
Qualification update
Our AS/A Level Mathematics provision is changing. New AS/A Level qualifications in Mathematics and Further Mathematics are being developed for first teaching from September 2017. To find out more visit our new qualification pages below.
You may also be interested in our Core Maths qualifications, designed to enable learners to strengthen the mathematical knowledge and skills which they have learnt at GCSE so that they can apply them to the problems which they will encounter in further study, life and employment.
This qualification is for all post-16 students who have achieved a grade C (or better) in GCSE Mathematics.
The key aim is to provide students using maths in Biology, Business Studies, Chemistry, Geography, IT or Psychology with the skills needed to solve mathematical problems arising in their other subjects, employment and everyday life.
Students can either take a 60 guided learning hour course, Introduction to Quantitative Methods, earning a Level 3 certificate, or progress to take a full AS Level in Quantitative Methods. The AS Level is attained when the unit Introduction to Quantitative Methods is combined with Decision 1 and Statistics 1 from the GCE Mathematics (MEI) suite. | 677.169 | 1 |
Maths
JEE Main and JEE Advanced Syllabus of Differential Calculus
Differential Calculus is one of the most important topics in the preparation of IIT JEE. This is the easiest part of Calculus and there is no doubt in the fact that it is scoring too. It is also important to attain proficiency in Differential Calculus as it is a prerequisite to the learning of Integral Calculus too.
Differential Calculus is a branch of mathematical analysis which deals with the problem of finding the rate of change of a function with respect to the variable on which it depends. So, differential calculus is basically concerned with the calculation of derivatives for using them in problems involving non constant rates of change. Applications also include computation of maximum and minimum values of a function.
The study of Differential Calculus includes Functions, Sets and Relations though
they are considered to be a part of Algebra. Limits, Continuity and Differentiability are
the favorite topics of those who have a bent towards Differential Calculus. It is
not only an easy topic but also fetches direct question in the examination. A person
who has already done a good practice of this chapter is also likely to do well in
the next topic of Differentiation. The lifeline of Differential
Calculus is basically the topics which include the application of Derivatives i.e.Tangent
and Normal and Maxima and Minima. Differential
calculus is closely related to integral calculus. In fact, differentiation is the
reverse process of integration.
Here we shall discuss the main heads that are counted under differential calculus.
These topics have been discussed in detail in the coming sections: Relation: A relation is a
set of ordered pairs and is usually defined by a rule. The domain of a relation
is the set of all first elements (usually x values) of its ordered pairs.
The range of a relation is the set of all second elements (usually y values)
of its ordered pairs. Function: A function is a relation
for which each value from the set of the first components of the ordered pairs is
associated with exactly one value from the set of second components of the ordered
pair.
Here is an example of a function:
It is an important example as students are likely to get confused as to whether
it is a function or not. As stated in the definition, since each value of x is associated
with exactly one value of y (though in this case that y is same for every x) hence
it is a function.
Example: Consider f to be defined by
{(0,0),(1,1),(2,2),(3,3),(1,2),(2,3),(3,1),(2,1),(3,2),(1,3)}
This is a relation (not a function) since we can observe that 1 maps to 2 and 3, for instance Limit of a function:
Suppose f : R → R is defined on the real
line and p,L ∈ R. Then we say that the limit of the function
f is l if
For every real ε > 0, there exists a real δ > 0
such that for all real x,
0 < | x − p | < δ
implies | f(x) − L | < ε.
Mathematically it is represented as Example: Find the limit of the function f(x) = (x2-6x
+ 8) / x-4, as x→5. Solution:
The limit is 3, because f (5) = 3 and this function is continuous at x
= 5.
Such easy questions are not asked in the exam so it was just meant to clear the
concept of limit. We now move on to a bit difficult question: Example: Find the limit of the function g(x) = √(x-4) -3 / (x-13)
as x approaches 13. Solution: In such a question you first need to reduce the function
in simple form so that the computation of limit becomes simple.
First rationalize the numerator and denominator by multiplying by its conjugate
So, [√(x-4) -3] / (x-13) x [√(x-4) +3]/ [√(x-4) +3]
On multiplying and solving we get the result,
1/ √( x-4) +3
Now since the terms have been simplified the limit can now be calculated by substituting the value of x as 13.
Hence putting x=13 in the last equation we get the limit as 1/6.
For more on limits, you may refer the video Continuity of a function
A function y = f(x) is continuous at point x=a if the following three conditions are satisfied:
(1) f(a) is defined ,
(2) exists (i.e., is finite)
A function is continuous when its graph is a single unbroken curve. This definition proves to be useful when it is possible to draw the graph of a function so that just by the graph the continuity of the function can be judged.
Differentiation: Differentiation is an operation that allows us
to find a function that outputs the rate of change of one variable with respect
to another variable. The derivative of a function at a chosen input value describes
the rate of change of the function near that input value. The process of finding
a derivative is called differentiation. Geometrically, the derivative at a point
is the slope of the tangent line to the graph of the function at that point, provided
that the derivative exists and is defined at that point.
Since Differential Calculus is new to the students as they do not study it
in their 10th standard examination, so they are advised to master the topic by
practicing questions on Limits, Continuity and Differentiability. The
preparation of Differential Calculus also gives another opportunity to prepare
and revise the chapter on Functions, Sets and Relations. To get an idea about
the types of questions asked you may also consult the Previous Year Papers. | 677.169 | 1 |
Painless Algebra
If you break out in a cold sweat at the very mention of algebra, this book will show you how to relax and master the subject without pain. The problems you now consider confusing are taken slowly, step by step. Simply follow the painless steps and soon you will wonder why you were ever confused in the first place! You start with integers, progress to simple equations with one variable, then move forward to gain a clear understanding of inequalities, systems of equations, exponents, and roots and radicals. Finally, you graduate to mastery of quadratic equations. Along the way, you will find fun-to-solve "brain tickler" problems in every chapter. Each "brain tickler" comes with an answer, but before you know it, you will be figuring out all the answers for yourself.
Product Options
Author: Lynnette Long
Publisher: Barron's
Type of Binding: Paperback
Number of Pages: 298
Scripture Version Used: N/A
For: Middle School and High School Students
Customer Reviews
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Algebra II is the fork in the road. Those who succeed in this second part of the algebra sequence are well on their way to precalculus, calculus, and higher mathematics, which open the door to careers in science, engineering, medicine, economics, information technology, and many other fields. And since algebraic thinking is found in almost every sphere of modern life, a thorough grounding in this abstract discipline is essential for many nontechnical careers as well, from law to business to graphic arts.
Algebra I is one of the most critical courses that students take in high school. Not only does it introduce them to a powerful reasoning tool with applications in many different careers, but algebra is the gateway to higher education. Students who do well in algebra are better prepared for college entrance exams and for college in general, since algebra teaches them how to solve problems and think abstractly—skills that pay off no matter what major they pursue.
'An Introduction to Neural Networks' falls into a new ecological niche for texts. Based on notes that have been class-tested for more than a decade, it is aimed at cognitive science and neuroscience students who need to understand brain function in terms of computational modeling, and at engineers who want to go beyond formal algorithms to applications and computing strategies… | 677.169 | 1 |
Matlab
MATLAB is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis, and numerical computation from Mathworks. Here on campus, we use it mostly in the department of Math and Computer Science. We have a network license for MATLAB.
MATLAB is available in the Barnes, Palmer 2, Math Department, and Library North Basement labs. | 677.169 | 1 |
Civics and economics eoc review - where added&
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Friendly Conversational Tone The lectures - one for each lesson in the textbook - provide hours of instruction. Activities teach prefixes will eof listening to (and watching) an explanation for each lesson rather than reading it out of a book. Designed for homeschoolers studying independently, Teaching Textbooks uses far less irrelevant jargon than other textbooks, while still retaining all the terms that students need to know for those important standardized tests, and the tone is friendly and conversational. This is a brilliant idea, long overdue and skillfully done. Workbook Includes Lesson Economicz The Teaching Textbooks program also civis a workbook in which your child will do daily math assignments. Designed specifically for independent learners, the Teaching Textbooks workbook contains a summary of the lectures from the CD, which allows your child to review key points from the lesson as necessary civics and economics eoc review working the problems. The workbook also comes with civics and economics eoc review answer key and a test bank.
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There is no integer that can go wholly into both 50 and 51. Both 27 and 84 are divisible by 3. Inequalities are not as hard as they look. Civics and economics eoc review multiplying or dividing by a positive number, the inequality direction stays the same. Interest calculations are most commonly used with civocs problems. First, define your terms. Second, calculate the interest.
Topic: "Download civics and economics eoc review"
We also have several solving quadratic equations by taking the square roots, factoring, with the quadratic formula, and by completing the square. Our Rational Expressions Worksheets are free to civics and economics eoc review, easy to use, and very flexible. These Rational Expressions Worksheets are a good resource for students in the 5th Grade through the 8th Grade. Telling Time and Elapsed Time Lesson Plans and Refiew We just wrapped up our elapsed time unit and let me just say. | 677.169 | 1 |
Mathematics 6 - Saxon Pre-Algebra - Live Online Course 2017-2018
Quick Overview
In this Live Online Course students will cover an introduction to geometry and discrete mathematics.
Details
This pre-algebra course provides an introduction to geometry and discrete mathematics. Topics covered include fraction, decimal, and mixed number operations, scientific notation, prime and composite numbers, order of operations, coordinates, exponents, square roots, ratios, algebraic expressions, solving equations with one variable, working with signed numbers, scientific notation, ratios, geometry fundamentals, probability, the Pythagorean Theorem and more. This course will solidify basic mathematics skills and prepare the student for success in Algebra I. Homework will average 3 - 4 hours per week.
Mathematics 6 - Pre-Algebra Saxon is taught by an expert instructor in the Veritas Virtual Classroom and is limited to only 20 students per course.
A Digital Tablet, a protractor and a ruler with inches and mm/cm are also recommended, but unfortunately, this item is not available through Veritas Press. ClickHERE | 677.169 | 1 |
Mathematics for Elementary School Teachers is designed to give you a profound understanding of the mathematical content that you are expected to know and be able to teach. The chapters integrate the National Council of Teachers of Mathematics (NCTM) Standards and Expectations and the new Common Core State Standards, as well as research literature. The five NCTM Process Standards of problem solving, reasoning and proof, communication, connections, and representation highlight ways that teachers present content, the ways that students learn content, and various ways that students can demonstrate procedural and conceptual understanding. The worked examples and homework questions provide prospective elementary school teachers with opportunities to develop mathematical knowledge, understanding, and skills that they can apply in their own classrooms effectively. The learning path begins with the "Where Are We Going?" Chapter Openers, worked Examples with Yellow Markers that indicate the Process Standards throughout the text, to the Concept Maps, to the Section Question Sets with their "refreshers" of Process Standards, to the Chapter Organizers with Learning Outcomes and a list of the corresponding Review Questions, and finally, conclude at the Chapter Tests with their overarching Learning Outcomes.
Meet the Authors
Ricardo Fierro,
California State University, San Marcos
Ricardo Fierro received a Bachelor of Science degree in Mathematics from the University of California, Davis, and a Ph.D. in Mathematics from the University of California, San Diego (UCSD). He was awarded the President's Dissertation Year Fellowship while completing his Ph.D. at UCSD, and the President's Postdoctoral Fellowship at University of California, Los Angeles, where he continued his research. He has been a faculty member in the Department of Mathematics at California State University San Marcos (CSUSM) since 1992. In addition to teaching mathematics for prospective elementary school teachers, he has taught such courses as numerical analysis and computing, optimization, modern geometry, probability and statistics, linear algebra, college algebra, modern algebra, discrete mathematics, and business calculus. To enrich his understanding of teaching at the grade school level, he spent a sabbatical leave teaching fourth, fifth, and sixth graders at an elementary school, and regularly volunteers as a mathematics teacher at local elementary schools. Professor Fierro is a member of the American Mathematical Association of Two-Year Colleges and the National Council of Teachers of Mathematics. He is married with two children.
Features
The relevant NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS (NCTM) PRINCIPLES AND STANDARDS OF MATHEMATICS (2000) appear in the exposition. These Principles and Standards that are adopted by the NCTM represent the most significant and influential collaboration among educators to improve mathematics education at a national level. It is the gold standard used by many states to meet the No Child Left Behind Act of 2001 that requires challenging standards for grades 3-8 mathematics and annual assessment.
The National Center for Education Statistics administers a nationwide standardized test—National Assessment of Educational Progress (NAEP)—to a pooled random sample of fourth, eighth, and twelfth graders. NAEP has released selective questions, called RELEASED ITEMS in the textbook, from various fourth- and eighth-grade tests to help improve student learning. A sampling of these questions appear in the text, as do questions from state tests, to illustrate what elementary students will see in standardized assessment tests.
BOXED DEFINITIONS AND THEOREMS/PROPERTIES: allow instructors and students to easily distinguish between definitions, which present the working vocabulary of mathematics, and properties and theorems, which are mathematical techniques and concepts.
COMMON CORE STATE STANDARDS (CCSS) are also referenced in the text. The CCSS are "aligned with college and work expectations; build upon strengths and lessons of current state standards; and include rigorous content and application of knowledge through high-order skills." The idea behind CCSS is that "Common standards will help ensure that students are receiving a high quality education consistently, from school to school and state to state. Common standards will provide a greater opportunity to share experiences and best practices within and across states that will improve our ability to best serve the needs of students." States that voluntarily accept the Common Core standards would eliminate their own state standards.
In addition to the NCTM Content Standards, there are five NCTM PROCESS STANDARDS: Problem Solving, Reasoning and Proof, Communication, Connections, and Representation. The Process Standards are integrated by an icon throughout the text that highlights where the standard appears and specifies which standard is being used. In addition, the homework problems are categorized by the applicable Process Standard to give prospective teachers a chance to explore a particular process in more depth and improve their perception of problems that assess the process. This unique differentiation is important because the processes connect students to the teaching and learning of mathematical content.
"Where Are We Going?" CHAPTER OPENERS identify upcoming topics and help to place the material to be presented in a manageable context.
Unique CONCEPT MAPS visually recap ideas and help you synthesize the material by showing how key mathematical ideas are related.
PreK–8 problems from actual elementary math textbooks appear in CLASSROOM CONNECTIONS—with explanations—giving prospective teachers another opportunity to see that the topics they are studying are relevant to the elementary curriculum. Actual pages from these textbooks are also shown as appropriate to provide context.
A VARIETY OF HOMEWORK PROBLEMS appears at the end of each section and chapter to increase interest and flexibility in teaching. They reflect the content and processes that prospective elementary school teachers need to know and teach. They support the national trend of integrating instruction, assessment, content standards, and process standards.
Over several hundred WORKED EXAMPLES are included to illustrate concepts, techniques, and processes of mathematics for students to master.
A CHAPTER ORGANIZER grid summarizes key learning outcomes and ideas presented in the chapter followed by a set of review questions which offers a variety of additional problems to reinforce students' learning. The chapter test is organized by learning outcomes so students connect the link between objectives and concepts, and how knowledge is acquired which reflects the national trend of integrating instruction, assessment, and NCTM content and process standards1133363729
The Instructor's Resource Manual provides worked-out solutions to all of the problems in the text.
PowerLecture with ExamView®
ISBN: 9781133363736
PowerLecture™ instructor resources are a collection of book-specific lecture and class tools on either CD or DVD. The fastest and easiest way to build customized, media-rich lectures, PowerLecture includes chapter-specific PowerPoint® presentations, ExamView® computerized testing, images, animations and video, instructor manuals, test banks, useful web links, and more. PowerLecture media-teaching tools are an effective way to enhance the educational experience.
Solutions Builder
ISBN: 9781133525431
Activities Manual
ISBN: 9781133363712
The activities manual is geared toward helping students grasp the main ideas of each section that is covered in the text with open-ended activities that allow students to practice and apply the knowledge that they have learned.
Student Solutions Manual
ISBN: 9781133363743
ontains fully worked-out solutions to selected exercises 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 of the book "Introductory Mathematics: Algebra and Analysis":
This text provides a lively introduction to pure mathematics. It begins with sets, functions and relations, proof by induction and contradiction, complex numbers, vectors and matrices, and provides a brief introduction to group theory. It moves onto analysis, providing a gentle introduction to epsilon-delta technology and finishes with continuity and functions. The book features numerous exercises of varying difficulty throughout the text.
Reviews of the Introductory Mathematics: Algebra and Analysis
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Geoff Smith
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Algebra I & Pre-Calculus
Algebra I Introduction to algebra and the concepts of solving problems for an unknown variable. This class will progressively prepare the student for the EOC Algebra I STAAR exam.
Pre-Calculus Intent of this higher level math class is to prepare the student for College level Algebra.
Recent Posts
Flipped Classroom
Pre-Calculus students, come prepared to experience a new way to learn the material. We are going to begin using the flipped classroom concept, view a lesson via the web, homework and problems done in class. | 677.169 | 1 |
SCIENCE AND SANITY - online book
An Introduction To Non-aristotelian Systems And General Semantics.
The notation by suffixes is very convenient and is very much used these days. The first suffix denotes the row, the second the column in which the element is situated. Usually the comma dividing the two numbers in the index is dropped and the coefficients are written simply an, instead of ai,\. In general the element ttj,*, or a,*, represents the element in row i and column k.
The elements lying in the diagonal joining the upper left-hand to the lower right-hand number are called the principal diagonal. In our example we notice that the elements in the diagonal are such that ik.
We have definite rules by which we can arrive at the solution of our equations, once the coefficients, which are the elements of the determinant, are given. In general, the determinants are treated as a functional form.
If m and n are positive integers, a manifold, or system of mn ordered quantities or elements arranged in m horizontal and n vertical rows, will be called a rectangular matrix and we may use the notation:
The numbers m and « are called the orders of the matrix. If m =« the matrix is called a square matrix. Without loss of generality we can treat any rectangular matrix in whichas a square matrix by supplementing the missing rows
and columns with zeros.
A matrix of the type,
where for, is called a unit matrix.
The matrix
is called a diagonal matrix. In the new quantum mechanics a diagonal matrix is independent of t and represents a constant of the classical theory. The reverse is not necessarily true. The operation of differentiation can be expressed in terms of multiplication of matrices with the aid of the unit matrix.4
Equations in which matrices are equated are called matrix equations. If the equations involve only one unknown matrix, which does not occur more than once as a factor, such equations are called matrix equations of the first degree. | 677.169 | 1 |
Top Algebra Errors Made by Calculus Students
Linear Function Behavior (LFB)
Lines through the origin are peculiar in that they have an
expression of the form , where is a constant (the
slope). This formula makes possible the following
``additive" property:
For the particular choices of and , we would have
Despite students' tendancies to treat every function as
additive, other functions just do not have this property.
Typical mistakes made include:
Cancelling Everything in Sight (CES)
Seeing a complicated fraction become less ugly as
elements are cancelled from both the numerator and denominator
can be something of an enjoyable experience. One's first
exposure to this magical process usually comes in grade school
when reducing fractions, such as
High school algebra classes build upon this, showing us that
we may also cancel expressions involving variables, as in
What some students do not notice is that these cancellations
only are performed once the numerator and denominator are
factored. Factoring a numerator (or denominator) turns
it into an expression which is, at its top level, held together
by multiplication. For instance, in the expressions
To be sure that one performs valid cancellations only, it is
necessary to
be patient, making sure to factor numerator and denominator
first, and cancelling only those factors common to both, and
accept that many times no factorization is possible, at
least none that leads to a common, cancellable factor.
With this in mind, cancellations such as those below may only
be labelled instances of someone ``cancelling everything in
sight", with no attention given to the discussion above, and
having no validity whatsoever.
Any attempt to simplify the original fraction (rational
expression) should start with factoring:
at which stage we see that there is no matching factor between
those of the numerator -- namely, and --
and those of the denominator -- and . Factoring,
in this case, did not lead to any cancelling, as is often the
case.
Confusing Negative and Fractional Exponents (CNFE)
Students can make a variety of mistakes when it comes
to working with exponents. Two of the most common are
Multiplying Exponents that should be Added (MEA),
and Adding Exponents that should be Multiplied (AEM).
This section does not deal with either of these, but rather
with a problem that some students have applying
two basic rules about exponents, the ones concerning
reciprocals and roots. Specifically, these are
respectively, where the understanding is that a square
root (
) is to be taken as
(
).
The first of these says that
a factor of the denominator (see the discussion on
CES) raised to a power (be it positive or negative)
may be written as a factor to the oppositite power of
the numerator (i.e., a power becomes , a
power becomes ). The only change is to
the sign of the exponent. An example of a valid
application of this rule is
The second rule shows how to write a root as a power,
which can be especially helpful in calculus when a derivative
is desired. Things like
Some students seem to confuse these two rules. The main
errors seem to come from students trying to reciprocate
the wrong thing
or from students putting a minus in when none is required
Multiplication Ignoring Powers (MIP)
Another law of exponents frequently misunderstood by students is
This means that such statements as
are correct. But many students ignore the significance
of having identical powers in these multiplications. They
make statements like the following, all of which are
incorrect:
Equation Properties for Expressions (EPE)
Early on in one's high school algebra courses one learns
several properties of equality -- namely
Addition/Subtraction Property of Equality:
One may add/subtract the same quantity to/from both
sides of a given equation, and the solutions of the
resulting equation will be the same as those of the
original (given) one.
