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Math 252 Sec 5.5
Section 5.5 Counting Techniques
Jessica plans to go to dinner and a movie. If he has 4 choices of restaurants and 3 choices of
movies, how many ways can he spend his evening?
This diagram shows that Jessica has _ ways to spend her evening
Math 252 Probability
Section 5.1 Intro to Probability
In Math 110 you learned about the _ approach to probability. Today well discuss
both the Classical and Empirical approach. But first, lets remember our terminology:
An _ is a process for which the outc
Intermediate Algebra Advice
Showing 1 to 3 of 4
I love math and this math was super easy for me. I loved Professor Woodbury. She made everything really understanding and helped you even more if you didn't understand what was going on. She made sure that you understood the things that we went over before all the test.
Course highlights:
I was able to help others understand what was being taught in that class. I felt good when they were able to get it when I would help them.
Hours per week:
0-2 hours
Advice for students:
Be sure that if you don't understand what is being taught that you ask questions. Things do build on top of each other. So it is better ask questions first then later on.
Course Term:Fall 2016
Professor:Sara Woodbury
Course Tags:Math-heavyMany Small AssignmentsParticipation Counts
Dec 04, 2016
| No strong feelings either way.
This class was tough.
Course Overview:
I took it as an online class, and would have to say, that unless you're a math genius that gets their daily fix from solving math problems, I would suggest going to the campus to learn math. It's very busy work that gets progressively harder through out the semester. So just do yourself a favor, and take it on campus, because we all have to pass math at some point.
Course highlights:
I learned a lot of important things in this class. It was a good refresher to the college prep math I took in high school, and although it was a difficult class, it prepared me for 1050.
Hours per week:
6-8 hours
Advice for students:
If you take Math 1010 online, make sure that you can set 1-2 hours aside 4-5 days a week to do math assignments, because there will be one everyday. Make sure to absolutely not get behind, and pace yourself.
Course Term:Fall 2016
Professor:Penrod
Course Required?Yes
Course Tags:Math-heavyMany Small AssignmentsA Few Big Assignments
Jun 14, 2016
| Would recommend.
This class was tough.
Course Overview:
It is a required course. It is average overall. Professor Penrod is a good professor.
Course highlights:
Basic college algebra. Good quantitative reasoning course.
Hours per week:
3-5 hours
Advice for students:
Do all the homework. Go to each class. Do your best and you will succeed.
Course Term:Fall 2016
Professor:Penrod
Course Required?Yes
Course Tags:Math-heavyGreat Intro to the SubjectMany Small Assignments | 677.169 | 1 |
Mathematics has developed over time as a means of solving problems and also for its own sake. Its importance is universally recognised and its language is international, transcending cultural boundaries.
Mathematics is a creative discipline that can stimulate moments of pleasure and wonder when students solve a problem for the first time, discover a more elegant solution, or notice hidden connections. Today Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine and social sciences such as economics and psychology. Applied Mathematics, the branch of Mathematics concerned with the application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in Pure Mathematics or Mathematics for its own sake, without having any application in mind, although what began as Pure Mathematics can often find itself a very practical application at a later date.
Year 7
3 lessons a week
Mathematics is a Core Subject in Key Stage 3. At JCG we build on the foundations established in Key Stage 2 and provide students with opportunities for steady progression. Regular assessments are used to track student progress and identify correct levels of support. During Year 7 students develop problem-solving and reasoning skills alongside their mathematical knowledge. Students have the opportunity to take part in the UKMT Junior Maths Challenge in April and regular Maths clinics run everyTuesday lunchtime. Students work from the Collins Maths Frameworking books which they can also access online
Year 8
3 lessons a week
Mathematics is a Core Subject in Key Stage 3. As students move into Year 8, the mathematical challenge increases. Students learn to solve more complex equations and meet pi for the first time. Stronger students are given opportunities to stretch themselves. Other students are supported in a class that is working at the right pace for them. We continue to use regular assessments to track student progress and identify correct levels of support. Students have the opportunity to take part in the UKMT Junior Maths Challenge in April, the UKMT Team Challenge and regular Maths clinics run every Tuesday lunchtime. Students work from the Collins Maths Frameworking books which they can also access online.
Year 9
4 lessons a week
Still in Key Stage 3, students continue to develop their core mathematical skills and build strong foundations for their GCSE. In the first half of Year 9 students complete their Key Stage 3 programme of study. In the second half they start the GCSE Mathematics course (Edexcel's 9-1 Mathematics specification). During Year 9 students in the top sets have the opportunity to attend the Royal Institution Masterclass programme, run annually at JCG. Students can also take part in the UKMT Intermediate Maths Challenge, the UKMT Team Maths Challenge, and the Southampton Maths Competition.
Year 10
3 lessons a week In Year 10 the students continue working on their linear GCSE course. We follow Edexcel's GCSE 9-1 Mathematics Specification. This is a linear course with all the examinations at the end of Year 11. Students in the top two sets also study for AQA's Level 2 Certificate in Further Mathematics, sometimes described as an IGCSE in Further Mathematics. Students are set into 3 bands and all students are entered for the Higher Tier qualification. Regular assessments are given to track progress and support is given at weekly drop-in Key Stage 4 Maths clinics.
Year 11
3 lessons a week In Year 11 the students continue working on their two year GCSE course and students in the top two sets prepare for the AQA Further Mathematics exam as well as their GCSE Mathematics. All public exams are sat at the end of Year 11. In order to provide as much support as possible in Year 11 students receive 4 Maths lesson per week and also benefit from the addition of another set.
Year 12 and 13
5 lessons a week Mathematics is no longer compulsory after Key Stage 4, but many students at JCG decide to continue with the subject beyond GCSE. Some recognise that studying A Level Mathematics gives them a set of skills that are crucial to success in the worlds of science, engineering and technology. Others appreciate the unique power of Mathematics and want to continue the journey of discovery that they have started during GCSE.
A Level Mathematics students study Pure Mathematics and Statistics over 2 years with external examinations at the end of Year 12 and 13. Students may also wish to study Further Mathematics. For students starting Year 12 or 13 in September 2016 the Further Mathematics course comprises either 3 units (for AS) or 6 units (for A2). These cover further topics in Pure and Applied Maths (including Mechanics and Decision Maths) and are studied in parallel to A Level Maths. For students starting A Level Maths in September 2017, the Further Mathematics courses will be delivered as part of the elective programme. Details of this can be found in the 6th Form Prospectus.