Multiplication/Division Property of Equality:
One may multiply/divide both sides of a given equation
by the same nonzero quantity, and the solutions
of the resulting equation will be the same as those of
the original (given) one.
Notice that both of these properties pre-suppose that we
start with an equation, usually one we are supposed
to solve (say, for ). These properties are helpful
in achieving that goal, as in:
Solve :
Add 1 to both sides:
Divide both sides by 3:
or,
solve
:
Multiply both sides by the never-zero quantity :
Subtract 5 from both sides:
Divide both sides by 4:
.
In contrast, these are not, generally speaking, properties
one uses when trying to simplify an expression. (There
are exceptions to this, such as in the simplifying of
and
using integration by parts, but these are relatively rare.)
Students asked to find the derivative of
may find it easier to work with the function
but they shouldn't be under any illusions that and
are the same functions, nor that they have
derivatives that are equal. If one is simplifying
an expression like
it may be tempting to multiply by , which gives
but, of course, multiplying by changed the expression.
One must both multiply and divide by (equivalent
to saying that we're multiplying by ) if the expression
is going to remain the same (but hopefully simplified):
Another example is in simplifying the difference quotient
.
which cannot be further simplified.
Multiplication Without Parentheses (MWP)
The discussion here necessarily must begin with an appeal
to the order of algebraic operations (OO).
These are rules
of hierarchy as to which operations to perform 1st, 2nd, etc.
when an algebraic expression requires more than one operation
be performed. There are three levels of hierarchy:
powers,
multiplication and division, and
addition and subtraction.
When faced with an expression like the one below that has both
an addition and a multiplication in it, the order of operations
dictates that the multiplication be performed first:
The levels above do not give the whole story, however. For
instance, what if an expression has both an addition and a
subtraction, operations which appear at the same level? The answer
here is that operations appearing on the same level are always
performed left-to-right:
Also, one may use parentheses to override these rules. Things
in parentheses are performed before things outside of those
parentheses, starting from the inside and working out. So
while
and
These order of operations apply to expressions involving
variables as well. Thus
In this light, acceptable notation for the product of two
expressions like and is
not, as so many students write,
Frivolous Parentheses (FP)
There really isn't an error, per se, with using
too many parentheses. Nevertheless, students who consistently
employ more parentheses than needed are demonstrating as much
of a lack of understanding of the order of algebraic operations
as those who use too few. Expressions such as
The properties of equality that were mentioned earlier are, by some
students, implemented incorrectly even when the situation calls for
their use. For instance, when solving an equation
like
two steps are called for:
and
Notice that, in the expression , the order of operations
dictates that the multiplication by 3 comes before the addition of
7, and the ``undoings" of these processes -- the subtraction of 7 and
the division by 3 -- were carried out in reverse order. That is not
to say that we could not have undone things in a different order, but
students who do so often make the following error. Dividing by
3, they often neglect the fact that all terms on both sides
are to be divided by 3. In other words, after dividing by 3 they
write
They are too set on the idea that they will be subtracting 7 from
both sides to realize that, having divided by 3 first, it is not
7, but rather , which must be subtracted, giving the same
answer as before. One other note is in order here. If
parentheses appear in an equation such as
then the order of operations are preempted (the subtraction within
the parentheses comes before the multiplication by 3). In solving
for , we may of course, distribute the 3, thereby eliminating
the parentheses and making the problem appear like the last one
discussed. Even fewer steps are required if one just ``undoes" the
multiplication and subtraction in their opposite order:
and then
Now let us return to the equation
and investigate the more telling errors that gave the titles
UMD and UAS to this section. Some
students recognize the need
for two steps (like those carried out when this equation was
being considered above) to isolate , but have little feel
for which operations will achieve this. For
instance, realizing that, like the on the right-hand side of
the equation, is a ``non-" term, a student may write
misunderstanding that she has subtracted 7 on the left
side, but divided by 7 on
the other side. The original equation and the new one no longer
have the same solutions as a result. The same student may then
recognize that she needs to move the over to the other side.
Since the 3 is multiplied by the , she should ``undo" this by
dividing both sides by 3. But she may (wrongly) write
having divided on the left but subtracted on the right. Again,
the solution is different from the one that solved the
original equation , namely .
Worse still is when a student thinks he can solve in one step
(that is, take care both of the multiplication by 3 and the addition
of 7 via one operation). Such a student may write something like
Again, the answer this student gets,
, is different
than the correct one .
Misunderstood Relationship between Roots and Zeros (MRRZ)
Much of one's mathematical experience prior to the calculus is spent
in solving equations. There are the kind of equations, known as
identities, where every number in the domain is a solution.
The equation
is such an identity.
It is not this, but the other type of equation, known as a
conditional equality, that one learns to solve, precisely
because solutions, also known as roots, of conditional
equalities are not everywhere to be found. Often there are very
few numbers, perhaps even none at all, which make a conditional
equality true.
Another fact about conditional equalities is that comparatively few
of them may be solved exactly. Leaps in technology have made it
commonplace for students, with the purchase of a handheld calculator,
to have at their fingertips powerful graphing capability and numerical
methods for finding approximate solutions to many, perhaps even
most conditional equalities. This does not mean that one should
forego learning the algebraic techniques which lead to exact solutions,
thinking that deftness in pushing the right pair of buttons is an
appropriate substitute for the thinking processes such algebraic
methods introduce. Still, there is added value in the knowledge one
gets by investigating graphical methods. By these methods
one comes to think of the solutions of, say,
as the -values of points of intersection between the graphs
of the two functions
As another example, solutions of the equation
would be found at points of intersection between the graphs of
It is in solving equations like this latter one that students become
confused. What some students do is the following:
In mathematical terms, the student who does these steps has found the
zeros of
; that is, the values for which
make the output of be zero. There are several ways to see that
this work is wrong. One way to see it is that, in the equation, we
want values of whose output value is , not zero. Another angle
which reveals the errors is the one that notes that, while there are a
lot of pairs of numbers which may be multiplied to give (-6) --
(-1) and 6, 12 and (-1/2), 55 and (-6/55) are three such pairs --
one thing which we can say for certain is that neither of the numbers
in the pair is zero, which is quite counter to the idea of setting
the factors equal to zero. (Of course, neither is it enough to set
the factors equal to (-6), as in
since it is not enough for either one of these conditions to
hold by itself; that is, if then we would need the other
factor to be equal to 1 in order for their product to be
, and clearly these things cannot occur at the same time.)
In summary, the error occurs in finding the zeros of a function
and taking to be the roots of the equation, when the two concepts do not
coincide. There is a simple way to make them coincide. We simply
make one side zero (using a valid algebraic step, of course).
The zeros of
are the numbers which make
equal zero, and that is exactly what we want in a solution
of the equation
, so the two concepts coincide.
Why do students mess this up? The most likely answer is that many
are looking to do as little work as possible, and bringing the
over makes factoring a more difficult job (it is harder
to factor than to factor ); of course,
the quadratic formula is an option for this case. What may help
to avoid this confusion is remembering this graphical interpretation
of what one is doing (still applied to the example above):
Solutions of an equation like correspond
to points of intersection between the two sides, considered
as functions, of the equation (i.e., the function
and the function, in this case a constant one, ).
If the two functions are combined into one function on one
side of the equation, there is still a second function, the
zero function, that remains on the other side. Now we have
in place of the old problem a new one (but entirely equivalent)
of finding the solutions that correspond to points of intersection
between the new left-hand side (in this case )
and the new right-hand side (here zero).
When our combining of terms has left one side of the equation
zero (which, when considered as a function, has the -axis
as its graph), one may solve the equation by finding the zeros
of the nonzero side of the equation.
Multiplication Not Distributive (MND)
In precalculus/algebra we become familiar with the distributive
laws that address interactions between multiplication and
addition/subtraction. Specifically, these laws say
We use these laws all the time, both in expanding
and in factoring
We even use it (although we don't often think about it this
way and usually don't include the middle step below) when combining
like terms, as in
The problem is when students misinterpret these laws, thinking they
also say something about interactions between more than one
multiplication; that is, they ``invent" for themselves a law that
looks something like:
This clearly is false, as most would see if these were all numbers
-- few (though I cannot go so far as to say no one) would
assert, say, that
But when the objects involved are expressions involving variables,
the error is frequently made, such as in this case:
or
Poor Use of Mathematical Language (PUML)
A prerequisite skill to writing good mathematics is the ability
to write well in one's native tongue. People who cannot write
a complete English sentence should take remediation in English
composition before reading on.
What may surprise some students is that good writing using
mathematical symbols (even in the write-up of homework problems)
consists of using complete sentences, setting up one's ideas
clearly and then following through on the details, much as
one expects from a good English essay. The language and symbols
of mathematics are used just like regular English words and phrases
to express ideas, albeit ideas which one would often struggle to
use any other means of expressing.
Nobody studies mathematical writing as a subject. Your mathematics
professor(s) got to be good writers of mathematics, if good they be,
by reading papers and books by other mathematicians,
not by reading a treatise such as this one. If a book on good
mathematical writing does exist (and there are probably a
number of such books), they will say much more than I say here.
I will only describe the most common example of poor mathematical writing
I see when grading students' work: Using Equals as a Conjunction
(UEC).
The word ``equals" has a very specific meaning. It requires two
objects, and it asserts that these two objects are the same. In
mathematics, the two objects are usually quantities, like the
mathematical expression , or the number 7. Even within
this tight definition, mathematical equations, as I mentioned earlier,
come in two varieties: identities and conditional equations.
A conditional equation is one such as the equation
which is only for particular values of (in this case one
particular value). In algebra courses
one often sees conditional equalities in homework problems accompanied
by the instruction ``Solve the equation". There are some quantities
that are the same regardless of the value of the variable. A familiar
example is the identity
which is true no matter what real value takes. These two types
of equations encompass the two most common (and only?) valid ways to
use an `equals' () sign.
Consider the typical calculus problem of evaluating a limit like
What we are given here is not an equation, but an expression. If
we begin writing a series of equalities to simplify/evaluate this
expression, we will want them to be identities, as in
The original expression, along with each of the ensuing expressions,
as it turns out, are all equal to the number .
In contrast, suppose we begin with a (conditional) equation like
which we are asked to solve. If a student who understands very well
the discussion of UAS and UMD (found earlier in this
piece) makes a mistake, she is most likely to do so writing
something like
UEC
Such a string of equalities asserts three things:
that ,
that ,
and that .
(i) and (ii) are conditional equations in their own right, but it
should be clear that they do not have the same solutions as the
original equation (nor does (i) have the same solution
as (ii)). And (iii) has no solution at all, for it is never true.
What I am really saying is that the string of equations
(1)
is really three equations, and there is no common solution between
them (and, even if there had been, such a solution would have no
relevance to the original problem, that of solving ).
The student most likely never intended to assert these three
equations in place of the original; she simply began writing
out her ideas, and used an equals sign to join them together whenever
it seemed some sort of conjunction was required.
The student who writes (1) actually appears to have
some facility in the techniques for solving linear equations,
but lacks the ability to put her ideas onto paper in a meaningful
fashion. One good way to express the solution of the previous
equation is
(2)
The symbol can be translated here as ``which implies".
Yes, (2) is more writing than (1), much in
the same way the complete sentence ``I am taking the train to Chicago
this weekend" requires more writing than the three words ``weekend,
Chicago, train". A more favorable comparison is between
(2) and the same ideas expressed in
English words:
If the sum of three times and five is seven, then subtracting
five from both sides and dividing by three yields the value of
two-thirds for ,
or, perhaps more literally,
Assuming that the sum of three times and five is seven,
this implies that three times is two, and that is
two-thirds. | 677.169 | 1 |
12/1/2011: The final exam page is up. Read this page for information on the format of the exam and a detailed discussion of the rules governing the exam. Return to the page on Saturday, Dec 3 2011 around 3pm to obtain a copy of the exam.
10/27/2011: The final project section of the
webpage is now up. You should read this after you are assigned your partner.
10/12/2011: Midterm information now updated in the exam section.
9/16/2011: First version of this webpage goes up. Large pieces of the
page are based on last year's webpage. If you are taking this class, please
read this webpage carefully, especially the sections on grading
and homework.
Math 25 is an introduction to the subject of number theory. It is not too much of a simplification to say that number theory is the study of integers and rational numbers, as opposed to the study of real numbers (calculus) or complex numbers. Number theory is a vast and ancient subject, and it is no exaggeration to say that one could spend a lifetime studying it and still not come close to understanding the entire field, but the formal requirements for beginning the study of number theory are minimal. We will survey a variety of elementary but important results, and hopefully illustrate some applications that basic number theory has in real life.
The ORC prerequisite for this class is Math 8 (Calculus II), but in reality virtually no calculus is needed in this class. Perhaps the most important determinant of success in a class such as this is the willingness to think deeply and diligently about mathematics - in other words, hard work! Students who have seen some algebra (Math 31, 71, 81) will recognize a nontrivial intersection between algebra and number theory, but we do not assume any knowledge of algebra in this class. We may point out some places where algebraic ideas naturally appear, so in some sense this class might serve as motivation for ideas from algebra.
Besides teaching you about number theory, a secondary objective in this class is to teach you how to write clear and logical solutions to mathematical problems. Some homework assignments may ask you to compute a certain number (akin to problems in calculus or linear algebra, where you may calculate integrals or solve systems of linear equations). In these problems, not only should you find the correct number, you should also explain how you arrived at your answer. Other questions may ask you to show that a certain statement is either true or false. In these problems, you need to give clear, logically correct explanations - in other words, proofs. A substantial part of the lectures in this class will be devoted to giving detailed proofs of mathematical statements.
Finally, number theory is naturally an algorithmic subject. A substantial percentage of the homework assignments
will be implementations of various algorithms related to subjects learned in class, using the programming language
Python. No prior knowledge of programming or computer science is assumed.
Your grade in this class will be determined by homework, exams, and a final presentation.
There will be two types of homework assignments: written and programming. Written assignments
are similar to conventional assignments in math classes, where you solve problems (with explanations of
why your solutions are correct) and hand them in. Programming assignments will be guided assignments
where you will be asked to write short programs that implement algorithms (such as calculating
the greatest common divisor or testing for primality) discussed in class. There will
usually also be components of programming assignments where you will be asked to mathematically
analyze various aspects of those algorithms in writing. See the homework page
for more details on what is expected.
There will be two midterm exams and a take-home final examination. The dates and times of these exams will be announced in the future. The two midterms will be closed book exams, while the final will be open book.
There will also be a final presentation which will take place at the end of the term. About halfway through
the term (near the end of October), the class will be randomly split into pairs. Each pair will select a topic related
to number theory, research that topic, and then give a 15-20 minute presentation on it. In addition, each pair
will write a short paper (about 3-4 pages) about the topic they chose. The paper will be due at the same time
the presentations are given.
Each of the above contributes to your final grade in the following fashion:
Homework, written: 25%
Homework, programming: 15%
Midterms: 15% each (30% total)
Final exam: 20%
Final presentation and paper: 10%
Your final letter grade is computed using a curve. Exactly what the distribution of letter grades cannot be
determined in advance, although it should not stray too far from the way grades were distributed
in previous terms.
Written homework assignments will be posted on this website and will be usually due about a week after they are posted. Late assignments will only be accepted when granted an extension, which must be requested from the instructor several days in advance. In general, extensions will only be granted for health-related reasons or family emergencies. Exceptions may be made for school-related travel.
Programming assignments will be given once every two weeks. Instructions for submitting the assignments
are available in more detail at the homework page.
The homework collaboration policy for this class is more or less in line with other Dartmouth math classes. You are allowed to collaborate with others on homework, but must write your own solutions. A good rule of thumb is that you should never be copying phrases or sentences from anyone else or any source. You may use theorems, lemmas, etc. that we have covered from the textbook, but in general you should not use theorems, lemmas, etc. from sections of the book we have not covered or from external sources. Also, please write down the people you collaborated with and outside sources (namely, anything besides the required textbook) you consulted on your homework assignments.
For the programming assignments, you are to never directly consult any code related to
the problems you are working on prior to handing in an assignment, whether that be
pre-existing code you find in books or the Internet, or the code of fellow students in the class.
(However, consulting pseudocode is fine.) Just like with the written assignments, a good rule
of thumb is that you should never copy any code you find anywhere. You are still allowed
to discuss how you might go about solving a particular problem with other students, but
you must write your programs independently.
The required book for this class is Elementary Number Theory, by Gareth A. Jones and J. Mary Jones, ISBN 3540761977.
There are many, many books written about elementary number theory, and even more books written about number theory in general. The following list of supplemental books is by no means all-inclusive:
An Introduction to the Theory of Numbers, by G.H. Hardy and E.M. Wright. This is a classic introduction to number theory and is a great book to read for anyone serious about studying the subject. A distinguishing feature of this book is the complete lack of exercises.
Elementary Number Theory, by Kenneth Rosen. This book has been used in some previous iterations of this class. It is long and has lots of exercises.
An Introduction to the Theory of Numbers, by Ivan Niven, Herbert Zuckerman, and Hugh Montgomery. This book is also long and has lots of exercises, and is well-written.
Our primary goal in this class is to cover through chapter 7 of the textbook. We begin by discussing divisibility, which naturally leads to the topic of prime numbers. This then leads to the study of "congruences modulo n", where n is a positive integer. In particular, we will consider analogues of familiar questions in algebra, such as solving linear and quadratic polynomials of a single variable, except instead of asking for solutions over real or complex numbers we will ask for solutions in some set of number-theoretic interest. Along the way we will give a very brief
introdution to applications of number theory to the subject of cryptography. | 677.169 | 1 |
Saturday, 16 August 2008
A huge system consists of smaller sub-systems with functions related to the system operation. Sometime the function of the individual sub-systems are known, but the function of the system as a whole is not clear. We just know that given a certain set of inputs, we will get another set of outputs.
But what are the constraints and limits to the system?
What is the strength or weakness of the system?
These are typical questions that system engineer need to know. How then does he know?
It is through modelling that we can get the answers to the scope of the system operation, its weakness, strength and limits.
Many techniques address this modelling issue, but the simplest is the Math Model.
Here, mathematical function or expression describes the relationship between the input and output. A complex drawing of sub-systems can be simplified into a single block indicated by the Math Model.
Let an example illustrate the usefulness of Math Model.
A negative feedback audio amplifier consists of a main amplifier (A) in the forward path with a feedback circuit (X) that returns a portion of the output signal for control purpose. The main input signal is fed into a circuit that subtracts the feedback signal from the main input signal. (This is the detail operation of the system involving its sub-systems).
To simplify this model, math is used to summarise the overall function. Math is therefore a system modelling tool, in this instance, to describe relationship between the input and output.
Brief explanation on derivation of math model expression:
Using algebra, we can see that the direct input to the amplifier (A) is V1 - XV2, and the output is V2.
The ratio of the (output of A) / (input of A) is V2 / (V1-XV2) = A.
Re-arranging the above expression, we will get V2/V1 = A / (1 + AX) which is the system gain ratio of the complete negative feedback amplifier.
This final ratio is then the Math Model of diagram 1 and is shown in diagram 2.
Diagram 2
After getting this simplified version, system analysis can be carried out to test the extent of its operation and discover its limits. Without this modelling, the testing will be tedious and time consuming.
From the above example, you can see the usefulness of math and its application as a system modelling tool. From an abstract case, math understanding can be used to solve an real-life situation through this specific application. | 677.169 | 1 |
First Word
The truly gifted students require outstanding academic programs to match their talent and hard work. We offer three such programs for school and college students who have above average interest in mathematical science.
Since 2010, our students have performed brilliantly in Math Olympiads. Many succeeded in entrances of I.S.I. & C.M.I. (India) and other challenging math contests.
If you find the school (or college) mathematics too easy and yearn for a greater challenge, you have come to the right place. Welcome!
Format
Typically 20 out of 30 correct objective attempts and 5 to 6 out of 10 correct subjective answers are required to get qualified for the interview (this varies from year to year).
C.M.I. Entrance is of 3-hour duration consisting of both subjective and multiple choice problems. The format of questions and cut-off score varies from year to year.
In both entrances, the successful candidates of the written tests are required to appear for an interview.
Apply
Admission to Cheenta I.S.I. & C.M.I. Entrance Program is highly selective. It consists of an online interview and a test.
Student of 11th grade onward may apply. Students who have graduated from high school may also apply. The only requirement is that: the candidate must have pure mathematics as a subject in high school. Age no bar.
E Mail us at [email protected] to schedule an interview. Send us your phone number and skype id during application.
Combinatorics I
This is the first course in combinatorics and elementary counting techniques:
Com.I.1 Multiplication and Addition rules
Com.I.2 Bijection Principles
Com.I.3 Combinatorial Coefficients
Com.I.4 Inclusion and Exclusion Principles
Com.I.5 Pigeon Hole Principle
Com.I.6 Recursions
Com.I.7 Shortest Route Problems
Algebra I
This is a first course is school algebra. (We assume that the student is familiar with algebraic expressions, and elementary algebraic identities)
Alg.I.1 Algebraic identities (Sophie Germain, Cube of three etc.)