In addition our A Level students have the opportunity to take part in the UKMT Senior Maths Challenge and the Senior Team Challenge. Students can find support at the weekly Key Stage 5 Maths clinic. We also encourage confident students to take part in coaching younger students at the KS3 and KS4 clinics. | 677.169 | 1 |
Funded by Bill and Melinda Gates Foundation this Math MOOC examines key topics such as: writing expressions in equivalent forms to solve problems, solving linear equations, systems of linear equations, linear inequalities, and quadratic equations, performing arithmetic with polynomial and rational expressions, modeling linear and quadratic functions. Each module within the Math MOOC imbeds at least two specific High School standards. These modules are also aligned to mathematics portions the ACT, SAT, and other college gateway examinations. | 677.169 | 1 |
Basic Algebra Shape-Up4.0
Publisher Description
Basic Algebra Shape-Up helps students master specific basic algebra skills, while providing teachers with measurable results. Concepts covered include creating formulas; using ratios, proportions, and scale; working with integers, simple and multi-step equations, and variables. Students start with an assessment and receive immediate instructional feedback throughout. Step-by-step tutorials, which introduce each level, can be referred to during practice. Problems are broken down into small, easily understood steps. The program is self-paced and self-monitored. Students advance as they demonstrate readiness. They may track their own improvement through progress-to-date and last session scores. Scores are kept in a record management system that allows teachers to view and print detailed reports. Designed for students in U.S. grades 6 through 9 (age 10 and up), the program can also be used by ESL and adult students interested in improving their algebra skills.
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MatBasic TRIAL MatBasic is a calculating, programming and debugging environment using special high-level programming language designed for solving mathematical problems. MatBasic programming language allows execution of difficult mathematical calculations, involving an exhaustive set of tools for the purpose... Download | 677.169 | 1 |
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Unformatted text preview: Maple for Math Majors Roger Kraft Department of Mathematics, Computer Science, and Statistics Purdue University Calumet [email protected] 1. Maple Basics This worksheet helps you get started using Maple and its user interface. It also introduces you to some of Maple's basic capabilities. This worksheet contains five sections. Click on a plus sign below to expand a section. 1.1. Introduction The main purpose of this worksheet is to introduce you to Maple. As you will soon see, this worksheet is an interactive document. You will do more than just read it, you will work with it. You can make changes to it and try variations on what is in it. In other words, as you work through this worksheet you will not just be reading about Maple, you will actually be doing something with Maple. Either click on the plus sign below or, if the cursor is on the next prompt, just hit the Enter key to open the next section of this worksheet and begin working. > 1.2. Getting started with Maple A Maple worksheet is made up of three components, Maple commands (in red), the output (in blue) that Maple produces for each command, and explanations (in black). Here is an example of a Maple command and its output. > 1+1; 2 Some of the commands in this worksheet, like the one just above, have already been executed and their output is right below the command. But most of the commands in this worksheet have not yet been executed and so you need to tell Maple to execute them so that you can see the results. Here is an example of a Maple command that has not been executed yet. To execute this command, click on it with the mouse and then hit the Enter key. > 2+2; Notice how Maple produced the output and then the cursor jumped down to the next Maple command, skipping over this explanation. From now on, this is pretty much how things will go in this worksheet; the cursor is on a Maple command, you hit the Enter key, Maple executes the command and displays the result, the cursor jumps down to the next Maple command, and you read the explanation (if any) that is between the commands. (Occasionally, this skipping over the explanation between commands can cause Maple to scroll what you want to read right off of the top of the screen. When that happens, you need to use the vertical scroll bar on the edge of the window to scroll back down the screen.) Every Maple command is next to a prompt (the greater than sign >), and every Maple command must be terminated by a semicolon or colon. The semicolon tells Maple to print the result of the command, the colon tells Maple not to print the command's result. Try executing the next command. > 3+3: A Maple command can contain a comment that is not really part of the command. A pound sign (i.e. # ) as part of a line of Maple input means a comment that Maple should ignore....
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This note was uploaded on 02/11/2012 for the course MTH 141, 142, taught by Professor Mcallister during the Spring '08 term at SUNY Empire State. | 677.169 | 1 |
About Us
Mathematics
Welcome to the Mathematics Department
The Mathematics Department at SXU strives to build a strong sense of community among
faculty and undergraduate students in exploring the beauty and importance of mathematics.
Our faculty members are dedicated to excellence in teaching and scholarship. The broad
range of faculty research interests in mathematics and mathematics education includes:
abstract algebra, applied mathematics, solitary waves theory, developmental mathematics,
differential geometry, discrete mathematics, history of mathematics, numerical analysis,
probability and statistics, representation theory of finite dimensional algebras,
mathematical knowledge for teaching, and processes by which mathematics teachers incorporate
technology into their teaching.
Quick Snapshot
All math courses are taught at the Chicago campus where students can enjoy small classes
with approachable and caring faculty. Most students enroll in an average of five courses
per semester to stay on a four-year track.
Why Study Mathematics or Mathematics with Secondary Education at SXU?
Faculty who are committed to a cutting-edge pedagogical and educational technology
focus to enhance students' understanding of mathematical concepts and develop mathematical
skills by using iPads, MyMathLab, MyStatLab, WebAssign, Minitab, StatCrunch, Graphing
Calculators, Geometer's Sketchpad, GeoGebra, Maple, and 3D printing in the classroom.
Learning that goes beyond the classroom. One-to-one mentorship in the Senior Seminar capstone project. Each semester, seniors present their research projects at a symposium
attended by students, faculty, family and friends.
Opportunity to work as a mathematics tutor in the Mathematics Lab.
Opportunities for fun and learning with peers through the Archimedeans Math Club which sponsors math game day, Pi Day, math movie night and career related events.
Join the SXU math team in the annual Associated Colleges of the Chicago Area (ACCA)
calculus competition.
Programs of Study
The Department of Mathematics offers a range of programs that fit the needs of not only mathematics majors but also the needs of general education
students and candidates for teacher licensure. The department offers majors in mathematics,
actuarial science and mathematics with secondary education. It also offers a minor
in mathematics.
Visit Us
The best way to learn more about our programs is to come visit our department. Sit
in on a class. Meet our faculty, current students and members of the Archimedeans
Math Club. See our classrooms, computer labs and our beautiful campus. | 677.169 | 1 |
Specially designed for students attending Calculus, AP Calculus AB, AP Calculus BC, Calculus I and Calculus II courses, the app can help them solve various calculus problems, with step-by-step guidance.
The program is powered by the Wolfram|Alpha computational knowledge engine.
What's New in This Release:
· Interactive tour and bug fixes.
Like it? Share with your friends!
If you got an error while installing Themes, Software or Games, please, read FAQ.
Fractals (iPhone/iPad) FractProtractor Deluxe Protractor Deluxe - In geometry, a protractor is a circular or semicircular tool for measuring an angle or a circle. The units of measurement utilized are usually degrees
WolframAlpha WolframAlpha - Get answers. Access expert knowledge. Wherever you are. Whenever you need it.
Find out how much vitamin C is in a bowl of ice cream. Learn what European country has the fourth largest population of children. Compute solutions to difficult trig and calculus problems. Balance complex chemical equations. Discover what is overhead as you gaze up at the stars
WolframAlpha for Android WolframAlpha for Android - The WolframAlpha app gives you access to the vast resources of the Wolfram|Alpha computational knowledge engine right from your Android device. The program provides optimized mobile access to answers in specific educational, professional and personal areas | 677.169 | 1 |
Chapter 4 -- Matrices 1. Introduction There are a certain number of terms that are used in matrix algebra with which you need to become familiar. Some of these terms are:-array, dimension, order, element, scalar, vector, identity matrix, transpose, inverse, determinant, reciprocal, adjoint, cofactor. • A matrix is a rectangular array of numbers, generally either one dimension or two dimensions and is usually denoted by a letter in bold type, e.g., A = 3 1 5 4 2 9- b = [ ] 1 3 4 1 2 c = 5 2 1 Note that we have denoted a two-dimensional matrix with a capital letter, e.g. A , and a one-dimensional matrix with a lower-case letter, e.g. b. • One way of defining a matrix is by its dimensions. Here the matrix, A , is said to be of order 2 x 3, as it has 2 rows and 3 columns. Note we always state the number of rows first, then the number of columns. The matrix, b , is usually referred to as a vector since b has only 1 row (its dimensions are 1 x 5 as it has 1 row and 5 columns). Similarly, c is also a vector as it only has 1 column and it is of order 3 x 1 as it has 3 rows and 1 column. Example 1. In recent years, the student enrolments in Econometrics in first , second and third year have been as follows: Year First Year Second Year Third Year 1993 700 85 35 1994 750 90 30 1995 1050 120 45 1996 1200 150 60 We could represent this information in a matrix. X = 700 85 35 750 90 30 1050 120 45 1200 150 60 • A matrix is also defined by its individual elements. We denote the location (or position) of an element in the matrix by specifying the row and column in which the element is found. For example, in the matrix X above, the number 750 is in the 2 nd row and the 1 st column. We would denote this element as a 21 . Note the row number is first and the column number is second. In general terms, the a ij element is in row i and column j. Another example is that the number 35 would be represented by a 13 as it is in the 1 st row and the 3 rd column. When are two matrices equal?
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Two matrices are equal if they have identical dimensions and the same elements in exactly the same positions. Thus, in the example below, the matrix A is equal to the matrix B but not to the matrix C . A = 3 1 5 4 2 9- B = 3 1 5 4 2 9- C = 3 1 9 4 2 5- Note that the matrix C has the same elements as A, but in a different order. 2. Matrix Addition Consider three students' results in their semester examinations in Accounting and Econometrics. These could be represented by two 3 x 2 matrices. Example 2. First Semester Second Semester Accounting Econometrics Accounting Econometrics Tim 45 65 55 73 Alice 58 60 67 72 Claire 75 70 80 78 We can add the results for both semesters for Accounting for Tim (45 + 55 = 100) and both semester results for Econometrics ( 65 + 73 = 138). A similar process is used for the results for Claire and Alice. If our results are summarized by two
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This note was uploaded on 04/07/2008 for the course MATH 1002 taught by Professor Cartwright during the One '08 term at University of Sydney. | 677.169 | 1 |
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Book Details
Contents
Book and CD explaining how to apply group theory to solve a range of popular puzzles.
Popular puzzles such as the Rubik's cube and so-called oval track puzzles give a concrete representation to the theory of permutation groups. They are relatively simple to describe in group theoretic terms, yet present a challenge to anyone trying to solve them. John Kiltinen shows how the theory of permutation groups can be used to solve a range of puzzles. There is also an accompanying CD that can be used to reduce the need for carrying out long calculations and memorising difficult sequences of moves. This book will prove useful as supplemental material for students taking abstract algebra courses. It provides a real application of the theory and methods of permutation groups, one of the standard topics. It will also be of interest to anyone with an interest in puzzles and a basic grounding in mathematics. The author has provided plenty of exercises and examples to aid study.
1. An overview of oval tracks 2. The transpose puzzle: an introductory tour 3. The slide puzzle: an introductory tour 4. The Hungarian puzzle: an introductory tour 5. Permutation groups: just enough definitions and notation 6. Permutation groups: just enough theory 7. Cycles and transpositions 8. The parity theorem 9. The role of conjugates 10. The role of commutators 11. Mastering the oval track puzzle 12. Transferring knowledge between puzzles 13. What a difference a disk makes!: changing the number of disks, and using Maple or GAP 14. Mastering the slide puzzle 15. Mastering the Hungarian rings with numbers 16. Mastering the Hungarian rings with colours 17. Advanced challenges. | 677.169 | 1 |
About this item
About this item
A graduate-level introduction balancing theory and application, providing full coverage of classical methods with many practical examples and demonstration programs. Striking a balance between theory and practice, this graduate-level text is perfect for students in the applied sciences. The author provides a clear introduction to the classical methods, how they work and why they sometimes fail. Crucially, he also demonstrates how these simple and classical techniques can be combined to address difficult problems. Many worked examples and sample programs are provided to help the reader make practical use of the subject material. Further mathematical background, if required, is summarized in an appendix. Topics covered include classical methods for linear systems, eigenvalues, interpolation and integration, ODEs and data fitting, and also more modern ideas like adaptivity and stochastic differential equations.
Specifications
Number of Pages
572
Original Languages
English
Subject
NUMERICAL ANALYSIS
Author
Miller, G.