Alg.I.2 Mathematical Induction
Alg.I.3 Binomial Theorem
Alg.I.4 Linear Equations
Alg.I.5 Quadratic Equation
Alg.I.6 Remainder Theorem
Alg.I.7 Theorems related to roots of an integer polynomial
Geometry I
Geo.I.1 Locus visualization
Geo.I.2 Straight Lines
Geo.I.3 Triangles
Geo.I.4 Geometric Constructions
Geo.I.5 Circles
Trigonometry I
Trig.I.1 Angle and rotation
Trig.I.2 Half arcs and Half chords – Genesis of trigonometric ratios
Trig.I.3 Elementary ratios and associated angles
Trig.I.4 Trigonometric identities
Trig.I.5 Geometry and trigonometry
Trig.I.6 Basic properties of Triangles
Trig.I.7 Compound Angles
Trig.I.8 Multiple and Submultiple Angles
Trig.I.9 Trigonometric Series
Trig.I.10 Height and Distance
Inequality I
This first course in inequality must be preceded by a basic course in algebra.
Ineq.I.1 Geometric Inequalities
Ineq.I.2 Arithmetic and Geometric Mean Inequality
Ineq.I.3 Cauchy Schwarze Inequality
Ineq.I.4 Titu's Lemma
Complex Number I
Complex.I.1 Geometry of Screw Similarity
Complex.I.2 Field Properties of Complex Number
Complex.I.3 nth roots of unity and Primitive roots
Complex.I.4 Basic applications to geometry
Calculus I
Calc.I.1 Sequences and Series
Calc.I.2 Limit
Calc.I.3 Functions
Calc.I.4 Continuity
Calc.I.5 Differential Calculus
Calc.I.6 Cauchy's Theorem and Mean value
Calc.I.7 Graphing Techniques
Calc.I.8 Integral Calculus
Higher Mathematics Program
Introduction
The higher mathematics program caters to advanced college and university students. It is useful for I.S.I. M.Math Entrance, GRE Math Subject Test, TIFR Ph.D. Entrance, I.I.T. JAM.
The program is problem driven. We work with candidates who have a deep love for mathematics. This program is also useful for 'continuing' mature students who wish to rediscover the world of mathematics.
Curriculum
The higher mathematics program consists of the following topics:
Linear Algebra
Abstract Algebra (Groups, Rings, Fields)
Real Analysis and Point Set Topology
Vector Calculus
Eligibility
The program has no age bar. Students aspiring for various Ph.D. and Masters level entrances in India as well as GRE Subject Mathematics Test may apply.
Adults, who wish learn and enjoy the world of advanced mathematics may also take the course.
Format
The tests of I.S.I., C.M.I., NBHM, T.I.F.R. are usually two-fold in nature. First, there is a written test. Next, the successful candidates are invited for an interview. The dates vary from year to year, hence keep an eye on the websites of respective institutions.
GRE Math Subjective Test if offered four times every year. It is a 66-problem, 170 minutes objective test covering a wide range of topics from college mathematics.
Apply
Admission to Cheenta Higher Mathematics Program is highly selective. It consists of an online interview and a test.
Students and adults from any background may apply. The zeal for learning great mathematics is the only important criteria.
E Mail us at [email protected] to schedule an interview. Send us your phone number and skype id during application. | 677.169 | 1 |
How is this Material Used?
webbmatte.se consists of material which can be used in many different ways and in many different situations. You as a student, teacher or parent can hopefully have great use of this material depending on the needs you have.
Student This material is intended to be used as a support for your ordinary math course. You may think that one subject is difficult or maybe that you want to learn more about some area. You can also use this material for example to review before a test or if you have been ill and missed some part of the course. Read more about how you can use the material under the area Student.
Teacher For you as a teacher, we would like to point out that webbmatte.se is a complement to your ordinary teaching and not course literature in itself. The focus lies on the mathematical concepts and the material can be compared to a mathematical reference book with explanations. You can use the material in a various number of ways, for example to prepare students for coming lectures, review for students who have missed area or want to prepare for coming test, to get others viewpoints on different problems etc. For more about how you can use this material, please read the area Teacher.
Parent With webbmatte.se you as a parent have the possibility to help your children with mathematics. By going through the material, you can get a good idea about how the different areas can be presented for students. Besides this, you also have the possibility of freshening up your own mathematical knowledge. We are helping you to help. Read more about how you can use this material under the area Parent. | 677.169 | 1 |
How to use the STEP Support Programme
What is the STEP Support Programme?
The STEP Support Programme is a course made up of assignments designed to develop your problem solving skills, in order to help you prepare both for sitting STEP and studying Maths at university. It has been created by Cambridge mathematicians who have taken STEP themselves and have many years of experience in supporting school students with their STEP preparation. The programme is particularly designed to provide help if your school cannot offer support with STEP preparation.
How to use the STEP Support Programme
Before you begin looking at the assignments, it is really important to keep in mind that STEP questions are hard. STEP questions are longer than A-level questions and require more persistence and insight, so don't be afraid if you find them difficult - you're supposed to! The best way to get better at STEP is to do STEP questions, and the more you do the better!
You will get stuck. Here are some tips that might help you to get unstuck:
Try a 'special case' (e.g. substitute some numbers in)
Try drawing a graph or diagram
If the answer is given, try working 'backwards' (and write up your argument the 'correct' way around)
If you are stuck on a later part, see if you can use the earlier parts to help (STEP questions are usually inter-connected)
Try a 'guess' (e.g. for integration by substitution – the substitutions are not usually given to you)
Have a break! Go for a walk, have some dinner, sleep on it before returning to the problem
This programme is designed to consolidate and extend your knowledge and problem solving skills, so even if a particular assignment feels like revisiting familiar territory we encourage you not to skip it. Working through all these assignments will help improve your mathematical fluency and build your confidence.
Using the Assignments
The Foundation modules are intended as a structured course, which means that there is a logical order to them. We tend to prove results (usually in the warm ups) before we use them, and if there are two STEP questions testing similar things the preparation for the earlier one will be longer. Even if you are not intending to sit STEP I we strongly recommend that you work through these resources, possibly in year 12, in order to develop your problem solving skills before attempting the STEP II (and later STEP III) modules. However, you do not have to do them in order, or do every one, if you have only limited time or start the programme later.
The STEP II and STEP III modules are designed to build upon the work you have done on the Foundation modules, and are aimed at year 13 students. Each one focuses on a different area of the STEP II or STEP III specification and contains 4 STEP questions. There are no preparation questions for these, but if you are stuck you can look at the "hints" file to give you some starting points. There is also a "solutions" file and "topic notes" available for each module.
Using the Discussion Forum
The discussion forum is a place for you to ask any questions that you have about the assignments, or STEP in general. For example, you may want to seek clarification on something said in the 'Hints and Solutions' files. You may have been tackling a different STEP question and want a hint for how to proceed. You may even have spotted a possible mistake (in which case we are very grateful!). Cambridge University staff and students act as mentors on the forum, and will be happy to respond to any questions you have. You may also wish to share suggestions, hints and advice with other students who are working on the STEP Support assignments. And of course, if you have any feedback in general on the programme, please do let us know. | 677.169 | 1 |
A particularly useful reference for those in math, science, engineering, and other technical fields. This comprehensive handbook includes the most-frequently used formulas, tables, transforms, functions, and graphs needed as tools in solving problems. The entire field of special functions is covered, as well as a large amount of scientific data used by scientists and engineers. An extensive and detailed index makes topics of interest easy to review and locate.This comprehensive handbook includes the most-frequently used formulas, tables, transforms, functions, and graphs needed as tools in solving problems. | 677.169 | 1 |
CURRICULUM EXPECTATIONS
identify geometric patterns, through inves
tigation using concrete materials or drawings, and represent them numerically;
make tables of values for growing patterns,
given pattern rules in words (e.g., start with 3, then double each term and add 1 to get the next term), then list the ordered pairs (with the first coordinate representing the term number and the second coordinate representing the term) and plot the points in the first quadrant, using a variety of tools
determine the term number of a given term in a growing pattern that is represented by a pattern rule in words, a table of values or a graph
describe pattern rules (in words) that generate patterns by adding or subtracting a constant or multiplying or dividing by a constant, to get the next term
ALGEBRAIC EQUATIONS
BIG IDEAS
(taken from "Big Ideas by Dr. Small")
Algebra is a way to represent and explain mathematical relationships and to describe and analyze change.
Using variables is a way to efficiently and generally describe relationships that can also be described using words.
STUDENT LEARNING GOALS
GOAL: I can identify the value of the variable in one-step equations.
GOAL: I can use formulas to solve problems.
CURRICULUM EXPECTATIONS
identify, through investigation, the quantities in an equation that vary and those that remain constant.
solve problems that use two or three symbols or letters as variables to represent different unknown quantities
determine the solution to a simple equation with one variable, through investigation using a variety of tools and strategies | 677.169 | 1 |
Advanced Mathematical Methods for Engineering and Science by G. Stephenson
This textbook offers an excellent starting place to a couple of very important issues in arithmetic of curiosity to technological know-how and engineering scholars. integrated are tensor algebra, usual differential equations, contour integration, Laplace and Fourier transforms, partial differential equations and the calculus of diversifications. The authors' strategy is straightforward and direct with an emphasis at the analytical knowing of the cloth. The textual content is almost selfcontained, assuming simply that the scholar has an effective realizing of ancillary arithmetic. every one bankruptcy features a huge variety of labored examples, and concludes with difficulties for resolution, with solutions behind the ebook.
Development. clearly, we're open to feedback from all readers of, and individuals to, the sequence concerning its strategy and content material. eventually, i need to thank all those that have helped the release of this sequence. The encouraging reaction got from authors who've contributed the drawing close volumes and from the subscribers to the sequence has indicated the necessity for this sort of e-book.
Extra info for Advanced Mathematical Methods for Engineering and Science Students
Example text
Tensor algebra and its associated calculus are important tools in the study of continuum mechanics and in the general theory of relativity. Problems 1 1. Write out aikXiXk in expanded form, assuming aik — akiy and i, k = 1, 2, 3. 2. Over which indices (if any) in the following expressions is summation implied? (i) dijbj, (ii) dijbjj, (iii) atibny (iv) au = bu. 3. Find the values of 6iy6iy, <5,y(5yVAm<5/m, ejklAkAh and dikeikmy all indices ranging from 1 to 3. 4. Evaluate €iklejki and €ijkeijky all indices ranging from 1 to 3.
V)B, where A and B are vectors. 9. If fk = xixjeijk + XiXiXk> show that dfk/dxs = 2xsxk + XiXtdte. Find also d2fk/dxr dxs, and deduce that d2fkldx2s = 2xk + 4xs8ksy no summation over s being implied. Verify the last result directly for the cases k = 1, s = 1, and k = 1, s = 2. 10. If Ak =xnxnxmxmxk, show that dAk/dxp = ocxpxkxmxm + xnxnxmxmdkp, and determine the constant a. Show also that = fixnxnxmxm and determine /3 for the cases (i) when all indices range from 1 to 3, and (ii) when all indices range from 1 to 7. | 677.169 | 1 |
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Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts. But its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective.
The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Editorial Reviews
Review
Carter presents the grojp theory portion of abstract algebra in a way that allows student to actually see, using a multitute of examples and applications, the basic concepts of group theory...The numerous images (more than 300) are the heart of the text. As this work enables readers to see, experiment with, and understand the significance of groups, they will accumulate examples of groups and their properties that will serve them well in future endeavors in mathematics. Recommended --J. T. Zerger, Choice
If you teach abstract algebra, then this book should be a part of the resources you use. While the phrase "visual abstract algebra" may seem to be a contradiction, the diagrams in this book are an existence proof to the contrary. They are clear, colorful and concise very easy to understand and sure to aid the students that have difficulty in internalizing the abstract nature of the subject matter. Especially appealing are the colorized tables of groups and their operations.
The approach is a very slow one in the sense that a foundation of common operations and rearrangements that are groups that are first examined with text and images. A large number of exercises are included at the end of each chapter and detailed solutions with colored images found in an appendix.
this book could also serve as a text in a first course in abstract algebra provided that the course is limited to groups only or you used supplementary material for rings and fields. If your course is restricted to groups only, then this is the best book available. --Charles Ashbacher, Journal of Recreational Mathematics
Book Description
This text approaches the learning of group theory visually. It allows the student to see groups, experiment with groups and understand their significance. It is ideal as a supplement for a first course in group theory or alternatively as recreational reading.
This is a great book for anyone interested in mathematics. I bought it just to read after reading about it in another text but find myself returning to it again and again to sharpen my understanding with the examples.
I was a physics B.S. who is now pursuing a Ph.D. in applied physics. Was very intimidated by the very math-y and formal books on group theory. Have been working through all the problems through the first 5/6 chapters so far, the ones whose answers are in the back of the book. Already feel much more confident about the fundamentals of group theory. The referenced software the author created is also very helpful and creative. Plan to continue to work problems all the way to the end, after which I'm confident I'll feel like I've got a solid grasp on group theory.
I am a self study student of mathematics having acquired a taste for it later in life. I only had 1st year calculus and linear algebra in university nearly 20 years ago. This book is a very readable introduction to group theory. I suppose it lacks some of the rigor a truly dedicated mathematician might require, but I have really been enjoying teaching myself group theory from this book.
There are lots of examples to think about and many problems to work through. Very readable.
I am reading this book half way through, it is amazing how 'readable' this book is compared to other Abstract Algebra books. Although this book inherits much ideas and notations from the other older book: "Groups and Their Graphs" by Grossman and Magnus, it elaborates with more Cayley Diagrams (over 300 of them) and more detailed explanations.
The book is well written and well illustrated. I took one night to read through the first 5 chapters, that shows how easy it is to understand the concepts. (It helps, may be, because I had read the Grossman and Magnus book, however the later is not a pre-requisite reading).
I am also very pleased that the author uses Cayley diagrams to show how Subgroups, Cosets and Normal Subgroups could be visualized. This is a real break-through in teaching abstract stuff like Group Theory - a real tough nut to crack for most Math students. Don't forget the inventor of Group - Evariste Galois - had hard time making himself understood by even the greatest mathematicians of his time - Cauchy, Fourier, Poisson, etc.
This is the book to read before anyone attempting to study Group Theory in a formal textbook way.
1. I give it a five as an introductory book. In terms of points for a book on its own, its a 5 out of 10. The best entrance to abstract algebra (in my opinion). 2. For math hobbyist, it will show you the beauty of mathematics. (This is vague, and sorry I don't want to elaborate on this) 3. For serious math learners, this certainly will not be your only algebra book, but by reading this you will have some useful tools/insights (really really useful insights) in hand when you begin your second book on the subject. 4. The problems in the book are okay~~~~~~~~, but the meat of the book lies in the main readings. 5. Many typos, mistakes, errors, and not conventional and sometimes confusing notations (especially those that have to do with "multiplication", where in a usual (abstract) algebra book ab means b first then a acts on b, but this is not always consistent in this book). 6. But what-the-hell to 5, this will not be your only book, take the things you need and move on. We don't need a diamond to kill a bird, any big enough rock will do the job. | 677.169 | 1 |
About this title:
Synopsis: The Student Solutions Manual to Accompany Linear Algebra with Applications, Eighth Edition is designed to help you get the most out of your linear algebra course. It provides the answers to selected exercises in each chapter of the textbook. This manual will help you to assess the progress you are making in understanding the concepts presented in each chapter. Students, use this tool to: - check answers to selected exercises - confirm that you understand ideas and concepts - review past material - prepare for future topics
Book Description Jones & Bartlett Learning. Book Condition: Good. 144968792X Bookseller Inventory # SKU104959505208
Book Description Jones & Bartlett1505664968792X-LOCATION-45513 | 677.169 | 1 |
Daily schedule, tests, and additional coursework for the one-year Elementary Algebra course. Elementary Algebra is designed to prepare the student with a foundational understanding of basic principles in Algebra. This Elementary Algebra Teacher's Guide includes: A convenient daily schedule with space to record gradesHelpful information on teaching the course and tests for student assessmentSet III exercise worksheets; as well as chapter, mid-term review, final exams, and answer keys. Jacobs' Elementary Algebra is highly regarded in the education market. This curriculum provides a full year of mathematics in a clearly written format with guidance for teachers as well as for students who are self-directed. Also available: The Solutions Manual for Elementary Algebra by Master Books® provides solutions and answers for all exercises in the course, as well as mid-term and final review tests.
Jacobs' best-selling Geometry course has become a highly respected standard for teaching high school math in both top schools nationwide and within the homeschool market. The Geometry Teacher Guide contains tests, solutions to tests, and a daily schedule. The Geometry Teacher Guide Includes: Convenient suggested daily schedule—saving you time!Tests (chapter, mid-term, final exam, & alternate test versions)Test SolutionsPractical 3-hole punched perforated pages for ease of use
Designed for high school students and revised for a new generation of learners! Jacobs Elementary Algebra has come to be highly regarded in the education market. This curriculum provides a full year of mathematics in a clearly written format with guidance for teachers as well as for students who are self-directed. Student textbook includes easy-to-follow instruction and selected answers in the back.Lessons are divided into 17 chapters, covering functions and graphs, integers, rational numbers, exponents, polynomials, factoring, fractions, and more.The course builds a solid foundational understanding and application of key concepts. Also Available: The Elementary Algebra Teacher Guide provides a detailed schedule, tests, and test answer keys as well as additional exercises. The Solutions Manual for Elementary Algebra helps the student with understanding the answers from the bookIs your child getting lost in the system, becoming bored, losing his or her natural eagerness to learn? If so, it may be time to take charge of your child's education—by doing it yourself. The Well-Trained Mind will instruct you, step by step, on how to give your child an academically rigorous, comprehensive education from preschool through high school—one that will train him or her to read, to think, to understand, to be well-rounded and curious about learning. Veteran home educators Susan Wise Bauer and Jessie Wise outline the classical pattern of education called the trivium, which organizes learning around the maturing capacity of the child's mind and comprises three stages: the elementary school "grammar stage," when the building blocks of information are absorbed through memorization and rules; the middle school "logic stage," in which the student begins to think more analytically; and the high-school "rhetoric stage," where the student learns to write and speak with force and originality. Using this theory as your model, you'll be able to instruct your child—whether full-time or as a supplement to classroom education—in all levels of reading, writing, history, geography, mathematics, science, foreign languages, rhetoric, logic, art, and music, regardless of your own aptitude in those subjects. Thousands of parents and teachers have already used the detailed book lists and methods described in The Well-Trained Mind to create a truly superior education for the children in their care. This extensively revised fourth edition contains completely updated curricula and book lists, links to an entirely new set of online resources, new material on teaching children with learning challenges, cutting-edge math and sciences recommendations, answers to common questions about home education, and advice on practical matters such as standardized testing, working with your local school board, designing a high-school program, preparing transcripts, and applying to colleges. You do have control over what and how your child learns. The Well-Trained Mind will give you the tools you'll need to teach your child with confidence and success.
* SIMPLE CLEAR EXPLANATIONS / SOLUTIONS for EVERY TEST PROBLEM for all eight tests & problems in the introduction section.* READING PASSAGES SUMMARIZED to help in comprehension.* The BEST, MOST DIRECT SOLUTION to each math problem with visuals and diagrams.* Why close answers are wrong, and which ones are TRAPS that students usually pick.* VOCABULARY WORDS DEFINED so you don't have to look them up in a dictionary.* GRAMMATICAL ERRORS highlighted for clear understanding of errors in the writing section.* SAMPLE STUDENT ESSAYS included. | 677.169 | 1 |
Common Core MathGrade2Practical Wire Antennas 2
... they are necessary to allow the reader to calculate the lengths of various antennas. Practical Wire Antennas 2 has chapters covering feed lines, dipoles, antennas with tuned feeders, loop antennas, end-fed ... of antenna building and includes designs for ATUs for almost every type of antenna.
Practical Wire Antennas 2 provides a collection of antenna designs and ideas that will help capture the enjoyment ...
Common Core MathGrade 3Common Core MathGrade 4 | 677.169 | 1 |
Partial Differential Equations(Hardback)
Synopsis
This is self-contained elementary introduction to partial differential equations. It assumes only advanced differential calculus and some Lp theory. Taking some basic physical models as a starting point, the author uses a classical analysis approach and a non-linear point of view to introduce the basic aspects of the theory and provide a background for some current research directions | 677.169 | 1 |
TI-Nspire Strategies: Geometry
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Maximize student use of TI-Nspire technology while processing and learning geometry concepts. The lessons delve into the five environments of TI-Nspire including calculator, graphs and geometry, lists and spreadsheets, notes, and data analysis. Problem-solving practice, and step-by-step instructions are included. This resource is correlated to the Common Core State Standards, is aligned to the interdisciplinary themes from the Partnership for 21st Century Skills, and supports core concepts of STEM instruction. 224pp. | 677.169 | 1 |
A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict.
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses | 677.169 | 1 |
Showing 1 to 2 of 2
Math 50
a Practice Test Chapter 3
Complete each of the following problems below on your own paper. Show all work in
:eaching your solution. At the end of class today, you will turn in a separate page with
only your answers. Keep this page and all of your
Calculus I Advice
Showing 1 to 1 of 1
Ryan Pedersen was a great professor. Explained topics very well and gave us the chance to provide him with feedback on how to help us learn better.