Target Audience
Scholarly & Professional
Book Format
Hardcover
Publisher
Cambridge Univ Pr
ISBN-13
9781107021082
Assembled Product Dimensions (L x W x H)
7.00 x 9.75 x 1.50 Inches
ISBN-10
11070210 | 677.169 | 1 |
Libro digital
Libro Papel
Your solution to MATH word PROBLEMS!Find yourself stuck on the tracks when two trains are traveling at different speeds? Help has arrived! Math Word Problems Demystified, Second Edition is your ticket to problem-solving success.Based on mathematician George Polya's proven four-step process, this practical guide helps you master the basic procedures and develop a plan of action you can use to solve many different types of word problems. Tips for using systems of equations and quadratic equations are included. Detailed examples and concise explanations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.It's a no-brainer! You'll learn to solve:Decimal, fraction, and percent problemsProportion and formula problemsNumber and digit problemsDistance and mixture problemsFinance, lever, and work problemsGeometry, probability, and statistics problemsSimple enough for a beginner, but challenging enough for an advanced student, Math Word Problems Demystified, Second Edition helps you master this essential mathematics skill. | 677.169 | 1 |
Description
This lively textbook, written by an experienced author and teacher, delivers comprehensive coverage of the IGCES Mathematics syllabus for both Core and Extended courses. Offering a wealth of questions, supported by worked examples and diagrams, with hints and tips along the way to reinforce skills and guide learning. The dynamic and quality text, endorsed by Cambridge International Examinations, has been made available in print and e-book formats.
The print book includes a CD-ROM of supplementary materials including interactive revision questions, worksheets, worked solutions and calculator support. These supplementary materials, except the interactive questions, are also included in the e-book version.
Covers the complete IGCSE Mathematics (0580) syllabus for both the Core and Extended courses in the one book.
Extended material is clearly marked, with useful hints in the margins for those students needing more support, leaving the narrative clear and to the point.
Worked examples are provided throughout to demonstrate typical workings and thought processes.
Progressive and repetitive exercises complete with answers at the back of the book, can be used for classroom work, homework or self-assessment.
Useful tips for the examinations are included in the margins for additional support.
Fast forwards / rewind boxes connect related topics in the coursebook, making it easy to navigate regardless of what order the topics are taught.
Exam and Exam-style questions at the end of each chapter to provide lots of exam practice.
A Glossary to explain new and difficult words.
The accompanying CD-ROM includes interactive revision questions, revision worksheets tailored for Core students and Extended students (complete with answers), and worked solutions to some of the exam questions set in the coursebook. There is also a calculator support chapter, and associated worksheets, to help you master your graphical display calculator.
Other resources in the Cambridge IGCSE Mathematics series are
Cambridge IGCSE Core Practice book – for targeted practice [ISBN to follow]; Cambridge IGCSE Extended Practice book – for targeted practice [ISBN to follow]; Cambridge IGCSE Teacher's Resource CD-ROM – for ideas and advice [ISBN to follow] | 677.169 | 1 |
Is Calculus Hard? Yup, but that's OK!
Is calculus hard? Sure. If it wasn't, we'd have more math majors or more high school students completing it before they graduated. But we don't. Getting into algebra is a bit frightening but most students can handle it. It's when you advance to the higher levels of math where calculus resides that you quickly become aware of the fact that calculus is definitely a new level of difficulty. But that's OK…just because it's hard doesn't mean it's unattainable. We are here to make it just a little easier! Calculus I Essentials is offered here at Udemy to give you that extra edge no matter where you are in your calculus journey.
What is Calculus?
Webster's definition of "calculus" is "an advanced branch of mathematics that deals mostly with rates of change and with finding lengths, areas, and volumes." OK, good start. So basically calculus deals with change and measurements of stuff. Another important aspect you need to understand about calculus is its ability to allow you to predict how things will change. Engineers and mathematicians everywhere will argue (quite correctly) that the use of calculus affects so much of the material in our everyday lives.
Calculus gives you the ability to find the effects of changing conditions on the system being investigated. By studying these, you can learn how to control the system to make it do what you want it to do. Calculus allows you to model and control systems which have extraordinary power over the material world.
The development of calculus and its applications to physics and engineering is probably the most significant factor in the development of modern science beyond where it was in the days of Archimedes. And this was responsible for the industrial revolution and everything that has followed from it including almost all the major advances of the last few centuries.
Where do we start?
The study of calculus begins with understanding single variable calculus. You first have to have a framework for describing such notions as position speed and acceleration.
Single variable calculus, which is what we begin with, deals with the motion of an object along a fixed path. The more general problem, when motion takes place on a surface, or in space, can be handled by multivariable calculus. We study multivariable calculus by finding clever tricks for using the one dimensional ideas and methods to handle the more general problems. So single variable calculus is the key to the general problem as well.
When we deal with an object moving along a path, its position varies with time. We can describe its position at any time by a single number, which can be the distance in some units from some fixed point on that path, called the "origin" of our coordinate system. The motion of the object is then characterized by the set of its numerical positions at relevant points in time.
The set of positions and times that we use to describe motion is what we call a function. And similar functions are used to describe the quantities of interest in all the systems to which calculus is applied.
What does a Calculus course look like?
A typical course in calculus covers the following topics:
1. How to find the instantaneous change (called the "derivative") of various functions. (The process of doing so is called "differentiation".)
2. How to use derivatives to solve various kinds of problems.
3. How to go back from the derivative of a function to the function itself. (This process is called "integration".)
5. How to use integration to solve various geometric problems, such as computations of areas and volumes of certain regions.
There are a few other standard topics depending on the course. These include a description of functions in terms of power series, and the study of when an infinite series "converges" to a number. But sometimes courses cut off early and you never reach the more intense topics.
Functions are sets of (argument, value) pairs of numbers. They are often described by formulae which tell us how to compute the value from the argument. Only one value is allowed for each argument. These formula usually start with the identity function, the exponential function and the sine function, and are defined by applying arithmetic operations, substitution and inversion in some manner to them.
The derivative of a function at any argument is the slope of the straight line it resembles near that argument, if that slope is finite. The straight line it resembles near that argument is called the tangent line to the function at that argument and the function describing that line is called the linear approximation to the function at that argument. If the function does not look like a straight line near an argument, (has a kink or a jump or crazy behavior there) it is not differentiable at that argument.
There are straightforward rules for calculating derivatives of the identity, sine and exponential functions, and for computing derivatives of combinations of these obtained by applying arithmetic operations, substitution and inversion in some manner to them.
Thus we have means to obtain formulae for the derivative of all functions of the kind described above. Armed with a spreadsheet, you can plot functions and determine their derivatives with great accuracy, most of the time, with little effort.