Course highlights:
This was an accelerated course on calculus 1. It was very fast paced and included many difficult concepts and complicated equations. Some equations had so much work that it would take up more than one blank page. I love math and science so I highly recommend taking it. This class begins relating math to real world examples on how we calculate everyday things we take for granted. | 677.169 | 1 |
Pages
Monday, 13 August 2012
Applications of Matrices
Prior to the activity, study the slides on matrices. In groups of 4 or 5, research on the application of matrices in the real world and put up at least one relevant, good quality resource regarding how matrices are used. Post (under comments) the link/ file for the resource and do a short summary (5 lines) on the application on the class blog. Be sure to acknowledge the source. | 677.169 | 1 |
CVTC uses current topics, real-life situations to teach math after switch to new Carnegie curriculum
Chippewa Valley Technical College (CVTC) math instructor Jim Bockenfeld started the class with a discussion about texting and driving, something that might already have been a part of some students' lives.
CVTC math instructor Jim Bockenfeld talks to students during a fall 2016 semester class where he used the new Carnegie math instruction methods. (CVTC photo)
The discussion went on to involve how long it takes a driver facing an emergency situation to stop a car, the various factors involved, and how a delay in recognizing an emergency can be costly. Answering these questions was going to take mathematical reasoning.
Along the way, the students solved not only math problems, but real-life problems they may encounter, and had classroom interactions that are rare in traditional math classes.
Welcome to an innovative new way to teach math developed by the Carnegie Foundation for the Advancement of Teaching. This academic year, CVTC implemented the program, becoming only the third college in the state to do so and the first in the nation to implement the program in its entirety without incremental transitions.
Math in a Real-Life Context
"All of the problems are in context," said math instructor Ruth Carlson in describing the fundamental difference in teaching the Carnegie method. "We read about a situation and answer questions about it. Students can bring their life experiences to the situations."
The situations involve current topics or common life situations, such as health care, politics, sports playoffs, cell phone plans – the possibilities are endless.
In a traditional math class, an instructor lectures on methods to solve a particular type of equation or problem. Assignments involve a set of problems to do, and often a few "word problems" that seek to apply the lesson. Little discussion is involved.
"Traditional math is formula-based, then looks for a way to apply the formula to real life," said Margo Keys, CVTC vice president of student services. "Carnegie starts with a real life situation and applies a formula to it. Carnegie starts with the relevance."
In a Carnegie classroom, students interact with input on relevant factors, and work together toward a solution. In assignments, answers are not just numbers or solved equations, but are given in the form of sentences, paragraphs and explanations.
"We want students to realize that they already know a lot," Carlson said. "You don't have to be a math whiz to be an effective member of the group."
The Carnegie method is not, however, a simplification of math. The competencies that students must demonstrate haven't changed, Bockenfeld emphasized.
"Part of the learning process is a productive struggle," he said. "We're not just teaching math concepts, but teaching thought processes as well."
The Goal: Increasing Student Success
Increasing student success is the goal of the Carnegie approach, according to Keys. Some 40% 0f CVTC's incoming students were being required to take a "developmental math" class before the enrolling in the math class needed for their program, which delayed progress toward graduation.
"It was a real access barrier," Keys said.
"The Carnegie courses are designed for the students to get the college level math with the developmental math," Carlson said.
Carnegie Math has two elements, Quantway, which deals with quantitative analysis, and Statway, which is the statistics curriculum. CVTC adopted both at once so the entire staff would be trained in the methods, which made this year one of transition for both students and instructors.
"It's very different than it was 10 years ago when I last had a math class," said Courtney Rauch, 28, of Eau Claire. "But it makes sense. It's a nice way to apply it to everyday life. I'm actually finding it easier.
"I love it, because with the old way it was a limited style and only a certain number of students would get it," said Yang Xiong, a 2008 Eau Claire Memorial graduate. "I think this method best accommodates the majority of the class. We can connect math to current events."
But Hannah Shankey, a 2015 Black River Falls High School graduate, likes the familiarity of the old way.
"All through high school and elementary school they teach you how to do it," she said. "You get to college and you expect it to be the same, but it switches. Not only is the math new, but the teaching style is new."
The Carnegie Foundation's first study of the new teaching method's results suggests that CVTC should expect more students completing college math. The results, announced April 5, show that Carnegie Math students since 2011 have double and sometimes triple the success rates completing college math, and do so in half the time compared with students in traditional courses. The study also found Carnegie Math students transferred from two to four-year colleges at a higher rate.
"Carnegie is a leader in national math reform and while other math curriculum products exist, Carnegie had the best track record and the five-year study results confirm their methods are working," Keys said | 677.169 | 1 |
Algebra: Year 9 by Steve Mills, Hilary Koll (Paperback, 2003)
$27.41
List price $40 is part of a series of three photocopiable maths activity books for secondary schools and home study. Each book contains over 50 pages of photocopiable activities that cover the key objectives of the algebra strand for year 9 at Key Stage 3. Included are fresh ideas for whole-class oral and mental maths starter activities (as recommended by the framework). Each activity is divided into three progressive steps, providing opportunities for differentiating the work. Included also are extension activities which reinforce and develop the pupils' learning. The books are also compatible with the 5-14 Guidelines for Scotland and the Curriculum for Northern Ireland.
Author Biography
The authors are well-known mathematics writers, educational consultants and INSET providers. Previously, they have both worked as school mathematics coordinators and as lecturers in maths education. Steve Mills was also a county maths advisory teacher. | 677.169 | 1 |
Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included.TheTheThis is a book which many mathematicians could enjoy browsing, and one which a good undergraduate could be encouraged to read to learn something of the interconnections, which exist between apparently disparate parts of mathematics.--Canadian Mathematical SocietyAs a source for information on the ''reach'' of number theory into other areas of mathematics, it is an excellent work.--Mathematical Association of America W.A. Coppel, Books, Science and Nature, Number Theory: An Introduction to Mathematics Books>Science and Nature, Springer New York
Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The "This is a book which many mathematicians could enjoy browsing, and one which a good undergraduate could be encouraged to read to learn something of the interconnections, which exist between apparently disparate parts of mathematics." --Canadian Mathematical Society "As a source for information on the 'reach' of number theory into other areas of mathematics, it is an excellent work." --Mathematical Association of America Number Theory: An Introduction to Mathematics Coppel, W. A., Springer. -, [SC: 0.00]., [SC: 0.00]
Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included.
The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics | 677.169 | 1 |
Mathematics for the Trades: A Guided Approach is the leader in trades and occupational mathematics, equipping students with a solid foundation in the math needed for a variety of technical and vocational trades, such as allied health, electrical trades, plumbing, construction, and many more. The math concepts are presented completely within the context of practical on-the-job applications, so students can make an impact on the job from day one.
For Basic Math, Math for the Trades, Occupational Math, and similar basic math skills courses servicing trade or technical programs at the undergraduate/graduate level. THE leader in trades and occupational mathematics,Mathematics for the Trades: A Guided Approach focuses on fundamental concepts of arithmetic, algebra, geometry, and trigonometry. It supports these concepts with practical applications in a variety of technical and career vocations, including automotive, allied health, welding, plumbing, machine tool, carpentry, auto mechanics, HVAC, and many other fields. The workbook format of this text makes it appropriate for use in the traditional classroom as well as in self-paced or lab settings. For this revision, the authors have added over 150 new applications, new chapter summaries for quick review, and a new chapter on basic statistics. Student will find success in this clear and easy to follow format which provides immediate feedback for each step the student takes to ensure understanding and continued attention.
The new edition of BEGINNING ALGEBRA is an exciting and innovative revision that takes an already successful text and makes it more compelling for today's instructor and student. The authors have developed a learning plan to help students succeed in BeginningPRACTICAL PROBLEMS IN MATHEMATICS FOR ELECTRICIANS, 9E will give your students the math skills they need to succeed in the electrical trade. It introduces them to the important math principles through problems designed for the electrical profession and offers them an excellent opportunity to develop and practice problem-solving skills while at the same time providing a valuable review of electrical terminology. This new edition uses the same straightforward writing style and simple, step-by-step explanations that made previous editions so reader-friendly. It minimizes theory and emphasizes problem-solving techniques and practice problems. This new edition also includes updated illustrations and information for a better learning experience than ever before! The book begins with basic arithmetic and then, once these basic topics have been mastered, progresses to algebra and concludes with trigonometry. Practical problems with real-world scenarios from the electrical field are used throughout, allowing your students to apply key mathematical concepts while developing an awareness of basic electrical terms and practices. This is the perfect resource for students entering the electrical industry, or those simply looking to brush up on the necessary math. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
FUNDAMENTALS OF MODERN DRAFTING, Second Edition, provides a thorough introduction to contemporary drafting, covering essential technical and engineering drawing concepts and key professional applications. The author uses a highly practical, building-block approach to help you quickly develop the knowledge and skills you need to prepare working drawings for production. Coverage encompasses freehand sketching, instrument drawing, CAD, drafting conventions and formats, multiview, development, pictorial drawing procedures, geometric tolerancing practices, descriptive geometry, and more. Every chapter includes vibrant illustrations to complement the text, as well as hands-on exercises that encourage you to apply what you're learning. Now updated to reflect the latest trends and technology, the new Second Edition reflects current ASME standards to help you make a smooth transition from study and skill development to professional success. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
The new edition of INTERMEDIATE ALGEBRA is an exciting and innovative revision that takes an already successful text and makes it more compelling for today's instructor and student. The authors have developed a learning plan to help students succeed in Intermediate procedures for trouble shooting and repair. Technically reviewed by instructors and industry experts and reflecting the latest NATEF Automobile Program Standards, this edition is ideal for students enrolled in NATEF-accredited programs. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Technical Drawing 101 covers topics ranging from the most basic, such as making freehand, multiview sketches of machine parts, to the advanced—creating an AutoCAD dimension style containing the style settings defined by the ASME Y14.5-2009 Dimensioning and Tolerancing standard. But unlike the massive technical drawing reference texts on the market, Technical Drawing 101 aims to present just the right mix of information and projects that can be reasonably covered by faculty, and assimilated by students, in one semester. Both mechanical and architectural projects are introduced to capture the interest of more students and to offer a broader appeal. The authors have also created extensive video training (120 videos, 15 hours total) that is included with every copy of the book. In these videos the authors start off by getting students comfortable with the user interface and demonstrating how to use many of AutoCAD's commands and features. The videos progress to more advanced topics where the authors walk students through completing several of the projects in the book. The CAD portion of the text incorporates drafting theory whenever possible and covers the basics of drawing setup (units, limits, and layers), the tools of the Draw, Modify, and Dimension toolbars, and the fundamentals of 3D modeling. By focusing on the fundamental building blocks of CAD, Technical Drawing 101 provides a solid foundation for students going on to learn advanced CAD concepts and techniques (paper space, viewports, xrefs, annotative scaling, etc.) in intermediate CAD courses. In recognition of the diverse career interests of our students, Technical Drawing 101 includes projects in which students create working drawings for a mechanical assembly as well as for an architectural project. We include architectural drawing because our experience has shown that many (if not most) first-semester drafting students are interested in careers in the architectural design field, and that a traditional technical drawing text, which focuses solely on mechanical drawing projects, holds little interest for these students. The multidisciplinary approach of this text and its supporting materials are intended to broaden the appeal of the curriculum and increase student interest and, it is hoped, future enrollments.
Prepare for a career in the commercial or residential plumbing fields with this popular book, which has been updated to reflect the very latest advancements in the plumbing industry. Plumbing Technology: Design and Installation, 4E has also been restructured to begin with instruction on the major, introductory concepts, and then progressing to more specific, advanced lessons, allowing readers a complete and thorough understanding of the material. This edition includes coverage of the very latest products, tools, codes, and drain cleaning equipment that have had a remarkable impact on the plumbing industry and how plumbers work successfully. The latest water heater technology, such as Flammable Vapor Ignition Resistant heaters, DWV system segments and sizing, new safety regulations, and all relevant code changes are also addressed.
This book presents a detailed, up-to-date discussion of today's most commonly used and emerging methods of nondestructive testingincluding background, explanation, benefits, limitations, applications, and comparisons to destructive testing.
INTERPRETING ENGINEERING DRAWINGS, 8th EDITION offers comprehensive, state-of-the-art training that shows readers how to create professional-quality engineering drawings that can be interpreted with precision in today's technology-based industries. This flexible, user-friendly textbook offers unsurpassed coverage of the theory and practical applications that you'll need as readers communicate technical concepts in an international marketplace. All material is developed around the latest ASME drawing standards, helping readers keep pace with the dynamic changes in the field of engineering graphics This book addresses advances in technology and introduces students to 2-dimensional drawing skills and commands using the current release of AutoCAD. It continuously builds on concepts covered in previous chapters, contains exercises combined with in-text notes, and offers examples that provide the "how and why" of AutoCAD fundamentals. Projects are included at the end of each chapter and provide hands-on experience creating various types of mechanical, architectural, civil and electrical drawings. This text is appropriate for Introductory and Intermediate AutoCAD courses.
This basic text for digital electronics offers complete, practical coverage of the latest digital principles, techniques, and hardware. Written in a concise, easy-to-read style, it includes everything from basic digital concepts to an introduction to microprocessors/microcontrollers. Perfect for a one-semester course, this is the only text that includes both hands-on labs and computer-simulated labs using Electronics Workbench. ALSO AVAILABLE Lab Manual, ISBN: 0-7668-0330-9 | 677.169 | 1 |
This invaluable resource will guide general readers, as well as students, through the often bewildering maze of equations and theorems encountered within the mathematical universe. Nearly 1,000 entries have been added for this new edition covering everything from pure and applied mathematics to statistics. Also included are entries on mathematics of more general interest, such as fractals, game theory, and chaos. Providing succinct definitions and clear explanations to a wealth of terms, A Concise Oxford Dictionary of Mathematics also enables readers to make new discoveries as they browse and check cross-references. With explanatory figures, diagrams, and tables for ready reference to compliment the text, clear and precise definitions, with helpful examples, of a wide range of mathematical terms and concepts, and brief biographical sketches of the great mathematicians, this comprehensive dictionary will serve as an indispensable and trustworthy guide to the dynamic world of mathematics.
Descrizione libro Oxford Paperbacks, 1996. Paperback. Condizione libro Codice libro della libreria mon0002357576
Descrizione libro Oxford Paperbacks, 1996. Paperback. Condizione libro Codice libro della libreria CHL1258947
Descrizione libro Oxford Paperbacks, 19960002360842
Descrizione libro -. Paperback. Condizione libro: Good. The Concise Oxford Dictionary of Mathematics (Oxford Paperback0192800411
Descrizione libro -. Paperback. Condizione libro: Very Good. The Concise Oxford Dictionary of Mathematics (Oxford Paperback0192800411 | 677.169 | 1 |
Detailed Information
Course Description
We will study algebraic geometry, one of the oldest and richest areas of
mathematics. During the 20th century, the theoretical and very
abstract side of the subject was prominent, but with the availability
of computers, the computational roots have been reinvigorated.
This course will develop the theory behind the computational tools.
What is algebraic geometry? Think back to high-school algebra where
you graphed polynomial equations and perhaps found the intersection
of plane curves defined by a line and a parabola or more general
curves defined by polynomials.
Now think about higher dimensional space and consider intersections of
hyper-surfaces defined by polynomial equations.
Such objects are called algebraic sets or algebraic varieties.
What is the dimension? How many components are there? What is the
simplest way to describe the intersection? These are some
fundamental questions of algebraic geometry.
The fundamental result in algebraic geometry is the algebra-geometry
"dictionary" which gives a precise relationship between geometrical
objects and algebraic ones: between varieties in n-dimensional
space and radical
ideals in the polynomial ring in n variables.
The fundamental tools in computational algebraic geometry are Grobner
bases for ideals and Buchberger's algorithm.
Grobner bases are a generalization of the greatest
common divisor of integers.
Just as the Euclidean algorithm may be used to
compute the gcd, Buchberger's algorithm is used to compute a Grobner
basis for an ideal.
The text is a well written book that is one of the
standard references in computational algebraic geometry.
I will cover the core
material on Grobner bases (chapters 1-3), the algebra-geometry
dictionary (chapter 4) and, in less detail, functions on a variety
(chapter 7), and projective space (chapter 8).
Student interest will also guide the course.
Sage is an open source mathematics software package that incorporates
numerous other open-source packages into a unified package.
The Sage tutorial will help you get started.
Prerequisites
A good understanding
of the basics of groups, rings and fields (Math 521A and 521B is enough).
In particular, I recommend you review the following topics.
Properties of the Integers: The division theorem and
divisibility, the Euclidean
algorithm, unique factorization, modular arithmetic.
Polynomial Ring in One Variable: The division theorem, greatest
common divisor, the Euclidean algorithm, unique factorization.
The correspondence between factors and roots.
Polynomial rings modulo a polynomial.
Commutative Rings and ideals: The general language of rings and ideals.
Integral domains, the quotient of an integral domain by an
ideal, homomorphisms.
Linear Algebra: nullspace, subspace, dimension, basis.
Take a look at my webpage for Math
521 A. The book by Hungerford is a great reference. Review
Chapters 1,2,4,5,3,6 in that order. | 677.169 | 1 |
a clear and concise exposition, numerous examples, and plentiful problem sets, Jerome E. Kaufmann and Karen L. Schwitters's COLLEGE ALGEBRA is an easy-to-use book that focuses on building technique and helping students hone their problem-solving skills. The eighth edition focuses on solving equations, inequalities, and problems; and on developing graphing techniques and using the concept of a function. Updated with new application problems and examples throughout, the eighth edition is accompanied by a robust collection of teaching and learning resources, including Enhanced WebAssign®, an easy-to-use online homework management system for both instructors and students.
Meet the Authors
Jerome E. Kaufmann,
Western Illinois University (Retired)
Jerome E. Kaufmann received his Ed.D. in Mathematics Education from the University of Virginia. Now a retired Professor of Mathematics from Western Illinois University, he has more than 30 years of teaching experience at the high school, two-year, and four-year college levels. He is the author of 45 college mathematics textbooks.
Karen L. Schwitters,
Seminole Community College
Karen L. Schwitters graduated from the University of Wisconsin with a B.S. in Mathematics. She earned an M.S. Ed. in Professional Secondary Education from Northern Illinois University. Schwitters is currently teaching at Seminole Community College in Sanford, Florida, where she is very active in multimedia instruction and is involved in planning distance learning courses with multimedia materials. She is an advocate for Enhanced WebAssign and uses it in her classroom. In 1998, she received the Innovative Excellence in Teaching, Learning, and Technology Award.
What's New
Classroom Examples: For every example in the text, there is an associated classroom example problem similar to the example problem. Answers to the classroom example problems are furnished in the Annotated Instructor's Edition but not in the Student's Edition. These classroom examples provide an excellent source of an additional problem to further the understanding of the example presented.
Chapter summaries: Chapter Summaries have taken on an entirely new look. The summaries are presented in a grid fashion by objectives. Each row contains the objective, pertinent information summarizing that objective, and an example problem with solution for that objective.
Objectives. Each section begins with a numbered list of objectives for that section. Then in the Problem Set following that section, groups of problems are identified by section objections.
Features
A Chapter test appears at the end of each chapter to give students ample opportunity to prepare for their exams.
Cumulative Review Problem Sets appear at the ends of Chapter 2-8 to ensure that students retain the concepts of earlier chapters.
Problems called "Thoughts into Words" are included in all problems sets except the review exercises. These problems are designed to encourage students to express, in written form, their thoughts about various mathematical ideas.
Problem solving is an integral part of this text, as is recommended by the standards produced by NCTM and AMATYC. With problem solving as its focus, Chapter 1 pulls together and expands on a variety of approaches to solving equations and inequalities. Polya's four-phase plan is used as a basis for developing various problem solving strategies. Applications of radical equations are a part of Section 1.5, and applications of slope are in Section 2.3. Functions are introduced in Chapter 3 and are immediately used to solve problems. Exponential and logarithmic functions become problem-solving tools in Chapter 5. Systems of equations provide more problem solving power in Chapter 6. Problem solving is the unifying theme of Chapter 9.
The Enhanced WebAssign component will include approximately 2500 homework questions and a YouBook.
Supplements
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
FOR INSTRUCTORS
Test Bank
ISBN: 9781111990428
The test bank includes test forms for each section of the text.
Complete Solutions Manual
ISBN: 9781111990435
The complete Solutions Manual includes solutions for every problem in the text.
PowerLecture with ExamView®
ISBN: 9781111990466Text-Specific DVDs
ISBN: 9781111990527
These text-specific instructional videos provide students with visual reinforcement of concepts and explanations given in easy-to-understand terms with detailed examples and sample problems. A flexible format offers versatility for quickly accessing topics or catering lectures to self-paced, online, or hybrid courses. Closed captioning is provided for the hearing impaired.
Student Solutions Manual
ISBN: 9781111990459
Contains fully worked-out solutions to all of the odd-numbered exercises 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 |
Includes test and answer key booklets. 758 pages, hardcover.
Please Note: This product is only available for purchase by homeschools, consumers, and public institutions.
This kit includes the student text, testing book, answer key, and a solutions manual with worked solutions to every problem in the textbook. Early solutions of each kind contain every step, with later solutions omitting steps considered unnecessary.
This set of additional tests is perfect for siblings or co-ops! Accompanying Saxon Math's Calculus curriculum, these test forms will easily let extra students get the practice they need! 37 Tests with Test solutions are included, with work shown for the test solutions.
Get everything you need for a successful and pain-free year of learning math! This kit includes Saxon's 2nd Edition Calculus textbook, and tests/worksheets book & answer key, as well as the DIVE Calculus CD-ROM. A balanced, integrated mathematics program that has proven itself a leader in the math teaching field, Calculus covers limits, functions, and the differentiation and integration of variablesBring in some outside instruction, and ensure that your students are really getting their Saxon math lessons! Designed to meet the needs of homeschoolers, Teaching Tapes features instruction by a state-certified teacher who explains and demonstrates each concept, example, and practice problem. Perfect for students working at their own pace, Teaching Tape DVDs will help students gain a solid understanding of the material they're working on. Each DVD is approximately 2 hours long. These DVDs cannot be used without the Saxon textbooks.
This set of DVDs is to be used with Saxon Math Calculus, 1st Edition. Please Note: this set is not compatible with Saxon's Calculus, 2nd Edition.
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MATH205B: SECOND HALF ALGEBRA
Course Description
This course contains the material covered in the second half of the Elementary Algebra Course. It will cover factoring polynomials, solving quadratic equations by factoring, rational expressions, radicals, and solving quadratic equations. In addition, the course will review applications involving linear equations of one and two variables, finding slopes and graphing linear equations, solving systems of equations with two variables, and solving linear inequalities. Math 205, 205A and 205B, and 206 have similar course content. This course may not be taken by students who have completed Math 205 or 206 with a grade of 'C' or better. PREREQUISITE: Math 205A with a grade of 'C' or better. ADVISORY: Concurrent enrollment in Guidance 563B is advised.
Learning Outcomes
Apply the laws of exponents to algebraic expressions.
Find the slope and equation of a line.
Graph linear equations.
Solve systems of equations in two variables and their applications.
Define a polynomial and perform the operations of addition, subtraction, multiplication, and division of polynomials. | 677.169 | 1 |
There is a newer edition of this item:
This market leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises and self contained subject matter parts for maximum flexibility.
Thoroughly updated and streamlined to reflect new developments in the field, the ninth edition of this bestselling text features modern engineering applications and the uses of technology. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. The material is arranged into seven independent parts: ODE; Linear Algebra, Vector Calculus; Fourier Analysis and Partial Differential Equations; Complex Analysis; Numerical methods; Optimization, graphs; and Probability and Statistics can't say I love it since it's only a school book, but considering what I've seen of it, it looks pretty much like the original version. I liked that it was a paperback cover, but at the same time I do wish there were hardback versions of this. At least I know I got my money's worth. --By Kyoko on August 28, 2013
The international's questions have different questions than the U.S. version (which is what I needed). Actually, the books are exactly the same content and order-wise, but the questions and examples use different numbers. Another example of textbook printers screwing U.S. students over by charging 2+ times the price. --By Luke on September 6, 2014
--This text refers to an out of print or unavailable edition of this title.
From the Back Cover
In today s world of increasingly complex engineering problems, powerful new mathematical and computational methods, and enormous computer capacities, you can get overwhelmed by little things you will only occasionally use. Instead, you need to learn how to think mathematically and gain a firm grasp of the interrelationship among theory, computing, and experiment. That s why Kreyszig s text helps you develop a solid understanding of the basic principles and methods of advanced engineering mathematics in all three phases of problem solving: Modeling, Solving, and Interpreting. This best–selling text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self–contained chapters.
Key Features
New problem sets.
New Computer Experiments, using the computer as an instrument of experimental mathematics for exploration and research.
Top customer reviews
The product came in excellent condition but the answers to the problems might not always be correct as highlighted by other users before. Recommend to double check your answers with other online software like wolfram alpha.
The actual maths is explained adequately, but the "Answers to Selected Problems"-section in the "International Student Version" is so riddled with blatant mistakes and wrong answers that I can't possibly give a positive review. In some of the exercises, the actual question is wrong like in problem 6.3.7 where e^(-Pi/(2*t)) should actually be e^(-(Pi/2)*t) (which could make you sweat for hours since it's hard - if not impossible - to transform the former equation, and the solutions contain the answer to the latter). As for problem 8.3.1, the solutions claim that the matrix is skew-symmetric. It isn't. The book actually says that "Every skew-symmetric matrix has all main diagonal entries zero".
How are you supposed to know when you've understood a subject when you can't recreate what the solutions state?
This is an absolutely great book. At over 1000 pages it's a real opus - covering everything from ordinary differential equations, linear algebra, vector calculus, fourier analysis, complex analysis and probability. It's exceptionally well written - with plenty of clear examples, diagrams and exercises - constantly cross referencing back to the particular idea or formula that an example is employing. It presupposes only elementary calculus - and so makes an excellent university textbook to accompany study, or as a self-study book to further your maths knowledge.
this is a great book and covers a great deal of material. The great thing about this book is that it will cover everything from first year all the way up to phd level! this is a book for anyone who wants to develop maths to an advanced level granted there are easier books but for the serious engineer/scientist at some point you have to put the baby books away and get this
I have an old version of this that I still occassionally use. It was one of our course books at University many years ago. This latest edition has an easier to read approach and covers most of the subjects with greater clarity and freshness.
Superb book, the author has written it in a context that is very useful for the learning process that most do not adopt by explaining what a topic is used and introducing topics in a logical progression. Shame the book was stitched and the first few pages fell out on opening, printers really need to improve quality control systems. | 677.169 | 1 |
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Mathematics90
What Math You Have to Take to Become a Lawyer
by Robin Elizabeth Margolis, Demand Media
Law students and lawyers use mathematics in many ways.
Law students and lawyers use mathematics in many ways.
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Outline to Become a Lawyer
What You Need to Study to Become a Lawyer
Law schools have traditionally accepted students with undergraduate majors in many different fields, but an American Bar Association (ABA) essay, "Preparing for Law School," currently recommends that undergraduates planning to attend law school acquire "basic mathematical and financial skills, such as an understanding of basic pre-calculus mathematics and an ability to analyze financial data." A look at how law students and lawyers use math skills can provide additional guidance on possible math courses future lawyers may wish to take.
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Background
The most popular undergraduate majors of students entering law school are political science, economics, business administration, history, English and rhetoric. The ABA's recommendation that future lawyers take more undergraduate math classes reflects a gradual shift in legal practice that began in the 1970s toward an increasing use of statistics and other forms of mathematics in trial preparation and other aspects of legal practice.
Law School
Students majoring in mathematics or physics achieved the highest scores on the Law School Admission Test, or LSAT, according to a 2009 study reported by Social Science Research Network. Anecdotal evidence suggests that law students with math backgrounds may benefit in two ways during law school. Some classes, such as tax law, require mathematical calculations. Secondly, law schools teach students a step-by-step method of logical analysis of legal problems called "legal reasoning," which students with math backgrounds may find easier to understand than humanities majors.
Related Reading: Requirements to Become a Prosecution Lawyer
Attorney Specializations
All newly credentialed law school graduates who go to work for law firms need basic math knowledge to fill out time sheets to bill clients and track their business expenses. Some junior attorneys enter legal fields that require business mathematics knowledge, including real estate, taxation, trusts and estates, securities, contracts and bankruptcy. Other lawyers need some acquaintance with pure mathematics such as calculus and statistics to work effectively in legal specializations such as health care law or patent law. Attorneys specializing in litigation often require knowledge of statistics, as many court cases hinge on using statistics to prove factual points.
Undergraduate Math Classes
There's no universal consensus on what types of undergraduate math classes future lawyers should take. The pre-calculus mathematics recommended by the ABA and anecdotal suggestions by math majors who became lawyers, imply that future lawyers should at a minimum take undergraduate courses in college algebra, trigonometry, geometry, logic and statistics. Students hoping to enter legal specializations involved with science, such as the patent area of intellectual property law or health care law, may wish to add two semesters of introductory calculus, as that is often a prerequisite for understanding scientific subjects connected with these areas of law, including physics and biology. The ABA's call for undergraduate students to learn how to analyze financial data can be addressed by signing up for introductory financial accounting and business math classes. | 677.169 | 1 |
9. ANALYTICAL TRIGONOMETRY
10. ADDITIONAL TOPICS IN TRIGONOMETRY
10.1 Right-Triangle Applications 10.2 The Law of Sines and the Law of Cosines 10.3 Vectors in the Plane: A Geometric Approach 10.4 Vectors in the Plane: An Algebraic Approach 10.5 Parametric Equations 10.6 Introduction to Polar Coordinates 10.7 Curves in Polar Coordinates 10.8 DeMoivre's Theorem | 677.169 | 1 |
Objectives: MathCounts Advanced course is appropriate for middle school students who have prior experience in MathCounts/AMC-8 competitions. Students should be familiar with Algebra-1 and Geometry topics.
Who should take this course: Can solve, without guessing, around 19 or more problems on AMC-8 or MATHCOUNTS Sprint round.
Who should skip this course:
AMC 8 Distinguished Honor Roll (24+)
Top 25 at Texas State MATHCOUNTS.
Homework: Daily HW will be assigned during summer classes. Weekly HW will be assigned during fall and spring semester classes.
Resources: Lecture and homework problem solutions will be posted on the classroom page link given above | 677.169 | 1 |
Graphing Skills
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Product Description
This graphing skills packet includes a brief page of graphing guided notes (to be used with the "graphing skills powerpoint") and 3 pages of graphing skills practice. This will your students build a foundation of graphing skills. These are critical skill sets for students to have in life - data literacy is huge in society, politics, economic, science and more! They are also important skills for students to have on all EoG tests | 677.169 | 1 |
Successful game programmers understand that in order to take their skills beyond the basics, they must have an understanding of central math topics; however, finding a guide that explains how these topics relate directly to games is t always easy. Beginning Math Concepts for Game Developers is the solution! It includes several hands-on activities in which basic math equations are used for the creation of graphs and, ultimately, animations. By the time you finish, you will have developed a complete application from the ground up that allows you to endlessly explore game development scenarios for 2D games. If you have a basic understanding of programming essentials and a desire to hone your math skills, then get ready to take a unique journey that examines what is possible when you combine game development with basic math concepts.
Key Features
Author(s)
Boris Meltreger, J. Adam Norris, John Flynt
Publisher
Cengage Learning, Inc
Date of Publication
09/11/2006
Language
English
Format
Mixed media product
ISBN-10
1598632906
ISBN-13
9781598632903
Subject
Mathematics
Publication Data
Place of Publication
Boston, MA
Country of Publication
United States
Imprint
Course Technology Inc
Content Note
illustrations
Dimensions
Weight
704 g
Width
188 mm
Height
231 mm
Spine
25 mm
Editorial Details
Contained items statement
Contains Paperback and CD-ROM
Edition Statement
International edition
Description
Table Of Contents
1. GETTING STARTED WITH C# AND THE MATH LIBRARY A. C# as a Game Development Language B. Setting up a Project C. Inspecting the Math Library D. Guess a Number 2. FUNCTIONS AND METHODS A. Understanding Functions as Patterns B. Creating Lab for Exploring Functions a.Generating Date for a Table b.Developing Classes c.Equations and Methods 3. CONCEPTS BEHIND FUNCTIONS A. Number Domains B. Restricted Values C. Handling Exceptions D. Making use of a List to Store Function Output E. Fields and Properties F. Division By Zero and Other Mysteries 4. EXTENDING THE LAB WITH A COORDINATE PLANE A. How to Graph B. Putting the List Values to Work C. Using a Flag D. Closing E. The True Value Game 5. LOCAL AND WORLD SPACE IN CARTESIAN TERMS A. Spawning a Cartesian Plane. B. Learning How to Do Things Twice C. Understanding Grids D. Axes and How to Make Them E. Making Your Point F. Finding the Curve 6. CHANGING THINGS: LINES, SLOPES, AND METHODS A. What Counts As a Valid Function B. Constant Functions C. How to Make a Profit D. Linear Things E. Making Things Visible F. Method Overloading H. The Factory Game 7. QUADRATICS AND OTHER FUNCTIONS A. Parabolas B. Minimum and Maximum C. Absolute Values D. Discontinuous Functions E. Stair Steps and Other Antics F. The Table Game 8. LIMITS AND METHODS FOR THEM A. Talk of Limits B. Bicycle Tires C. Different forms of Limits D. Continuity E. Infinity F. Creating Graphics That Merge 9. ANIMATING THE WORLD A. Threads and Timers B. Eliminating Flicker C. Derived Classes D. Working with Arrays of Continuous Values E. Queues and Coordinates F. Event Generation G. Event Detection 10. IN TO THE GAME A. Derivation and Acceleration B. Controlling Flight C. Multiplying Complexity D. A Target Game E. Extended Intelligence in Games
Author Biography
John P. Flynt, Ph.D., works in the software development industry, has taught at colleges and universities, and has authored courses and curricula for several college-level game development programs. His academic background includes work in information technology, the social sciences, and the humanities. Among his works are In the Mind of a Game, Simulation and Event Modeling for Game Developers (with co-author Ben Vinson), and Software Engineering for Game Developers. John lives in the foothills near Boulder, Colorado. Boris Meltreger graduated from a top mathematics and physics high school in Russia. He went on to earn an advanced degree in optical engineering. After completing a dissertation on acoustics and optics, Boris took up work for the Russian government developing optical computers. He has been the recipient of engineering awards for his work and has owned his own engineering company. Boris has in recent years performed pioneering work in the development of optical technologies for medical applications and currently works as a software engineer. Boris lives in Aurora, Colorado | 677.169 | 1 |
17 Equations That Changed The World
Calculus visuals:
desmos-graph-5
desmos-graph-4.png
Math Teacher Mambo: Calculus Graphical Organizer
Precalculus will be moving beyond their introduction to functions and function notation from Algebra II and into a in-depth development ...
Properties of polynomial functions
End behavior "discovery" intro - start with a basic introduction to vocabulary (degree, leading coefficient). Give each group a copy of the first page to cut out and sort based on the degree and leading coefficient. We'll then compare the end behavior of the graphs in each group to come up with the "rules" for polynomial end behavior. | 677.169 | 1 |
Department of Mathematics
Integrated Algebra-ME21, ME22, ME43, ME44
This is the first mathematics course in high school. The course set forth here is not the algebra course of 30 years ago. The focal point of this course is the algebra content strand. Algebra provides tools and ways of thinking that are necessary for solving problems in a wide variety of disciplines, such as science, business, social sciences, fine arts and technology. This course will assist students in developing skills and processes to be applied using a variety of techniques to successfully solve problems in a variety of settings. Students take a Regents exam at the end of the course.
Geometry-MG21, MG22, MGS33
This is intended to be the second course in mathematics in high school. There is no other school mathematics course that offers students the opportunity to act as mathematicians. Within this course, students will have the opportunity to make conjectures about geometric situations and prove in a variety of ways, both formal and informal, that their conclusions follow logically from their hypothesis. This course is meant to employ an integrated approach to the study of geometric relationships. Students take a Regents exam at the end of this course.
Algebra 2 and Trigonometry-MR21, MR22
This is the capstone course of the three units of credit required for a Regents diploma. This course is a continuation and extension of the two courses that precede it. While developing the algebraic techniques that will be required of those students that continue their study of mathematics, this course is also intended to continue developing alternative solution strategies and algorithms. For example, technology can provide too many students the means to address a problems situation to which they might not be otherwise have access. Students take a Regents exam at the end of this course.
Pre-Calculus-MPS21, MPS22
This is a yearlong elective honors course for students who have completed their high school and regents math requirements. This course is considered an introduction to higher-level math and is essential for students who want to enroll in calculus.
Advanced Placement Calculus-MCS21X, MCS22X
This is a yearlong elective honors course for students who wish to have the opportunity to receive college credit from a high school class. Students can take the Advanced Placement exam after completing the course and receive college credit if they do well enough on the exam. This is considered the first course of higher-level math. | 677.169 | 1 |
Mathematical Methods Units 1 and 2
Overview
There are four broad Areas of Study in this course: functions and graphs, algebra, calculus, probability and statistics. You will progressively develop skills and knowledge from each of these four areas, and the connections between them.
Who is it for?
This subject is for students who would like to do further study with a view of a career in computer science, physics, chemistry and engineering.
It is also for students with an interest in how aspects of our world can be explained by mathematical processes, for example, Mathematics underlies the modelling of weather patterns.
What do you do?
Throughout the course, you will be completing weekly assignments, practice exercises, activities, modelling and problem-solving tasks, and do a test at the end of each semester.
What skills do you need?
Students need to have good algebraic skills. Those who have not studied mathematics for some time are advised to revise the algebraic component of the Year 10 Mathematics course.
What skills do you develop?
On completion of this course students should be able to:
apply mathematical processes in non-routine contexts and discuss these applications
use technology to produce results and carry out analysis in situations that require problem solving, or investigative techniques.
Requirements
You must have access to the internet in order to access this course. All weekly work will be completed and submitted online.
OR
Interactive textbook powered by HOTmaths
CAS calculator
For this study, students need access to a VCAA-approved CAS calculator. DECV course notes are written using the TI-Nspire CAS and Casio ClassPad. Students are highly recommended to get one of these, if they are going to buy a new calculator. However, any of the listed VCAA approved CAS calculators can be used. | 677.169 | 1 |
MATH 107 – Math in Society
The purpose of this course is to expose you to the wider world of mathematical thinking. There are two reasons for this. First, for you to understand the power of quantitative thinking and the power of numbers in solving and dealing with real world scenarios. Secondly, for you to understand that there is more to mathematics then expressions and equations.
Readings from a complete textbook, available in printed form for ~$15, or online for free.
A playlist of videos, corresponding to the examples in the text.
Exercises are available in the book, or algorithmically generated online homework and quizzes are available on WAMAP.org (for Washington faculty) or MyOpenMath.com (for everyone else).
A writing assignment, requiring the students to think beyond calculations. For example:
Find an article in a newspaper or magazine (or the online equivalent) describing a recent study in which the researchers collected data through observation or an experiment to draw a conclusion. A simple poll (like "43% of Americans like to eat sushi") is not sufficient; you should be looking for something describing a significant research study. Some examples (don't limit yourself to these):
an experiment testing a new drug or medical procedure
a study linking a food or exercise with causing or reducing the risk of a disease
a study about how some new teaching approach improves learning
a study about how people behave (example: a study showing incentives can cause us to be less efficient)
Create a new thread in the discussion forum. In it:
Give a brief summary of the article's findings (5 pts)
Discuss whether the article provides enough information to determine the validity of the conclusions (5 pts)
Whether there is information that would be useful that was left out of the article (5 pts)
A list of things that are missing from the article that would help you determine the validity of the study (4 pts)
Be sure to cite the source of the article that you base this on. Include the web address to the specific article if the article is online. Include the article title, source, and date if the article is not online. (+1 pts for including, -10 pts if missing)
For many topics, some in-class activities and paper quizzes are available. The textbook includes exploration questions which can be used to guide in-class discussion or for group activities.
Student feedback on this course:
"I was fearful about taking a strictly "on-line" course, especially one dealing with math, since I haven't taken a math course in over 30 years and the on-line option was very new to me. Your course was so well organized I found it to be incredibly easy to follow. Your clear objectives, requirements, grading system, and quick replies made this one of the most pleasurable classes I have ever experienced. I found the use of videos to supplement the text extremely helpful." | 677.169 | 1 |
Textbook:
Grading:
Your grade will be determined by mastering the 10 course topics listed above. Grading is very simple: if you master 9 or 10, you get an A; 7 or 8 a B; 4-6 a C; 2-3 a D; 0-1 an F.
Mastering a topic means understanding it from all angles. You should understand the definitions, theorems, and examples we've discussed in class. You should be able to apply the theorems and methods to problems you've never seen before (and not just be able to do problems of the same type you've seen). Understanding a theorem means understanding how it can be used (know some examples); understanding why each of its conditions is necessary (and know counterexamples); understand why its conclusion cannot be made more strong.
There will be several ways to demonstrate that you've mastered a topic:
A short oral quiz (10 minutes) at the time of your choosing. You will have 2 attempts for each topic.
We will have 4 tests scheduled, and on each you will have the chance to show mastery of 2 - 4 topics.
The final exam will be a last chance for any topics you still have left.
Once you've showed that you've learned a topic, you're done with it for the whole semester. The tests are an indication of where you are and a guide so you don't fall behind. But you are welcome (and encouraged) to pass all of the topics with the oral quizzes whenever you feel you have learned the topics.
Here's link to Georgia Tech's honor code (please read it). It applies to the tests and final exam, but for everything else in the class I encourage you to work together.
Course Discussion Site
We will be using a website called piazza.com as our course discussion site. Sign-up here.
I'd like you all to be active on the site, asking questions, answering questions, and helping each other learn the material. Here are some possible uses:
Any question about the class, an assignment, or the material you should ask on the discussion site instead of emailing me. That way everyone can see the answer.
I encourage you to post your answers to the homework questions on the site. If someone else has posted the same answer as yours you can ``agree'', or if you have gotten a different answer you can explain yours. I will `endorse' the best answer I see. | 677.169 | 1 |
Algebra for College Students (7th Edition)
Author:Margaret L. Lial - John Hornsby - Terry McGinnis
ISBN 13:9780321715401
ISBN 10:321715403
Edition:7
Publisher:Pearson
Publication Date:2011-01-29
Format:Hardcover
Pages:936
List Price:$226.40
 
 
Is there anything more beautiful than an "A" in Algebra? Not to the Lial team! Marge Lial, John Hornsby, and Terry McGinnis write their textbooks and accompanying resources with one goal in mind: giving students all the tools they need to achieve success.