In a Nutshell …
Learning calculus is just like learning anything else. You have to break it down to its smaller parts and spend some quality time with areas you have trouble with. That's it. Keep doing the problems for those rough areas over and over again until you completely understand how to work them. Calculus, in the end, is more intimidating than it is hard. Happy derivatives! | 677.169 | 1 |
Mathematics is one of those human endeavors that mainly requires brain power,
and a little time. It can be entertaining, frustrating, satisfying, relaxing,
very easy and very complicated. Sometimes it is possible to do a lot with
a little effort. Sometimes a lot of effort is rewarded with no results. As
in so many other areas, mathematics is subject to the universal law of
achievement:
In order to be lazy you have to work very hard first.
Unfortunately, it usually takes a long time before mathematics can be enjoyable,
and even more time before it can be done in a leisurely manner. There are,
however, elements of mathematics that can be entertaining from the very beginning.
For some it is observing the behavior of a live mathematician.
The study of mathematics can be made less frustrating by an appropriate choice
of textbooks. There is no "one size fits all" approach. Some prefer to begin
with a lot of examples and no theory, yet others begin by learning the concepts.
Here, the preference is on concepts. This approach is described by the
first law of learning:
Know the meaning of the words you are speaking.
Mathematics requires and improves, problem-solving skills. Fairly often,
a student faced with finding a solution to an exercise will begin by looking
for an example that is just like the exercise. The solution is then found
by mimicking the procedures described in the example. It works; for a while.
Yet, this does not lead to understanding. The recommended approach can be
described by what we call the second law of learning: | 677.169 | 1 |
This book is about teaching Algebra to middle school students. This book contains different lessons, learning theories and practices which are useful in teaching algebra during students' transition from an arithmetic environment to an algebraic environment. This book also highlights group and pair work, planning and use of material as promoting factors in the enhancement of students' algebraic thinking and reasoning skills. I think the book may be equally useful for teachers, teacher educators and the researchers. | 677.169 | 1 |
Equations and Inequalities Notes
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3.6 MB | 7 pages
PRODUCT DESCRIPTION
These guided notes are created to help differentiate and guide instruction for the math curriculum. This set of notes has been written based off of 6th grade standards, but can be used for similar grades. Each page of notes includes an "I can" statement, vocabulary, student notes, step-by-step guides, examples, and story problems. Each notes is reduced to one page for quick reference. The vocabulary cards that go along with the vocabulary within the notes can be found on my page as, "Math Vocabulary Cards-Green".
Answer keys are included!
This set of notes includes:
-Writing equations in one variable
-Solving equations using addition or subtraction
-Solving equations using multiplication and division
-Writing equations in two variables
-Writing and graphing inequalities
-Solving inequalities using addition or subtraction
-Solving inequalities using multiplication or division | 677.169 | 1 |
It is assumed that students will need to carry out a minimum of 2 hours independent study each week.
What do I need?
Specific Requirements
There are no specific entry requirements, although students who already have GCSE grades D, E or equivalent are likely to benefit most.
Where can it take me?
Access to Higher Education. AS/A Level Mathematics or Statistics. Also a useful qualification for University courses or jobs.
Additional Information
Diagnostic Assessment
All students take an online diagnostic assessment. The diagnostic will identify strengths and areas needing support. It will also help decide whether Foundation or Higher is to be studied. It may suggest that the part-time GCSE course is not suitable.
A student who is in doubt about the suitability of the course should ask to speak to a member of the Maths Department on 0121 602 7777 ext 251 or 0121 602 7632 (direct line).
You may contact the PSD Team (Ext. 291) if you think that you need other numeracy support.
The diagnostic test is taken during the first week of the course, on Monday or Wednesday evening. It takes about 1 hour. Students can opt to study Foundation or Higher tier. The highest grade achievable on Foundation is C. The highest grade achievable on Higher is A*. There will be classes doing Higher and classes doing Foundation.
What do I need for the classes?
Writing materials, paper, maths instruments (i.e. a geometry set) and a scientific calculator will be needed. If you require a calculator you could purchase it through the department. Your lecturer can advise you of which models are appropriate.
If you are eager to get started before then you could purchase a textbook. This is not essential as we will use a variety of resources during the course, but access to a text book, particularly for independent study, will help. | 677.169 | 1 |
CPMP
Course 4 1st Edition Units
The mathematical content and sequence of units in Course 4 allows considerable flexibility in tailoring a course to best prepare students for various undergraduate programs. For students intending to pursue programs in the mathematical, physical, and biological sciences or engineering, we recommend the following sequence of units:
Develops student understanding of the fundamental concepts underlying calculus and their applications.
Topics
include:
Average and instantaneous rates of change, derivative at a point and derivative functions, accumulation of continuously varying quantities by estimation, the definite integral, and intuitive development of the fundamental theorem of calculus.
Develops student understanding of two-dimensional vectors and their use in modeling linear, circular, and other nonlinear motion.
Topics
include:
Concept of vector as a mathematical object used to model situations defined by magnitude and direction; equality of vectors, scalar multiples, opposite vectors, sum and difference vectors, position vectors and coordinates; and parametric equations for motion along a line and for motion of projectiles and objects in circular and elliptical orbits.
Systematic
counting, the Multiplication Principle of Counting, combinations,
permutations; the Binomial Theorem, Pascal's triangle, combinatorial
reasoning; the General Multiplication Rule for Probability;
and the Principle of Mathematical Induction.
Extends student understanding of the binomial distribution, including its exact construction and how the normal approximation to the binomial distribution is used in statistical inference to test a single proportion and to compare two treatments in an experiment.
Topics
include:
Binomial probability formula; shape, mean, and standard deviation of a binomial distribution; normal approximation to a binomial distribution; hypothesis test for a proportion; design of an experiment; randomization test; and hypothesis test for the difference of two proportions.
Extends student ability to manipulate symbolic representations of exponential, logarithmic, and trigonometric functions; to solve exponential and logarithmic equations; to prove or disprove that two trigonometric expressions are identical and to solve trigonometric equations; to reason with complex numbers and complex number operations using geometric representations and to find roots of complex numbers.
Extends student ability to visualize and represent three-dimensional shapes using contours, cross sections, and reliefs and to visualize and represent surfaces and conic sections defined by algebraic equations.
Topics
include:
Using contours to represent three-dimensional surfaces and developing contour maps from data; sketching surfaces from sets of cross sections; conics as planar sections of right circular cones and as locus of points in a plane; three-dimensional rectangular coordinate system; sketching surfaces using traces, intercepts and cross sections derived from algebraically-defined surfaces; surfaces of revolution and cylindrical surfaces. | 677.169 | 1 |
The Year 9 Mathematics course follows Levels 3 to 5 of the New Zealand Mathematics Curriculum. Students are banded into separate classes based on their mathematical ability. The three bands: 9MATA, 9MATB and 9MATC, work at different levels of difficulty and pace, but all courses are considered the first step in the three year programme leading to success in NCEA Level 1. | 677.169 | 1 |
I have noticed that the major problem students have while solving math problems is that they start working a problem out without pausing to wonder what the question is really asking. Read problem more than two times. Make sure you understand every key words. If not, go to the index of your math book and quickly look what those mathematical term means. After you find meanings of these special words,...
read more | 677.169 | 1 |
This manual draws on the capabilities of Mathematica to enrich the subject of differential equations
and boundary value problems and can be used with any introductory differential equations course. The manual
includes a wide variety of stand-alone worksheets that lead students into insights that would be difficult to
obtain without the computer. No prior knowledge of Mathematica is assumed, but students learn the
basics of Mathematica syntax as they gain experience with the assignments. | 677.169 | 1 |
Pure mathematics defines as the math in which we study concepts. This type of mathematics is also known as speculative mathematics. It is different from applied mathematics in terms of its nature and application. Entirely based on abstract concepts, it is apparently not possible to study the real life effects of these concepts.
Mathematicians state it as a social phenomena (naturally) that provides tools and inspiration for conducting hypothetical research.
Important aspects of pure mathematics:
Abstraction & Generalization
Theorems are generalized for providing sufficient proofs and understanding. Results are simplified and precise that make it possible to conclude results. Generality also makes it compatible with other mathematical concepts and theories.
As far as the teaching skills are concerned it is obvious that highly developed skills are required to understand its disciplines. Mathematics tutor should have the ability to relate facts with mind bending realistic concepts. Studentlance.com provides you tutoring services and gives you the opportunity to find a tutor with all these qualities. They are able to carefully cater the minute details by providing sufficient reading material and support. | 677.169 | 1 |
book covers a variety of topics in mathematics as they relate to industrial technologies including manufacturing, electricity/electronics, graphics, communication, transportation, industrial management, materials and related science principles. Organized by topics, the main objective is to develop strong, logical problem-solving skills. ..A brief description of each math principle is presented with step-by-step examples. The explanations are designed to emphasize the correct use and application of math principles. Graphs, drawings and charts relating to the applications reinforce the use of the skills developed. ALSO AVAILABLE INSTRUCTOR SUPPLEMENTS CALL CUSTOMER SUPPORT TO ORDER Instructor's Guide, ISBN: 0-8273-6975-1 | 677.169 | 1 |
for a one semester or one-term algebra-based introductory statistics courses. Drawing on the author's extensive teaching experience and background in statistics and mathematics, this text promotes student success in introductoryMore...
This title is for a one semester or one-term algebra-based introductory statistics courses. Drawing on the author's extensive teaching experience and background in statistics and mathematics, this text promotes student success in introductory statistics while maintaining the integrity of the | 677.169 | 1 |
These higher level math courses assume fluent knowledge with Algebra but to have this fluency requires a strong foundation of all the Algebraic fundamentals. Knowing what is in store for those students aspiring to take the higher level math courses, my focus is squarely on those necessary fundam...
...I work in the Pharmaceutical industry and apply these concepts to my work everyday. My
...By Trig... | 677.169 | 1 |
Synopsis
Master Math Algebra 2 by Mary Hansen
Master Math: Algebra. Master Math: Algebra 2 carefully introduces the foundational concepts in each topic area - from linear equations to polynomials, radical functions, and beyond - and provides a wealth of tips, step-by-step examples, practice problems, and solutions. Whether you're a student, parent, or teacher, this book will provide clarifying, encouraging help for any learner hoping to master Algebra 2.
About the Author
Mary Hansen received her B.A. in mathematics and her M.A.T. in education from Trinity University in San Antonio, Texas. She has taught mathematics and special education and has worked at the elementary school, high school, and college levels in Texas, North Carolina, and Kansas. She is the co-author of Algebra I: An Integrated Approach, Algebra 2: An Integrated Approach, and Geometry: An Integrated Approach, and she is the author of Business Math, 17th Edition. Mary currently works as an educational consultant and freelance writer. | 677.169 | 1 |
Fourth edition.
Wonder Book - Member ABAA/ILAB
MD, USA
$6.89
FREE
None(1 Copy):
Fair Highlights. 0982423837New:
New 09824238371 Copy):
Fair 0982423837About the Book
b]The Geometry Guide[/b] illustrates every geometric principle, formula, and problem type tested on the GMAT. Understand and master the intricacies of shapes, planes, lines, angles, and objects.Each chapter builds comprehensive content understanding by providing rules, strategies and in-depth examples of how the GMAT tests a given topic and how you can respond accurately and quickly. The Guide contains a total of 83 'In-Action' problems of increasing difficulty with detailed answer explanations. [b]The content of the book is aligned to the latest Official Guides from GMAC (12th edition).[/b][b]Special Features:[/b]Purchase of this book includes one year of access to ManhattanGMAT's online Geometry Question Bank (accessible by inputting a unique code in the back of each book). | 677.169 | 1 |
MathematicsThis book contains a collection of papers presented at the 2nd
Tbilisi Salerno Workshop on Mathematical Modeling in March
2015. The focus is on applications of mathematics in physics,
electromagnetics, biochemistry and botany, and covers such
topics as multimodal logic, fractional calculus, special
functions, Fourier-like solutions for PDE's,
Rvachev-functions and linear dynamical systems. Special
chapters... more...
This volume contains a collection of clever mathematical
applications of linear algebra, mainly in combinatorics, geometry,
and algorithms. Each chapter covers a single main result with
motivation and full proof in at most ten pages and can be read
independently of all other chapters (with minor exceptions),
assuming only a modest background in linear algebra. The topics
include a number of well-known mathematical gems, such as Hamming
codes, the... more...
This book presents a mathematical introduction to the theory of
orthogonal wavelets and their uses in analyzing functions and
function spaces, both in one and in several variables. Starting
with a detailed and self-contained discussion of the general
construction of one dimensional wavelets from multiresolution
analysis, the book presents in detail the most important wavelets:
spline wavelets, Meyer's wavelets and wavelets with compact
support. It then... more...
Accessible to students and flexible for instructors, College Trigonometry, Sixth Edition, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing... more...
Building bridges between classical results and contemporary
nonstandard problems, this highly relevant work embraces
important topics in analysis and algebra from a problem-solving
perspective. The book is structured to assist the reader in
formulating and proving conjectures, as well as devising
solutions to important mathematical problems by making
connections between various concepts and ideas from different
areas of mathematics.... more...