With this revision, the Lial team has further refined the presentation and exercises throughout the text. They offer several exciting new resources for students that will provide extra help when needed, regardless of the learning environment (classroom, lab, hybrid, online, etc)–new study skills activities in the text, an expanded video program available in MyMathLab and on the Video Resources on DVD, and more!
Booknews
New edition of an algebra text that presents up-to-date strategies for helping students to succeed. Lial (American River Collete) and Hornsby (U. of New Orleans) introduce functions and graphs early in the third chapter (following a review of the real number system and linear equations and inequalities), thus providing groundwork for the function/graph emphasis throughout. Subsequent chapters introduce graphs of polynomial, rational, and radical functions; expressions and equations; and additional topics such as quadratic functions, translations, symmetry, and inverse, exponential, and logarithmic functions. Annotation c. Book News, Inc., Portland, OR (booknews.com) | 677.169 | 1 |
JEE Main Maths Syllabus
JEE Main, thus, becomes a very important exam as not only it is necessary for getting admission into NITs and IIITs, but even if someone wants to qualify for JEE Advances, he/she has to score good in JEE Main. More than 12 lakh candidates appear for this exam every year and thus, the level of competition is huge. To clear this exam, candidates do need to do a lot of efforts.
Mathematics is an important section for JEE Main as it occupies 1/3rd of the paper. So a candidate cannot even think to take this subject lightly. Let us take a look at syllabus and preparation strategy for Mathematics for JEE Main:
JEE Main Examination Pattern
JEE Main examination pattern is quite simple. The test is held in both offline and online mode and candidates have to answer 90 questions in 3 hours. There are three sections, namely Mathematics, Physics and Chemistry, each having 30 questions. Each question carries 4 marks and there is a negative marking of 1 mark for each incorrect answer.
For majority of courses the examination pattern is like as mentioned above. However, for B Arch course, the pattern is a bit different. For B Arch, JEE Main will have 50 questions on Aptitude and 2 on drawing and importantly, this paper will also have 30 questions on Mathematics. Timing and Marking Scheme will remain the same. JEE Main for B Arch is held in offline mode.
JEE Main Mathematics Syllabus
Syllabus for Mathematics under JEE Main is huge. But the majority of syllabus includes topics which a candidate has already studies. So candidates only need to increase the depth of their knowledge and need to solve higher level questions of concepts already studied. The syllabus for JEE Mains for Mathematics section in as follows:-
Algebra and Type of Matrices and Determinants, Properties, evaluation and area of triangle using determinants, Test of consistency and solution of Linear Equations using these two
Permutation and Combination
1
Basics of Counting, Meaning of P and C, Arrangement, Combination, Selection and Applications of concept
Mathematical Induction
1
Meaning and Application
Binomial Theorem
1
Theorem for Positive Integral Index, General Term and Middle Term, Properties and Applications
Sequence and Series
2
AP and GP, Insertion AM GM in two numbers, Relation between AM GM, Arithemetico Geometric Expression, Sum of Special Series
Limit, Continuity and Differentiability
1
Real Valued Fucntions, Algebra of – Functions, polynomials, rational, trigonometric, logarithmic and exponential functions, also derivatives up to order two. Application of Derivatives, Graphs of simple functions. Limits, continuity and Differentiability. Differentiation of Sum, different product and quotient of two numbers. Mean value theorem, Application of Derivatives
Integral Calculus
3
As Anti-derivative, Fundamental Integrals, Integration using trigonometric identities, Integral as limit of sum, fundamental theorem of calculus, Properties and evaluation by definite integrals, are of region enclosed
Cartesian system of rectangular co-ordinates in a plane, distance and section formula, locus and its equation, slope, intercept of a line, straight lines, circles and conic sections
3D Geometry
3
Co-ordinates of a point in space, distance and section formula, direction ratios and cosines, angle between two intersecting lines, shortest distance and equation, intersection of line and plane, coplanar lines.
Vector Algebra
1
Vectors and Scalars, components of vector in 2D and 3D space, sum of vectors, scalar and vector products and triple products
Usage of or, implies, implied by, if and only if, tautology contradiction, converse and contrapostitve.
JEE Main Mathematics Preparation Tips
One thing that is clear is that candidates will need to have deep conceptual knowledge of mathematic concepts, in order to solve the questions of JEE. Therefore, doing the syllabus properly, along with needed amount of practice is necessary. So here are some preparation tips for preparing for JEE Main Mathematics:
Start preparation at proper time
It's very important that you give yourself time to prepare for JEE Main. If you want to prepare during your 10+2, then start preparation right from the start of session. And if you want to prepare after your 10+2 , then you should give a whole year to JEE Preparation, thus should start right after your exams. As syllabus is huge and deep understanding is needed, proper time needs to be devoted.
Be good with basics
Before jumping on to high level questions, it is very important to be good at basics. So candidates, rather than cramming and mugging up formulae and shortcuts, should try to be good with basics. NCERT books are a great source for this purpose.
Do time based practise
Candidates must note down the time they take to solve each question. Solving a question correctly is good, but not at the cost of a lot of time. Therefore, focus should be on time based practice.
Identify strength and weakness
Now there will be many people who will suggest you to do 'xyz' topic, and other will suggest you to do 'abc' topic. However, the real secret is that you should yourself identify your weak points and strong points, and thus work collectively on them. It's only you who knows where you are good and where you are not.
Give proper time to all subjects
Now this might seem unrelated to mathematics preparation, but it is very important to give time to all three subjects. Doing one subject all day might make you feel monotonous and may thus reduce your efficiency. Therefore, do study all three subjects every day to keep the rhythm correct.
Make a formula Sheet
Formula sheets might be available at many places, but it is very important that you make your own formula sheet, as you will be able to use it a better way. Also, things are easily traced back when they are prepared by us. Therefore, one should make his/her own formula sheet for Mathematics, rather than referring to someone other's formulae.
Solve past year JEE papers
This tip might be written at the last, but probably this carries a lot of weightage in your preparation. Solving Past year JEE papers is a must as it introduces you to actual exam-like problems. Also, identify patterns and topics of most importance from these papers. This will take your preparation to next level.
JEE Main Mathematics Study Material
It is very important that one uses proper study material for preparing for JEE Main. Proper books and material expose to more type of topics and are a core part of your preparation. Here are some books which should be followed for JEE Main Mathematics:
Book Name
Publisher/Writer
Class 11 and 12 Mathematics
NCERT
JEE Main Complete Mathematics
McGraw Hill
A MASTER Resource for Mathematics in JEE Main
Praful K Agarwal
Objective Mathematics for JEE
R D Sharma
Integral Calculus for JEE Main & Advanced
Amit Agarwal
Differential Calculus for JEE Main & Advanced
Amit Agarwal
The importance of this exam lies in its scope. There are a lot of colleges that grant admission under JEE Main and thus it becomes important that candidates studies for this exam properly. Studying all three subjects with balance is the key to get a good rank, thus candidates should follow a well made strategy for tackling this exam. | 677.169 | 1 |
...Designed to enable adults with no formal qualifications to prepare in one year for entry to a Degree/HND/HNC course in Mathematics, Applied Mathematics or Computing. Successful students are GUARANTEED a place on a Degree/HND/HNC course... Learn about: Data analysis, Engineering Mathematics...
...Our ambition is to give you a sound preparation for a career in which Mathematics plays a role, whether it be in research or through applications... Learn about: Data analysis, Mathematics Series...
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...This programme will train you in both mathematics and finance, making you highly desirable to employers, and uses guest lecturers and tutors from the financial sector... Learn about: GCSE Mathematics, Financial Training...
...The M.A. in Primary Education with Mathematics is one of a suite of six programmes which replaces the B.Ed in Primary Education (Hons), in response to the Scottish Governments recent endorsement of Teaching Scotlands Future: Report of a review of teacher education in Scotland (Donaldson:... Learn about: GCSE Mathematics, Teacher Education...
... with an in-depth understanding of a range of topics in mathematics. In addition, students who meet the appropriate criteria and proceed to the project will gain experience in presenting results in mathematics in a clear and concise manner. The MSc has at its core fundamental courses in pure mathematics... Learn about: GCSE Physics, Part Time, Mathematical Physics... | 677.169 | 1 |
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MSP:MiddleSchoolPortal/Algebraic Thinking: A Basic Skill
From Middle School Portal
Numbers at Work! - Introduction
Algebraic thinking should be considered a basic skill for middle school students because it is compatible with their changing, maturing intellectual capabilities. Glenda Lappan, a teacher educator and author of textbooks for the middle grades, noted consequences of this intellectual growth for school mathematics programs:
Students in middle grades are growing in their ability to reason abstractly. They become capable of generalization, abstraction, and argument in mathematics. This signals the need for programs that give students the opportunity to expand their experiences with "doing mathematics," with controlling variables and examining the consequences, with experimenting, making conjectures, and developing convincing arguments to support or disconfirm a conjecture (Lappan, 2000, p. 23).
The resources highlighted here aim to reflect students' growing mathematical capacity over the span of the middle school years. The activities and lessons, intended as supplementary materials, range from introduction to the fundamentals of algebra to work on linear functions. Uniformly, they take into consideration the preference of the middle school student for concrete models, visual representations, and interactive tasks. You will find resources on:
Working with algebraic expressions
Solving equations
Understanding graphs
Moving from patterns to rules to functions
Some are games, others are online simulations that can complement a lesson, and yet others are full-blown lesson plans. We believe you will find tasks here that motivate your students to expand their basic skills in algebra.
Background Information for Teachers
Being expected to teach algebra—at any level of middle school—can arouse anxiety. Questions may range from the actual teaching of the material to the content knowledge needed to teach such an abstract subject. The first three resources here speak directly to these questions. Each is a professional course offered free and online. The next two are large sets of activities, virtual treasure troves!
Insights into Algebra 1: Teaching for Learning
In this online professional development workshop for middle and high school teachers, participants explore strategies for teaching 16 topics found in most Algebra 1 programs. In each session, teachers view two half-hour videos that feature effective strategies for teaching specific algebra topics. Then, using a workshop guide, teachers participate in activities designed to help them incorporate these strategies in their own practice. From Annenberg/CPB: Teacher Professional Development.
Learning Math: Patterns, Functions, and Algebra
An online course designed for K-8 teachers who want to explore or deepen their understanding of the "big ideas" in algebraic thinking. Each of 10 sessions centers on a topic, such as understanding linearity and proportional reasoning or exploring algebraic structure. The teacher-friendly design includes video, problem-solving activities, and case studies that show you how to apply what you have learned in your own classroom. From Annenberg/CPB: Teacher Professional Development.
Algebra in Simplest Terms
This video series could be valuable for teachers who want to review algebra. Intended for high school classrooms and adult learners, the course offers 26 half-hour video programs and coordinated books. From Annenberg/CPB: Teacher Professional Development.
Algebra Problem of the Week
You will find excellent algebra problems from a variety of sources here, at varying levels of difficulty. The problems challenge students to think through their solutions and put them in writing. A small subscription fee is charged for entry to the problems section.
King's List of On-line Math Activities
This comprehensive site contains links to numerous online math activities. What makes it invaluable to the teacher is its listing of specific topics. For example, under Pre-algebra/Algebra, you will find links to activities on functions machines, order of operations, and solving equations.
Working with Algebraic Expressions
These activities can provide a first encounter with positive and negative numbers, order of operations, and factoring polynomials. Ranging from games to full lesson plans, these resources could supplement your classwork in these areas of algebraic manipulation.
Space Coupe to the Rescue
In this online activity, students key in a positive or negative number to raise or lower their space coupe. The challenge is to line up the coupe with a virus pod on the screen; this destroys the pod, one of eight to be destroyed within a given time. The distance the ship needs to travel to destroy each pod is counted using a scale on the left side of the screen. An excellent first experience with integers!
Late Delivery
In this game, the student helps the mail carrier deliver five letters to houses with numbers such as 3(a + 2). The value of a is held by the dog. This is a good exercise in substituting for variables. Three levels of difficulty are available. The game is part of the Maths File Game Show.
Amby's Math Resources: Order of Operations
This resource is a tutorial and practice on a topic that often frustrates the younger middle school student. Immediate feedback is given when an incorrect answer is chosen, plus a full explanation of the correct solution.
Explaining Order of Operations
How would you explain the order of operations to a fifth or sixth grader who has not yet studied the subject? This is a question from a teacher. An answer from Dr. Math sets out how he would develop the accepted order of operations in much the same way that students might develop the rules for a game.
Balance Pans-Expressions
This interactive pan balance allows students to enter numeric or algebraic expressions. They can "weigh" the expressions by entering them on either side of the balance and seeing if they are equivalent.
Understanding Algebraic Factoring
An excellent set of lesson plans that introduce factoring through finding areas of rectangles! Each step in the procedure is well explained and illustrated. Questions for the class are included. This unit is meant to be worked with algebra tiles, either the usual plastic ones or cut-out paper shapes.
Difference of Squares
Designed for two class periods, this lesson begins with computing the squares of any two consecutive integers and finding the difference of the squares. Students build on further arithmetic experiences as they are led to generalize to the algebraic rule on factoring the difference of two squares. Steps are carefully set out. As an extension of the lesson, a geometric interpretation of the rule is explained and illustrated.
Solving Equations
Each activity here involves solving equations or investigating the rationale underlying the basic rules for solving equations. All challenge students in unique ways.
Gone Fishing: My, My, Little Fish-How You've Grown!
The activity opens with a cartoon showing the weights of three combinations of fish. The challenge is to determine the weight of each fish. Three solutions are set out graphically and in terms that can be easily translated to algebraic symbols. An excellent introduction to the manipulation of equations and the reasoning that underlies it!
Equation Match
Students must solve equations, from the most simple to more complex, and in this way find pairs of equations that "match"; that is, both equations in the pair have the same value of x. When a match is found, part of a picture is revealed. At each return to the game, a new set of equations is given. From the Maths File Game Show.
Algebra-Fun with Calendars
Clever tricks-sleight of mind, if you will-involve calendars and the patterns of numbers on them. Each "trick" is found to be an equation that simplifies to an algebraic expression. Students end by creating their own calendar problems and simplifying their own equations. From Mathematics Lessons That Are Fun! Fun! Fun!.
Balance Beam Activity
This simulation of a balance beam allows students to explore the meaning of balance, a key concept in developing mathematical understanding of solving equations. Working with two to four shapes of differing weights, the students must experiment to balance the virtual scale by adding shapes of unknown weights. Finally, although the weight of one shape is known, students must use basic equation principles to find the weights for the other shape or shapes.
Algebra Balance Scales-Negatives
Like the Balance Beam Activity above, this online manipulative also features a virtual balance scale, but the challenge is very differentUnderstanding Graphs
Graphing holds a central place in algebra. It connects the algebraic statement to a geometric representation. These resources begin at the beginning—plotting points—then move on to examining slope and the graphs of linear and nonlinear functions. Lots of opportunity for experimenting with graphs!
General Coordinates Game
Here is a game for those just learning the Cartesian coordinate system. An applet allows players to name the coordinates of a house placed on the grid by the computer, or input their own coordinates for the house. A brief history of Descartes' invention and a good discussion on plotting points are provided, but, unfortunately, no game rules are included. Your students will enjoy inventing their own.
Maze Game
The game is to move a robot from the bottom corner of an x-y grid to the top right corner, but mines block the way. To move the robot, players have to give the coordinates of the next point; one mistake and BAM! Students can request up to 30 mines and, after a little experience with the game, will probably want that many. Good practice on locating and naming x-y coordinates.
Understanding Distance, Speed, and Time Relationships
In these two lessons, students use an online simulation of one or two runners along a track. Students control the speed and starting point of the runner, watch the race, and examine a graph showing time versus distance. Students can use the activity to come to conclusions on the distance, speed, and time relationship. They can also use it to consider the graphical representation and the concept of slope.
Stressed Out-Slope as Rate of Change
A story and a graph begin this activity. The graph shows how performance is related to stress; questions ask students to analyze the graph in terms of the story situation. Students then consider a graph of speed over time, and are asked to create their own graph showing "a direct relation between the rate of change of a function and the slope of its lines." This activity is part of Mathematics Lessons That Are Fun! Fun! Fun!
Planet Hop
You are traveling through space. You must find the coordinates of four planets and then write the equation of the line you have created. This game is part of the Maths File Game Show.
Lines and Slope
A chameleon named Joan helps illustrate how to graph linear equations, first using only two points that are solutions to an equation, then gradually introducing the idea of slope, and building to the slope-intercept form of the equation. The goal is to visualize the concept of slope and understand the reasoning behind the standard formulas.
Slope Slider
Using this simulation, students can manipulate a linear function of the form f(x)=mx+b and explore the relationship between slope and intercept in the coordinate system. They can see the slope of the line change as they change the value of m.
Grapher: Algebra (Grades 6-8)
An interactive tool for practicing graphing or for visualizing functions! Students can graph one to three functions, of different colors, in the same window. Functions can be written with absolute value, square roots, exponents, or algebraic fractions, and the domain can be restricted.
Function Flyer
This simulation tool allows students to graph not only linear but also exponential and polynomial functions. Students create the function, see it graphed, and can then change the constants, noting the effects visually and immediately on the graph.
From Patterns to Relations to Functions
Since elementary school, your students have worked with patterns. The lessons and activities featured here move students mathematically forward to consideration of the rules underlying the patterns and then to formulation of those rules in algebraic terms.
Barbie Bungee
Looking for a "real-world" example of a linear function? In this lesson, students model a bungee jump using a Barbie doll and rubber bands. They measure the distance the doll falls and find that it is directly proportional to the number of rubber bands. Since the mathematical scenario describes a direct proportion, it can be used to examine linear functions.
Function Machine
Operating under a secret rule, the function machine uses numbers input by the students to generate output. Students compare the input (domain) to the output (range) to find the function rule. The analogy of a function machine is a basic, strong visual that holds up even in advanced study of functions.
Walk the Plank
One end of a wooden board is placed on a bathroom scale and the other end is suspended on a textbook; students can literally "walk the plank" and record the weight shown on the scale as their distance from the scale changes. It turns out that the relationship between the weight and distance is linear, and this investigation leads to a real-world occurrence of negative slope. An activity sheet, its solutions, and questions for class discussion are included in this one-period lesson.
The Handshake Problem
This two-lesson unit allows students to discover patterns in a fictional but real-world scenario: How many handshakes occur when the nine Supreme Court justices shake hands with each other? Students explore—through a table, a graph, and finally an algebraic formula—the number of handshakes in any size group. A second pattern is explored, that of triangular numbers; again, students generalize the pattern with variables. The lessons are well illustrated and include background information for the teacherExploring Linear Data
This lesson connects statistics and linear functions. Students construct scatterplots, examine trends, and consider a line of best fit as they graph real-world data. They also investigate the concept of slope as they model linear data in a variety of settings that range from car repair costs to sports to medicine. Handouts for four activities, spread out over three class periods, are provided. Equations and Graphing.
Careers
The FunWorks
Visit the FunWorks STEM career website to learn more about a variety of math-related careers (click on the Math link at the bottom of the home page).
NCTM Standards
In presenting its "ambitious, focused mathematics program for all students in the middle grades," the National Council of Teachers of Mathematics identifies "ambitious expectations . . . in algebra and geometry that would stretch the middle-grades program beyond a preoccupation with number" (NCTM, 2000, p. 211). Algebra is not proposed as a one-year course for a select few but as an integrated component of a program that extends throughout the middle school math curriculum.
The NCTM Principles and Standards for School Mathematics document presents algebra as more than an exercise in manipulating symbols or even solving equations; it is a way of thinking that permeates a broad range of math content. The document states that "students in the middle grades should learn algebra both as a set of concepts and competencies tied to the representation of quantitative relationships and as a style of mathematical thinking for formalizing patterns, functions, and generalizations" (p. 223). In particular, the Standards recommend that students see "algebra and geometry as interconnected," experiencing "both the geometric representation of algebraic ideas, such as visual models of algebraic identities, and the algebraic representation of geometric ideas, such as equations for lines represented on coordinate grids" (p. 212).
You will find the resources featured here to be appropriate for a wide range of students. Moreover, they focus not only on facility with algebraic manipulation but also on algebra as a way to represent a mathematical situation. The connection between geometry and algebra is highlighted through activities that focus on students' understanding of graphs, from simply plotting points to actually graphing linear functions.
For more information on the NCTM Standards, check out the nine specific expectations for algebra at the middle school level. For more insight into how to reach those expectations, Navigating through Algebra in Grades 6-8 offers problems and activities that show how students can model mathematical situations through algebraic thinking.