This book provides an accessible introduction to algebraic
topology, a field at the intersection of topology, geometry and
algebra, together with its applications. Moreover, it covers
several related topics that are in fact important in the
overall scheme of algebraic topology. Comprising eighteen
chapters and two appendices, the book integrates various
concepts of algebraic topology, supported by examples,... more...
This classic of the mathematical literature forms a comprehensive
study of the inequalities used throughout mathematics. First
published in 1934, it presents clearly and lucidly both the
statement and proof of all the standard inequalities of analysis.
The authors were well-known for their powers of exposition and made
this subject accessible to a wide audience of mathematicians.
This is a matrix-oriented approach to linear algebra that covers
the traditional material of the courses generally known as Linear
Algebra I and Linear Algebra II throughout North America, but it
also includes more advanced topics such as the pseudoinverse and
the singular value decomposition that make it appropriate for a
more advanced course as well. As is becoming increasingly the norm,
the book begins with the geometry of Euclidean 3-space so that... more...
Introduction to Abstract Algebra, Second Edition
presents abstract algebra as the main tool underlying discrete
mathematics and the digital world. It avoids the usual groups
first/rings first dilemma by introducing semigroups and monoids,
the multiplicative structures of rings, along with groups.
This new edition of a widely adopted textbook covers applications
from biology, science, and engineering. It offers numerous
updates based... more... | 677.169 | 1 |
School Leavers
A LEVEL
Further Maths
What is Further Maths?
If you get a grade 7 in GCSE Maths, you should seriously consider studying Further Maths, as it develops some of the concepts met in A Level Maths and brings it to a higher plane. It attracts students who thoroughly enjoy the subject and are keen to extend their understanding and knowledge. It will appeal to you if Maths is one of your favourite subjects at school, as it gives you the chance to see a wide variety of fascinating topics, including some more demanding and abstract areas of Maths. Lessons are fast-paced, interesting and should really make you think!
What Will You Study?
September 2017 sees the introduction of a reformed Further Mathematics A Level. Students will sit four examinations at the end of Year 13. Two of these exams will be compulsory Pure Mathematics modules and the other two will be optional from Pure, Mechanics, Decision and Statistics modules.
What Next?
Nearly all of our A Level Further Maths students go on to university to study Maths or a Maths related degree subject, such as Physics, Engineering or Computer Science. Further Maths is often listed as a preferred or essential A Level subject by top universities for entry onto these degree courses.
Exam Board
Edexcel
Entry Requirements
At least two Bs and three Cs at GCSE plus at least a Grade A (7) in GCSE Mathematics.
NOTE You must also be studying AS Maths at college as part of your course of study. | 677.169 | 1 |
David R. Brooks An Introduction to MAPLE for College Algebra
1997, Brooks/Cole Publishing Company, ISBN 0-534-34757-6.
The purpose of this book is to help you learn and apply the power of
algebra by harnessing the power of computers to do symbolic
manipulation. It uses the University of Waterloo's MAPLE software,
one of several computer algebra systems that are revolutionizing the
teaching and learning of high school and college mathematics (as well
as the way many mathematicians do their jobs). The book is intended
as a supplement to, and not a replacement for, a conventional "pencil
and paper" algebra text. It can be used in conjunction with any text
that covers the material found in a typical college algebra course.
My approach to writing the book was to examine the computational
demands (both symbolic and numerical) of each topic and ask: "How can
students apply Maple's capabilities to enhance their understanding and
build confidence in their ability to solve problems?" Whenever
mathematical matters have arisen, I have tried to strike a balance
between making the book readable on its own and at the same time
minimizing duplication of material likely to be covered in detail in a
textbook.
This text is suitable for both high school and undergraduate algebra
and pre-calculus courses. | 677.169 | 1 |
Monday, January 27, 2014
Excellent Exercises − Completing the Square
The is the first of an occasional series that I'd like to post about intelligent exercise design for use in a math class (whether as part of a presentation, homework, or test). My primary point is that if someone just thinks that they can solve problems, and walks into a classroom and starts making up random problems to work on -- disaster is sure to strike. There are so many possible pitfalls and complications in problems, and such a limited time in class to build specific skills, that you really have to know absolutely every detail of how your exercises are going to work before you get in the classroom. Not expecting to do that is basically BS'ing the discipline.
So in this series I'd like to show my work process and objectives for specific sets of exercises that I've designed for my in-class presentations. Are my final products "excellent"? Maybe yes or no, but certainly that's the end-goal. The critical observation is that a great deal of attention needs to be paid, and the precise details of every exercise have to be investigated before using them in class. And that some subject areas are surprisingly hard to design non-degenerate problems for.
For this first post, I'll revisit my College Algebra class from last week, where I lectured on the method of "completing the square" (finding a quantity c to add to x^2+bx such that it factors to a binomial square, i.e.: x^2+bx+c = (x+m)^2... which of course is solved by adding c=(b/2)^2.). As per my usual rhythm, I had four exercises prepared: two for me and two for the students. Each pair had one that would be worked entirely with integers, and a second that required work with fractions. The first three went as expected, but the fourth one (worked on by the students) turned out much harder, such that only 3 students in the class were able to complete it (which sucks, because it failed to give the rest of the class confidence in the procedure). Why was that, and how can I fix it next time?
First thing I did at home was turn to our textbook and work out every problem in the book to see the scope of how they all worked. Here I'm looking at Michael Sullivan's College Algebra, 8th Edition (Section 1.2):
What we find here is that all of the problems in the book share a few key features. One is that after completing the square, when the square-root is applied to both sides of the equation, the right-side numerator never requires reduction (it's either a perfect square or it's prime). Second and perhaps more important is that the denominator is in every case a perfect square -- so the square-root is trivial, and we never need to deal with reducing or rationalizing the denominators. Third is that with one exception, in the last step the denominators of the added fraction are always the same and need no adjustment (the exception is in #43, where we adjust 1/2 = 2/4; noting that even when combing fractions on the complete-the-square step, I had a few students flat-out not understand how to do that). That does simplify things quite a bit.
Now let's look at my fraction-inclusive exercises from class:
As you can see, item (b) (the one I did on the board) works out the same way, featuring a right-side fraction with a prime numerator and a perfect-square denominator. But item (d) (that the students worked on) doesn't work that way. The denominator of 18, after the square root, needs to be reduced, then rationalized, and that causes another multiplication of radicals on the top; and then to finish things off we need to create common denominators to combine the fractions. That extends the formerly 8-step problem to about 14-steps, depending on how you're counting things.