Connect with colleagues at our social network for middle school math and science teachers at
Copyright June 2006 | 677.169 | 1 |
Mathematical Reasoning: Middle School Supplement
About the Book
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Synopsis: Mathematical ReasoningTM Middle School Supplement reinforces 7th and 8th grade math concepts and skills by asking students to apply these skills and concepts to non-routine problems. Applying mathematical knowledge to new problems is the ultimate test of concept mastery and mathematical reasoning. This user-friendly, engaging book is made up of 50 theme-based collections of problems, conveniently grouped in self-contained, double-sided activity sheets that provide space for student work. Each collection contains relevant math facts at the end of the worksheet in case students need hints to solve the problems. Calculators are allowed on activity sets that have a calculator icon at the top of the front side of the set. Each activity set is accompanied by a single-sided answer sheet containing strategy tips and detailed solutions. Teachers and parents will appreciate the easy-to-understand, comprehensive solutions. This book is a wonderful enrichment tool, but also can be used to assess how well students have learned middle school math concepts 31050 1601446446-LOCATION-31173 | 677.169 | 1 |
Queueing systems
Use queuing theory to determine which queue to join at the checkout
Queuing theory is the mathematical study of waiting lines, or queues. In queuing theory, a model is constructed so that queue lengths and waiting time can be predicted. Applications of this theory can be seen in telecommunication, traffic engineering, computing and in the design of factories, shops, offices and hospitals.
Activity info, teachers' notes and curriculum links
An engaging starter activity in which students will use queuing theory to determine which queue to join at the checkout
Activity overview
Queues activity description, teachers' notes and curriculum links.
Presentation
Use the queuing theory to estimate the best queue to join at the checkout. | 677.169 | 1 |
Main Menu
Our educational philosophy
A systematic approach to teaching and learning of college maths/math
Common misconceptions
At college level maths is simply a language for describing relationships between measurable quantities. It is best learnt when presented in a systematic way. Contrary to a common misconception adults can learn this language much faster than children: It is very logical and adults can rely on their experience of logic better than children.
Another common misconception is that ordinary people find it difficult to understand abstract concepts. Again, when presented in a systematic way, most ordinary adults find basic mathematical abstractions understandable and helpful. Practice shows that they learn much faster and retain knowledge much longer when – rather than learning by rote – they are shown the underlying logic of the course and thus various connections between the underlying concepts.
This type of learning still requires students to do a considerable amount of self-study and exercises – but less so than the standard approach. It can succeed only if the teachers keep reinforcing the students' mathematical skills throughout the course – or students do it themselves. Of course, once the skills become hard-wired into the students' brains there is no need for conscious recollection of all the connections and students begin to function as ordinary competent users of mathematics.
Competence through comprehension
Developed over 16 years in a UK University of widening access/broadening participation, the mathematics teaching and learning techniques we advocate are deeply rooted in the best educational practices tried over the centuries, adapted to modern conditions and supported by modern pedagogical findings. They lead to competency the fastest possible way – through comprehension. Once students become competent users of algebra, pre-calculus and calculus they significantly increase their chances of success on STEM courses.
The methodology is geared towards STEM students, increasing their engagement and therefore retention. It rests on two corner stones, Socratic Dialogue and Eulerian Sequencing.
Socratic Dialogue
Socratic Dialogue is a process of systematic inductive questioning used to lead a learner to knowledge through small steps. It has been repeatedly shown to be best suited for teaching those with poor motivation and since the 1990s has been used to revolutionise US undergraduate physics teaching. We believe it can revolutionise the teaching of college algebra and basic calculus. It provides instant feedback to both teacher and learner, increases learner engagement and reduces the need for testing.
Contrary to a widespread belief, Socratic dialogue can be practised in large classes. We can show
you how.
Eulerian Sequencing
Eulerian Sequencing is a systematic approach to teaching mathematics as a language in a way first promoted by Euler (see Bibliography). It focuses on teaching learners to sequence mathematical expressions and solution steps. Sequencing shows learners not only WHAT they are supposed to do but also WHY. This is important because it has been shown that the amount learnt is proportional to the number of self-explanations learners can generate.
Contrary to a widespread belief, it is not that hard to teach explanatory reasoning.
We can show you how. | 677.169 | 1 |
The Goal of This Class
The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields. Either of these will open up and clarify our thinking on a subject, and if category theory can help us do that consistently, then we should all be prepared to consider the class a success.
However, it is possible that the class will fail this test. That is, in order to be really honest we must be willing to acknowledge that maybe category theory is not useful in expanding scientific thinking. But we will only admit defeat if we first make a good faith effort to prove its usefulness to ourselves and find that we come up short.
To that end, I am requesting your help. I have written a book with several scientific applications, but it could use many more. Once you understand a mathematical topic we discuss, look into your field to see how it might apply there. Such an application might be obvious and "on the surface" or creative and "deep", but anything of the sort will be useful to us. I want you to tell me what resonates with you, what works for you, what expands your thinking. You can express this in class or in written correspondence.
I also want to hear from you what is missing. If we are to make a powerful impact on our thinking, we should be on the lookout for what we'd hope to find but seem to miss. We admit from the beginning that category theory is not intended to provide formulas that take in initial data and make predictions about the future. This is the domain of differential equations, linear algebra, and other well-known subjects in applied mathematics; it is not something we are attempting to improve upon with category theory. Instead we look into the possibility that some of the very structure of our thinking can be adequately represented and articulated in the language of category theory. To the degree that it can, the infusion of mathematics into our thinking will afford additional rigor, which should lead us to new insights. Be on the lookout for such openings. The overall point is that your engagement is very important for our success. Please speak up often in class and come to office hours.
Grading
Attending lecture is mandatory. Class participation is 33% of your grade. It's crucial that you ask questions when you don't understand.
Homework is also worth 33% of your grade. It will be collected weekly. Late homework will generally not be accepted. Just turn in what you have when the homework is due.
The rest of your grade is based on your final project. This can either be an oral presentation or a publishable document. See the Projects section for more details | 677.169 | 1 |
Get the confidence and math skills you need to get started with calculus.* Serves as a course guide to help you master pre-calculus concepts* Covers the inside scoop on quadratic equations, graphing functions, polynomials, and more* Covers the types of problems you'll encounter in your courseworkWith the help of Pre-Calculus Workbook For Dummies you'll learn how to solve a range of mathematical problems as well as sharpen your skills and improve your performance. Bücher / Naturwissenschaften, Medizin, Informatik & Technik / Mathematik / Analysis, [PU: Wiley]
Get the confidence and math skills you need to get started with calculus
Are you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the
course.
* Serves as a course guide to help you master pre-calculus concepts
* Covers the inside scoop on quadratic equations, graphing functions, polynomials, and more
* Covers the types of problems you'll encounter in your coursework
With the help of Pre-Calculus Workbook For Dummies you'll learn how to solve a range of mathematical problems as well as sharpen your skills and improve your performance. | 677.169 | 1 |
Harold R. Jacob's text is a lively and clearly written introduction to elementary algebra. Jacobs engages the reader through puzzles, including the number trick with which he starts the book, humor, and references to actual persons and events. He finds intriguing ways to introduce topics, then explains the concepts well. Concepts are introduced incrementally. Often, Jacobs introduces a concept in a particular context so that the student gets the idea before reintroducing it later in a broader context after the student has learned additional material. This reinforces the concepts and contributes to the student's conceptual understanding of the material, as do his problem sets. While Jacobs makes sure that the student can perform the algorithms presented in the text, the problems that he poses are designed to reinforce the concepts by exploring all aspects of the topics that he covers.
Each section concludes with four problem sets. The first set is a brief review of earlier topics (aside from the first five sections of the first chapter). The second covers the topics in the section. Jacobs provides answers to the problems in the second set in the back of the text, making the book suitable for self study. The third set is a variation on the second. The fourth set consists a puzzle or a problem that extends the concepts learned in the section. I particularly enjoyed these problems, often turning to them to see what Jacobs was asking before I finished the other problems. Each chapter concludes with a chapter summary and two sets of review problems.
Jacobs begins the text with a review of arithmetic, including the order of operations and properties of integers and rational numbers. He introduces algebraic concepts gradually as he does this. This leads to a discussion of functions, linear equations, lines, systems of linear equations, and exponents. Jacobs pauses for a midterm review. Then he covers polynomial, rational, and radical expressions and equations. He also discusses the properties of the real numbers, inequalities, and number sequences before finishing his text with a final review.
Such a great math text! Really a lot of mental problem solving required. I love the conversational style and enjoy reading the text and doing the exercises. My son and I are having a good time together working through this book, I highly recommend it.
I bought this for homeschooling my half brother but my husband and I had a lot of fun working the problems too. As far as the intended user, his math interest and skills leaped ahead greatly with this book. I'm saving it for my own kids to use someday too.
Excellent text which approaches the material in a straight-forward, understandable manner. Nothing cutesy. Students are not expected to "come to" a gut-level understanding before they learn the rules. If all USA schools adopted this text as part of their math core curriculum, our children would have a much better understanding of math that would serve them well in their adult lives. Math WASL scores would go up as well, incidentally. P.S. Of course, the math teachers would also need to know how to teach the material as well.
This book was exactly as described. I have a son struggling with math as he missed out on basics in elementary school and we are going to use this book to help him understand the basics and then move on. It is easy to follow and gives great examples. | 677.169 | 1 |
Curriculum 2005 (legacy) AS/A Level MEI Structured Mathematics
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MEI Structured Maths Series Textbooks
This best-selling series, known for its student-friendly style, provides a thorough mathematical education for students, in-line with the current MEI AS/A2 Specifications. The series comprises flexible Student Books covering one or two modules. Accessible in both design and content, each book contains activities, investigations and worked examples to guide students into new topics and concepts within real world contexts. To ensure exam success there are plenty of up-to-date exam questions, plus warning signs to indicate common pitfalls.
For this third edition the compulsory modules Core Mathematics 1 (Introduction to Advanced Mathematics) and 2 (Concepts for Advanced Mathematics) have been published as a handy single-volume text book, giving you the flexibility to teach/learn the content of these modules in the order that suits you. Covered in these modules: (C1) mathematical processes, algebra, coordinate geometry, polynomials, curve sketching; (C2) sequences and series, trigonometry, algebra, calculus.
For this third edition the compulsory modules Core Mathematics 3 (Methods for Advanced Mathematics) and 4 (Applications of Advanced Mathematics) have been published as a handy single-volume text book, giving you the flexibility to teach/learn the content of these modules in the order that suits you. Covered in these modules: (C3) proof, exponentials and natural logarithms, functions, numerical methods; (C4) algebra, trigonometry, parametric equations, calculus, vectors, comprehension.
Further Pure Mathematics 1 (Further Concepts for Advanced Mathematics) is the core component in the AS Further Mathematics qualification. Covered in this module: complex numbers, curve sketching, proof, algebra, matrices.
Statistics 1 is an Applied AS unit of Advanced Mathematics, and enables students to build on and extend the data handling and sampling techniques they have learnt at GCSE. Covered in this module: processes, data presentation, probability, discrete random variables, the binomial distribution and its use in hypothesis testing.
Statistics 3 is an Applied A2 unit of Advanced Mathematics, and introduces students to more advanced statistical ideas, based on the foundation provided by S1 and S2, particularly involving continuous random variables and inference. Covered in this module: continuous random variables, expectation algebra, inference.
Statistics 3 is an Applied A2 unit of Advanced Mathematics, and provides students with the opportunity to explore ideas in more advanced statistics to a greater depth. Covered in this module: estimation, generating functions, design and analysis of experiments.
Mechanics 1 is an Applied AS unit of Advanced Mathematics, and introduces students to mathematical modelling and to the basic concepts in kinematics, statics and dynamics which underlie the study of mechanics. Covered in this module: modelling, vectors, kinematics, force, Newton's laws of motion, projectiles.
Mechanics 2 is an Applied A2 unit of Advanced Mathematics, and builds on the work in Mechanics 1 by extending the range of mechanics concepts which students are able to use in modelling situations. Covered in this module: work, energy and power, force, momentum and impulse, centre of mass.
Mechanics 3 is an Applied A2 unit of Advanced Mathematics, and builds on the work in Mechanics 1 and Mechanics 2, further extending the range of mechanics concepts which students are able to use in modelling situations. Covered in this module: dimensional analysis, circular motion, Hooke's law, simple harmonic motion, solid bodies and plane laminae.
Mechanics 4, is an Applied A2 unit of Advanced Mathematics, and prepares students for more advanced courses at university by extending the use of calculus in mechanics. Covered in this module: variable forces, variable mass, stability, rotation of a rigid body.
Decision Mathematics 1 is an Applied AS unit of Advanced Mathematics, and gives students experience of modelling and of the use of algorithms in a variety of situations, and develops modelling skills. Covered in this module: modelling, algorithms, graphs, networks, linear programming, critical path analysis, simulation
Decision Mathematics 2 is an Applied A2 unit of Advanced Mathematics, and gives students experience of modelling and of the use of algorithms in a variety of situations, and develops modelling skills. Covered in this module: linear programming, networks, logic, decision trees.
Numerical Methods is a Pure AS unit of Advanced Mathematics, and provides students with an understanding that many mathematical problems cannot be solved analytically but require numerical methods. The module develops a repertoire of simple numerical methods and gives experience in using them. Covered in this module: solution of equations, errors, numerical differentiation, numerical integration, approximations to function
Differential Equations is an Applied A2 unit of Advanced Mathematics, and extends the work in Applications of Advanced Mathematics (C4) on the formulation and solution of differential equations. This book looks at how you can use differential equations to describe real-life situations, using real contexts throughout the book. Covered in this module: modelling with differential equations, first order differential equations, second and higher order differential equations, simultaneous differential equations, numerical methods.
978 0340 905272
Revise for MEI Structured Maths Series
Revise for MEI Structured Mathematics has been written by experienced authors and examiners especially for A Level Mathematics students and provides ideal preparation for the exam. The series accompanies the MEI Structured Mathematics Student's Books. Each topic is put into context in terms of its general application, and its links to other modules in the course. It contains reminders of related topics covered previously, whilst worked solutions guide students through all the necessary steps in solving typical questions.
The books also contain handy reminders about related topics which have been covered previously, and worked solutions guide students through all the necessary steps in solving typical questions. 'Key facts' summarise the essential points to remember and there is guidance on how to avoid the most common exam pitfalls.
Revision Guides also have an accompanying website/CDROM featuring:
'Test Yourself' - interactive multiple choice questions on every topic, with diagnostic answers which identify any weaknesses or common errors
Exam-style questions - covering every topic, these audio-visual 'Personal Tutor' worked examples explain exactly how each type of question should be tackled.
Other AS/A level books you might find useful:
This accessible, comprehensive textbook is the only book supporting MEI AS Statistics. The book covers all three AS modules: Z1, Z2 and Z3. It has been designed especially for students with a non-mathematical background, but who nevertheless will need to understand some mathematical concepts when studying their other A levels. These students include those following Business Studies, Psychology, Geography and Biology courses. Worked examples guide students into new topics and concepts within real world contexts. Activities, investigations and graded exercises are included, along with an IT investigation at the end of each chapter.
This book is an ideal source of reference for students (and teachers) in a variety of subjects, including mathematics. It contains all the essential reference information required during AS and A level courses in mathematics and statistics, as well as many Higher Education and vocational courses, in a single handy volume. The book contains a large number of formulae, explanations of the meanings of terms, statistical tables and other useful information. Students will use this handy reference book throughout their post 16 studies and beyond.
'Although the statistics element of the book is quite considerable, it does contain sufficient material from other areas of mathematics to warrant buying it as a companion to a pure mathematics course. This is a book that will become 'well-thumbed' very quickly.'
Graham H. Storr, Mathematical Gazette | 677.169 | 1 |
This book is written for beginners and students who wish to learn MATLAB. One of the objectives of writing this book is to introduce MATLAB to students in high schools.The material presented is very easy and simple to understand - For the paperback edition, visit Amazon.com.
Essential MATLAB for Engineers and Scientists, Sixth Edition, provides a concise, balanced overview of MATLAB's functionality that facilitates independent learning, with coverage of both the fundamentals and applications. The essentials of MATLAB are illustrated throughout, featuring complete coverage of the software's windows and menus. Program design and algorithm development are presented clearly and intuitively, along with many examples from a wide range of familiar scientific and engineering areas. This updated edition includes the latest MATLAB versions through 2016a, and is an ideal book for a first course on MATLAB, or for an engineering problem-solving course using MATLAB, as well as a self-learning tutorial for professionals and students expected to learn and apply MATLAB. Updated to include all the newer features through MATLAB R2016a Includes new chapter on complex variables analysis Presents a comparison of execution time between compiled and un-compiled code that includes examples Describes the new H2 graphics features
MATLAB is a high-level language and. MATLAB Differential and Integral Calculus introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving a short introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work with ease in differential and integral calculus in one and several variables. Among other core topics of calculus, you will use MATLAB to investigate convergence, find limits of sequences and series and, for the purpose of exploring continuity, limits of functions. Various kinds of local approximations of functions are introduced, including Taylor and Laurent series. Symbolic and numerical techniques of differentiation and integration are covered with numerous examples, including applications to finding maxima and minima, areas, arc lengths, surface areas and volumes. You will also see how MATLAB can be used to solve problems in vector calculus and how to solve differential and difference equations.
later versions. In addition, the CD-ROM contains a complete solutions manual that includes detailed solutions to all the problems in the book. If the reader does not wish to consult these solutions, then a brief list of answers is provided in printed form at the end of the book. Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwi- out which this book would not have been possible. I would also like to acknowledge the help of the editior at Springer-Verlag (Dr. Thomas Ditzinger) for his assistance in bringing this book out in its present form. Finally, I would like to thank my brother, Nicola, for preparing most of the line drawings in both editions. In this edition, I am providing two email addresses for my readers to contact me ([email protected] net. jo and [email protected] edu). The old email address that appeared in the ?rst edition was cancelled in 2004. December 2006 Peter I. Kattan PrefacetotheFirstEdition 3 This is a book for people who love ?nite elements and MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing ?nite element analysis. Problems will be solved mainly using MATLAB to carry out the tedious and lengthy matrix calculations in addition to some manual manipulations especially when applying the boundary conditions. In particular the steps of the ?nite element method are emphasized in this book. The reader will not ?nd ready-made MATLAB programsforuseasblackboxes. Insteadstep-by-stepsolutionsof?niteelementpr- lems are examined in detail using MATLAB.
Fulfilling the need for a practical user's guide, Statistics in MATLAB: A Primer provides an accessible introduction to the latest version of MATLAB® and its extensive functionality for statistics. Assuming a basic knowledge of statistics and probability as well as a fundamental understanding of linear algebra concepts, this book: Covers capabilities in the main MATLAB package, the Statistics Toolbox, and the student version of MATLAB Presents examples of how MATLAB can be used to analyze data Offers access to a companion website with data sets and additional examples Contains figures and visual aids to assist in application of the software Explains how to determine what method should be used for analysis Statistics in MATLAB: A Primer is an ideal reference for undergraduate and graduate students in engineering, mathematics, statistics, economics, biostatistics, and computer science. It is also appropriate for a diverse professional market, making it a valuable addition to the libraries of researchers in statistics, computer science, data mining, machine learning, image analysis, signal processing, and engineering.
Based on a teach-yourself approach, the fundamentals of MATLAB are illustrated throughout with many examples from a number of different scientific and engineering areas, such as simulation, population modelling, and numerical methods, as well as from business and everyday life. Some of the examples draw on first-year university level maths, but these are self-contained so that their omission will not detract from learning the principles of using MATLAB. This completely revised new edition is based on the latest version of MATLAB. New chapters cover handle graphics, graphical user interfaces (GUIs), structures and cell arrays, and importing/exporting data. The chapter on numerical methods now includes a general GUI-driver ODE solver. * Maintains the easy informal style of the first edition * Teaches the basic principles of scientific programming with MATLAB as the vehicle * Covers the latest version of MATLAB
This is a book containing Classic Sudoku puzzles for children in kindergarten - ages 4 - 8 years and up. All the puzzles in the book are 4 x 4 Sudoku puzzles designed specially for these children in mind. Classic Sudoku rules are easy - each number 1, 2, 3, and 4 must appear only once in each row, column, or block. There are 96 classic puzzles in the book. In addition, there are two example puzzles that are solved in a step-by-step manner. The puzzles are of three types - Easy, Medium, or Difficult. The solutions to all the puzzles in the book are available at the end of the book. The book has a website at where you can download and print additional puzzles like the ones in the book. This is a companion book to the best selling book "Kindergarten Sudoku: 4x4 Sudoku Puzzles for Kids".
MATLAB PROGRAMMING WITH APPLICATIONS FOR ENGINEERS seeks to simultaneously teach MATLAB as a technical programming language while introducing the student to many of the practical functions that make solving problems in MATLAB so much easier than in other languages. The book provides a complete introduction to the fundamentals of good procedural programming. It aids students in developing good design habits that will serve them well in any other language that he or she may pick up later. Programming topics and examples are used as a jumping off point for exploring the rich set of highly optimized application functions that are built directly into MATLAB. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
MATLAB is an interactive system for numerical computation that is widely used for teaching and research in industry and academia. It provides a modern programming language and problem solving environment, with powerful data structures, customizable graphics, and easy-to-use editing and debugging tools. This third edition of MATLAB Guide completely revises and updates the best-selling second edition and is more than 30 percent longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox. Key features are a tutorial in Chapter 1 that gives a hands-on overview of MATLAB; a thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers; and a web page at that provides example program files, updates, and links to MATLAB resources. The new edition contains color figures throughout; includes pithy discussions of related topics in new ?Asides" boxes that augment the text; has new chapters on the Parallel Computing Toolbox, object-oriented programming, graphs, and large data sets; covers important new MATLAB data types such as categorical arrays, string arrays, tall arrays, tables, and timetables; contains more on MATLAB workflow, including the Live Editor and unit tests; and fully reflects major updates to the MATLAB graphics system. This book is suitable for both beginners and more experienced users, including students, researchers, and practitioners.
MATLAB is a high-performance technical computing language. It has an incredibly rich variety of functions and vast programming capabilities. SIMULINK is a software package for modeling, simulating, and analysing dynamic systems. MATLAB and SIMULINK are integrated and one can simulate, analyse, or revise the models in either environment. The book MATLAB and SIMULINK for Engineers aims to capture the beauty of these software and serve as a self study material for engineering students who would be required to use these software for varied courses.
Lattice Boltzmann Method introduces the lattice Boltzmann method (LBM) for solving transport phenomena – flow, heat and mass transfer – in a systematic way. Providing explanatory computer codes throughout the book, the author guides readers through many practical examples, such as: flow in isothermal and non-isothermal lid driven cavities; flow over obstacles; forced flow through a heated channel; conjugate forced convection; and natural convection. Diffusion and advection-diffusion equations are discussed with applications and examples, and complete computer codes accompany the coverage of single and multi-relaxation-time methods. Although the codes are written in FORTRAN, they can be easily translated to other languages, such as C++. The codes can also be extended with little effort to multi-phase and multi-physics, if the reader knows the physics of the problem. Readers with some experience of advanced mathematics and physics will find Lattice Boltzmann Method a useful and easy-to-follow text. It has been written for those who are interested in learning and applying the LBM to engineering and industrial problems and it can also serve as a textbook for advanced undergraduate or graduate students who are studying computational transport phenomena. | 677.169 | 1 |
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Showing 1 to 9 of 9
1
Math 140 Lecture Notes
1.
SETS
A set is a well-defined collection of objects called elements.
By well-defined we mean that there is a rule that helps us to determine whether an
element belongs to the set.
e.g.
cfw_People who like broccoli not well-definUnit 2 Exam Practice
4B The Power of Compounding
Course Outcomes:
1. Demonstrate the astonishing power of compound interest and the role it plays in
investments.
2. Explain the difference between simple and compound interest.
3. Describe the difference be | 677.169 | 1 |
The first chapter algebra, trigonometry formulas and elementary functions
Here the collection and collation of elementary algebra ( see Chapter III of algebraic equations part ) , some commonly used formulas plane and spherical trigonometry triangle, but also introduces some common elementary functions ( a real independent variable ) the nature and simple graphics, so this chapter basically includes the main content of secondary school algebra and trigonometry .
§ 1 algebraic formulas
First, the number of expansion, classification and basic arithmetic rules
1 . number of expansion and classification
2 . real number four arithmetic rules
[ Modified regulations are ] the same number two numbers together, absolute values, symbols and addend same; different number two numbers together, the absolute value subtraction ( large decrease ) , and the absolute value of a big plus sign Number of same; any real number and zero sum, equal to the real number itself . subtraction is the inverse operation of addition, subtraction of two numbers as long as the subtrahend into opposite number with its symbol, you can rule by the addition operation .
[ multiplication and division regulations are ] the number is multiplied with the number two, the absolute value is multiplied by the sign is positive; different numbers multiplying two numbers, the absolute value is multiplied by a negative sign; any number multiplied by zero is zero; any number with a phase Take equal to its own . division is the inverse of multiplication, division number with number two, the absolute value of the division, the sign is positive; different number divided by two numbers, the absolute value of the division, the sign is negative; any number divided by an equal its own; zero divided by any number is not zero is equal to zero; zero divisor can not do .
[ four mixed computing rules ] to multiplication and division, addition and subtraction; within the first brackets, outside the parentheses .
3 Number of three basic laws of arithmetic
[ commutative ]
[ associative ]
[ distributive ]
4. involution and prescribing
[ power of ] N number of a multiplying
n months
Called a a n times ( multiply ) party, also known as a the n -th power . a known power base, N is called the exponent .
Obtained directly from a power symbol symbol rule multiplication rule: Any power of positive numbers is positive; negative dual power of a positive number; negative odd power of negative; any power of zero is zero .
Provision does not equal zero zero power equal to the number of one , namely a 0 = 1 , a 1 0 .
[ square root ] If a 2 = b , then a called b of the square root, denoted by , the square root of the square root operation is called . general approach illustrated by the square root of the examples below .
Cases seeking 316.4841 square root .
Solution The first step , the first number is the square root of the decimal point to the left and right position every two comma "," segments, such as the number 316.4841 segmented into 3,16.48,41 . second step, find the first Manufacturers of digital the initial period, so that the beginning of the first stage does not exceed the square's number, and the beginning of the provider plus a square of the first segment is greater than the number, this number is the first paragraph of Example 3 , provided for the beginning of 1 , because the 1 2 = 1 <3 , and (1 + 1) 2 = 4> 3 . third step, by subtracting the square of the first stage's digital First and second digital moved down, the remainder consisting of the first, in the present Examples of the first remainder 216 . fourth step, try to find providers, so (20 ' early commercial + test providers ) ' test provider does not exceed the first remainder, while [20 ' early commercial + ( test provider +1 )] ' ( test provider +1) is greater than the first remainder . fifth step, the first remainder minus (20 ' early commercial + test providers ) ' test providers, and move under the third paragraph numbers, the composition of the first Second remainder, in this case the test provider for seven , the second remainder is 2748 . shall thereafter continue to do so until all of the sections of the shift, if the last remainder is zero, the root operation ended . If the remainder is never zero, you can only take a certain precision approximation . sixth step, set the decimal point position, the position of the square root of the decimal point should be aligned with the square root of the number of decimal point position . this example formula is as follows:
[ Open Cube ] If a 3 = b , then a called b of the cube root, denoted by , find the cube root of the operation called open cube .
Square root and cube root of a number can be found from the "square root" and the "cube root table" .
5 real binary system
[ binary system of base and digital ] any positive number can be expressed as a finite or infinite decimal decimal usual sense, the position of each digit numeric value and where relevant, any location numbers to the right of the decimal point when its value expanded 10 -fold, when the decimal point to the left one when its value is reduced 10 -fold . example
Generally, either a positive number a can be expressed as
This is the 10 binary numbers, denoted a (10) , the number 10 is called binary system group wherein a i in {0,1,2, L , 9} in the value called 10 -adic number, Obviously there is no reason to say that the basic binary system can not take another number . now take q is any greater than a positive integer binary system as the base, so they get q into the number indicates
(1)
Wherein the number a i in {0,1,2, L , q -1} of values, a N a N -1 L a 1 a 0 is called q -adic a ( q ) is the integer part, referred to as [ a ( q ) ];
a -1 a -2 L is called a ( q ) the fractional part, denoted by { a ( q ) } . usual binary system, in addition to 10 decimal, there are two binary, 8 hex, 16 hex, etc. , it follows
2 binary 0, 1
8 binary 0, 1, 2, 3, 4, 5, 6, 7
16 hexadecimal 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
[ 2 , 8 , 16 hex addition and multiplication tables ]
2 binary adder table
Two decimal multiplication table
+
0
1
0
1
0
0
1
0
0
0
1
1
10
1
0
1
8 binary adder table
+
0
1
2
3
4
5
6
7
0
00
01
02
03
04
05
06
07
1
01
02
03
04
05
06
07
10
2
02
03
04
05
06
07
10
11
3
03
04
05
06
07
10
11
12
4
04
05
06
07
10
11
12
13
5
05
06
07
10
11
12
13
14
6
06
07
10
11
12
13
14
15
7
07
10
11
12
13
14
15
16
8 decimal multiplication table
0
1
2
3
4
5
6
7
02
00
02
04
06
10
12
14
16
3
00
03
06
11
14
17
Twenty two
25
4
00
04
10
14
20
Twenty four
30
34
5
00
05
12
17
Twenty four
31
36
43
6
00
06
14
Twenty two
30
36
44
52
7
00
07
16
25
34
43
52
61
16 hex Addition Table
+
0
1
2
3
4
5
6
7
8
9
0
00
01
02
03
04
05
06
07
08
09
1
01
02
03
04
05
06
07
08
09
0
10
2
02
03
04
05
06
07
08
09
10
11
3
03
04
05
06
07
08
09
10
11
12
4
04
05
06
07
08
09
10
11
12
13
16 hex Addition Table
5
05
06
07
08
09
10
11
12
13
14
6
06
07
08
09
10
11
12
13
14
15
7
07
08
09
10
11
12
13
14
15
16
8
08
09
10
11
12
13
14
15
16
17
9
09
10
11
12
13
14
15
16
17
1816 hexadecimal multiplication table
+
0
1
2
3
4
5
6
7
8
9
0
00
00
00
00
00
00
00
0008
09
2
00
02
04
06
08
10
12
14
16
18
3
00
03
06
09
12
15
18
Twenty one
Twenty four
27
4
00
04
08
10
14
18
20
Twenty four
28
30
34
38
5
00
05
14
19
Twenty three
28
32
37
41
46
6
00
06
12
18
Twenty four
30
36
42
48
54
7
00
07
15
Twenty three
31
38
46
54
62
69
8
00
08
10
18
20
28
30
38
40
48
50
58
60
68
70
78
9
00
09
12
Twenty four
36
48
51
63
75
87
00
14
28
32
46
50
64
78
82
96
00
16
Twenty one
37
42
58
63
79
84
00
18
Twenty four
30
48
54
60
78
84
90
00
27
34
41
68
75
82
00
38
46
54
62
70
00
69
78
87
96
[ 8-2 , 16-2 digital conversion table ]
8 binary numbers
0
1
2
3
4
5
6
7
Two binary numbers
000
001
010
011
100
101
110
111
16 into the number of
0
1
2
3
4
5
6
7
Two binary numbers
0000
0001
0010
0011
0100
0101
0110
0111
16 into the number of
8
9
Two binary numbers
1000
1001
1010
1011
1100
1101
1110
1111
[ various binary system of mutual conversion ]
1 ° q Õ 10 conversion is generally applicable to the 10 -adic four rules of arithmetic, according to the formula (1) may be the q -adic a ( q ) is converted to 10 binary numbers represented . e.g.
2 ° 10 Õ q converted into integer and fractional must be part of the conversion .
For integer part of its steps are:
(1) with q removal of [ a (10) ] , the quotient and remainder .
(2) Write down the remainder as q enter the last digit number .
(3) Replace with suppliers [ a (10) ] position to repeat (1) and (2) a two-step, until the quotient is equal to zero .
For the fractional part of its steps are:
(1) with q to multiply { a (10) } .
(2) the product of the integer part of a note as q into the fractional part of the first digit of the number .
(3) the product of the fractional portion is replaced with { a (10) } of position and repeat (1) and (2) steps, until the product of the integer has been changed, or until the desired number of bits is reached . e.g.:
103.118 (10) = 147.074324 L (8)
The integer part of the grass-type
Fractional portion of the grass-type
3 ° P Õ q converter usually comprises the following steps: a ( P ) Õ a (10) Õ a ( q ) . if P , q is the same number s of different powers, comprises the following steps: a ( P ) Õ a ( s ) Õ a ( q ) . example, eight into the number 127.653 (8) converted into 16 binary numbers, since 8 = 2 3 , 16 = 2 4 , so s = 2 , the steps are: First, the eight into Each digit number according to the 8-2 conversion table into two binary numbers ( three group )
127.653 (8) = 001 010 111.110 101 011 (2)
Then the two numbers from all the numbers into the decimal point onwards ( left and right ) of each grouping a set of four, from 16-2 individually write down the corresponding conversion table 16 into the number of digits, namely
Second, the complex
1 concept plural
[ · real and imaginary parts of the mold and the radiation angle and a complex conjugate of ] the complex z is typically expressed as z = a + ib , which is called the imaginary unit, a and b are real numbers, called z real part and the imaginary part , referred to as a = Re z , b = Im z .
Two complex only when the real and imaginary parts are equal equal .
Called the complex z die .
Called the complex z spoke angle, so there is an infinite number of complex convergence angle, but one called Lord spoke angle, denoted by Arg z , which satisfies
[ Vector notation ] The a , b considered a vector in the x -axis and y -axis projection of the vector ( Figure 1.1) can be expressed the complex z = a + ib , and P the point on the x -axis point of symmetry referred to as vector represents the complex conjugate .
Called the number of columns, denoted by { a N }. If the number of the number of columns and link up with:
a 1 + a 2 + a 3 + L + a N + L
It is called the series, denoted by . a N called the number of columns or the corresponding series of general term (or referred to in general terms) .
2 . Arithmetic sequence and arithmetic (arithmetic) progression
a 1 , a 1 + d , a 1 +2 d ,
a 1 +3 d , L ( d is a constant )
Called tolerance d arithmetic sequence . arithmetic sequence with the corresponding series called arithmetic progression, also known as the arithmetic progression .
General term formula
Before n items and
Items in arithmetic
3 . Geometric sequence with geometric (geometric) series
a 1 , a 1 q ,
a 1 q 2 , a 1 q 3 ,
L ( q is a constant )
Called the common ratio of q geometric columns . geometric sequence with the corresponding series called geometric progression, also known as geometric progression .
General term formula
Before n items and
Geometric mean
Infinite decreasing geometric progression and
4 . Arithmetic - geometric series
≥ 1)
5 . Harmonic Series
1 O if for arithmetic progression, then a + b + c + L called the harmonic series . reconcile the entry for
2 O set A , G , H , respectively, for a term of two numbers in arithmetic, geometric mean and reconcile the item,
AH = G 2
6 . Higher-order arithmetic progression
There is a number of columns
a 1 , a 2 ,
L , a N , L
(1)
* If successively subtracting the latter from its one, then get the number of columns of the original (1) constituting the difference between the first number of columns
a 2 - a 1 , a 3 - a 2 ,
L , a N - a N-1 , L
(2)
Then successively the (2) subtracting one of the previous one, and to give the number of columns (1) the difference between the number of columns in the second configuration . and so on:
a 1 a 2 a 3 a 4 L
The first difference d 1 = D a 1 D a 2 D a 3 L
The second difference d 2 = D 2 a 1 D 2 a 2 L
The third difference d 3 = D 3 a 1 L
LL
Where
If you do a r times, the number of columns (1) Each section r times poor are equal, then the poor are equal to zero after each time, called the number of columns (1) of r -order arithmetic sequence . with such number of columns corresponding series called for r -order arithmetic progression . an order arithmetic progression is the usual arithmetic progression .
Set (1) is a r -order arithmetic sequence, and let d 1 is (1) the difference between the form of the first series of the first term, d 2 is (1) a second time difference constitutes the first item number column, L , d r of (1) the first r columns constituting the difference between the first line item, then there
General term formula ( N > r )
Before n items and
7 . Part and certain series
Fourth, multiplication and factorization formula
Five, fractional
1. fractional arithmetic
2. partial fraction
Any irreducible Fraction ( numerator and denominator have no common factor, the number of molecules times lower than the denominator ) can be decomposed uniquely shaped like or fraction of a basic truth and its operation is called partial fraction expansion . If it is false Fractional ( molecular number is not less than the denominator number ) , should be translated into Zhengshi fraction of the true and then carried on Franctions partial fraction expansion . each partial fraction coefficients can be determined by the method of undetermined coefficients . Below are several different points briefing .
Set
[ linear factor Repeat ]
1 O
Where N ( x ) the maximum number of r ≤ m -1 ; A 0 , A 1 , L , A m -1 for undetermined constants determined by the following formula:
2 O
Where A 0 , A 1 , L , A m is determined constant, determined by the following formula:
≤ s -1
Coefficients f J and m concerned, is determined by the following table:
The above-mentioned 1 O , 2 O method for determining the A 0 , A 1 , L , A m -1 and F 1 ( y ) , then y = x - a generation back . following formula can be used to determine the coefficients A 0 , A 1 ,
L , A m -1 :
[ linear factor does not repeat ]
1 O
Where N ( x ) the maximum number of r ≤ 2 , a 1 b 1 c ; A , B , C as determined constant, determined by the following formula:
2 O
Where the polynomial F ( x ) the maximum number k ≤ s-1 ; A , B is a constant determined by the following formula:
A , B determined, then the same polynomial equation on both sides must be equal to the coefficient rules to determine F ( x ) of the coefficients .
Case
Solutions to be considered according to the above formula
The A , B substituting the original style, the common denominator and finishing too
Compare both sides of the equation have the same coefficient times
So there
[ higher-order factor ]
[ general method for calculating the coefficient of ]
1 O on both sides of the equation is multiplied by D ( x ) into Zhengshi, the press x combined with the power, and then list the equations the unknown coefficients derived solved .
2 O on both sides of the equation multiplied by D ( x ) into Zhengshi, then the x value with a simple ( e.g. x = 0, 1, -1 , etc ) is substituted, then the unknown coefficients listed equations, the solution of obtained .
Six, the proportion of
1 O if ( or written as a : b = c : d ) , a , b , c , d is not zero,
2 O if , then
Where L i ( i = 1, 2, L , N ) for a group of an arbitrary constant, b i ( i = 1, 2, L , N ) is not equal to zero .
3 O if y and x is proportional to ( denoted by y mu x ) , then
If y and x is inversely proportional , then
If y and x proportional, y and z are proportional ( i.e., y mu x , y mu z ) , the x and z is proportional to the
And y and xz proportional, ie
Seven, radical
1. radical concept
[ root and radical ] number a of the n -th root refers to seek a number of its n -th power is exactly equal to a . a the n -th root denoted by ( N is greater than a natural number ). as algebra, called radical . N called the root index, a foundation called the number . within the range of real numbers, negative numbers can not be opened even th power, even power of a positive open with two root, the same absolute value, the opposite sign .
[ square root of the product ] is equal to the square root of the product of each factor with th root of the product; turn, is equal to the product of the same th root of the product of the same th root, namely
≥ 0, b ≥ 0)
[ Fraction root ] fractions equal to the square root of the numerator and denominator with th root division, namely
≥ 0, b > 0)
[ Radical involution ] ≥ 0)
[ radical simplification ]
≥ 0)
≥ 0, d ≥ 0)
≥ 0, d ≥ 0)
[ similar radical and addition and subtraction ]
root index and the foundation have the same number of similar radical radical known only available to be consolidated with similar radical addition and subtraction .
Only if the equal sign are true . this inequality indicating that a corner ( takes real value ) is always less than the cosine of a , or the product of the second product is less than the second vector within the vector length .
[ Herder inequality ]
1 O located a i , b i , L , L i ( i = 1, 2, L , N ) is a positive number, and a , b , L , L is a positive number, and a + b + L + L = 1 , then
[ optional arrangement ] from n distinct elements, each removing k a ( k £ N ) of different elements, arranged according to a certain order, called the election arrangement . their arrangement species for
[ full array ] from n distinct elements, each removing n distinct elements, arranged according to a certain order, called the whole arrangement . their arrangement species for
[ not the full array of different elements ]
If the n elements, there are N 1 are the same elements, there are N 2 elements identical to each other, L , there are N m -th element are the same ( N 1 + N 2 + L + N m = N ) , then this n full array elements called full array countless different elements . their arrangement species for
[ ring arrangement ] from n distinct elements, each removing k elements, only by the relative position between the elements and end to end to form a circle, regardless, this arrangement method called cyclic arrangement . their arrangement species number
3. combination
[ usually a combination of sense ]
from n distinct elements, each removing k distinct elements, regardless of the order combined into one group, called the combination . their portfolio species for
And regulations .
[ multiple combinations ] to n distinct elements into m groups, first i group N i distinct elements, namely , the number of species of this group is
Combination of common sense is a special case .
[ duplicate combinations ] from n different elements, each removal k elements, allowing repeated, regardless of the sequence are combined into a group, this combination is known to have a combination of repeating, the combination of species
[ combination formula ]
X. Triangle Theorem and polynomial
[ binomial theorem ]
Wherein n is a positive integer called the two coefficients .
[ Triangle ] of the Southern Song Dynasty mathematician Yang Hui in his book "Explanation IX algorithm" ( 1261 year ) recorded in the study about the two coefficients . the binomial theorem, when n were taken 0, 1, 2 , 3, 4, 5, 6 , the second coefficient expressed in Figure 1.2 , the so-called "Triangle" . Frenchman Pascal have similar results ( 1650 years ) , so foreign books referred to as "Pascal's triangle", but nearly four hundred years later than Pascal .
[ mathematical induction ] to contain integer n formulas, that is, from a pair of integers from behind all integers n have established formulas, and sometimes can be used to prove mathematical induction . following steps:
2 O is assumed that when N = k when the formula was established, to verify when N = k +1 is also true when the formula .
Because when the formula N = N 0 are true, so that the 2 O shows that, when N = N 0 +1 is also true when the formula; then by 2 O shows that, when N = N 0 + 1 + 1 = N 0 +2 when the formula also set up, continue to push down so we can see, for all greater than N 0 integer n formulas are established .
[ drawer principle ] N +1 an object into n a drawer, at least one drawer with two or more objects, this principle is called the drawer principle, it proves the existence theorem when certain useful . drawer principle points or less three forms:
1 O N +1 elements into n groups, there must be a group that contains at least two elements . | 677.169 | 1 |
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