You can see on the side of that work paper that I'm trying to figure out what parameters cause those problems to work out differently. One is that if there's any GCD between the first coefficient and any of the others, then some fraction will reduce and produce non-like denominators in the last step. And that it turn will result in a non-perfect-square denominator on the right after you complete the square (because of adding fractions with initially different denominators). So my primary problem in item (d) was using the coefficients 6, 4, and 9, which have GCDs between the first and each of the others.
Finally, here's me trying to find a reasonable replacement exercise, which is harder than it first sounds (of course, trying to avoid all the combinations previously used in the book or classroom);
It took me 4 tries before I was satisfied. The first attempt had a GCD in the coefficients (and thus a denominator radical needing reduction/rationalizing), before I figured that part out. The second attempt fixed that, but accidentally had a reducible numerator radical, which makes it unlike all the stuff before that (√44 = √4*11 = 2√11). The third worked out okay, but I was unhappy with the abnormally large numerator radical of √149, which is a little hard to confirm that it's not reducible (the "100" and "49" kind of deceptively suggest that it is). So on the fourth attempt I cut the coefficients down some more, so the final radical is √129, which I'm more comfortable with.
Now we could ask: shouldn't students be able to deal with those reducible and rationalizable denominators when they pop up? In theory, of course yes, but in this context I think it distracts from the primary subject of how completing-the-square works. More specifically, the primary (but not sole) reason we want completing the square is to use in the proof of the quadratic formula -- and coincidentally, neither of those complications appear if you work the proof out in detail (the numerator radical is irreducible, the denominator is a perfect square, and like denominators appear automatically). So as a first-time scaffolding exercise these are really the parts we need. If students were to encounter more complications in book homework on their own time, then that's great, too (although as we've seen in the Sullivan textbook, that doesn't happen).
In summary: Completing the square exercises can get extremely bogged down with lots of radical and fraction work if you're not careful about how they're structured in the first place, losing the thread of the presentation when that happens. More generally: It may be necessary to work out every exercise in a textbook, as well as all your in-class presentations, beforehand in order to scope out expectations and challenge level. Hopefully more examples of this on a later date. | 677.169 | 1 |
10th Grade Common Core Mathematics Complete Year Bundle of 6 Units
Be sure that you have an application to open
this file type before downloading and/or purchasing.
9 MB|100 pages
Product Description
This bundle is a complete collection of 6 units, approximately 7 lessons each for a grand total of 44 lessons. Tests are included for all but Unit 5. There are also extra activities for each unit. The 10th Grade Common Core covers mostly Algebra 2 (heavy on quadratics) and a little bit of geometry. Answer keys are included for all exams and some individual lessons.
A description of each of the units:
Unit 1: Quadratic Sequences (7 lessons, 2 activities, 2 versions of tests with answer key)
the distributive property (multiplying a monomial with a binomial)
given a table of values--identifying which is arithmetic, geometric and quadratic
writing explicit and recursive expressions for arithmetic, geometric and quadratic table of values
graphing geometric, arithmetic and quadratic sequences
graphing a line and then shifting the line vertically and changing the slope and making connections about vertical shifts and slope change and the function
given a story problem, a table of values and a graph determining which is linear, exponential and quadratic.
Unit 2: Introduction to Quadratics (6 lessons, one activity and 2 tests with solution key)
identifying quadratic, linear and exponential expressions
given one form of a quadratic (graph, table of values, vertex form, or standard form) and then coming up with the other three forms
factoring a quadratic in standard form.
multiplying two binomials using a 2-way table
given a factored quadratic and a quadratic in vertex form--finding the vertex, the x and y-intercepts, and the stretch
Unit 4: Piecewise and Absolute Value Functions (7 lessons, 1 activity, 2 versions of tests with soultion key)
solving absolute value functions
graphing piece-wise functions and stating the domain and range
writing the equation for a quadratic given the vertical and horizontal shift, the stretch factor and a reflection about the x-axis.
writing inverses given a set of points
given a table of values and given a graph
writing the domain and range of an inverse and the original function given a graph
there is a review on perfect square factoring
multiplying two binomials with radical terms.
Unit 5: Geometric Figures (7 lessons, 4 activities, NO TESTS INCLUDED FOR THIS UNIT)
supplementary angles
constructing perpendicular line segment bisectors
angle bisectors with a compass and straight edge
finding the missing sides of a right triangle
solving for different angle measurements given complimentary or supplementary angles
finding angle measurements given angle bisector information
performing a rotation, translation and reflection of a given triangle
congruence statements (ASA, SSS, SAS)
drawing altitudes, medians, perpendicular bisectors and angle bisectors
reflecting and translating a triangle
bisecting angles
bisecting line segments
constructing triangle medians
constructing perpendicular bisectors of triangles
bisecting triangle angles with a straight edge and compass
Determining if statements about quadrilaterals and triangles are true or false.
Unit 6 - Probability (4 lessons, one version of a test--no solution key)
Calculating probabilities using information given in a Venn Diagram.
Calculating probabilities using information given in a tree-diagram.
Calculating simple probabilities given situations.
Creating a Venn Diagram given a situation.
Calculating probabilities given a Venn Diagram and a situation.
Organizing information into a 2-way table
Organizing information into a tree diagram
Completing a 2-way table and creating conditional statements.
Independent and dependent events.
Calculating probabilities of independent and dependent events.
Creating a 2-way table given a situation.
Creating a Tree diagram given a situation.
Creating a Venn diagram given a situation.
Comparing and contrasting information contained in a 2-way table, a Venn diagram and a Tree diagram.
Interpreting probabilities using information organized in a 2-way table, a Venn diagram and a Tree diagram.
Given information, create a 2-way table, Venn Diagram and a Tree diagram to organize.
Calculate probabilities based on information given in a 2-way table, Venn Diagram or a Tree diagram. | 677.169 | 1 |
Real problems
I am searching the materials that is related with practical problems.
Particularly differentiation and integration equations
How does one get into solve to use this equations....
Also what are the applications,results how much accuracy with practical ...etc | 677.169 | 1 |
Reviewed OER Library
Curriki Geometry
Note that this resource was reviewed during the Spring 2014 review period. The resource may or may not have been updated since the review. Check with the content creator to see if there is a more recent version available.
Intended Audience
License
License: CC BY NC
Note: This course contains content produced by other organizations which may use a different open license. Please confirm the license status of these third-party resources before reusing them.
Format and Features
Format: Web;PDF
Resource is Printable
Common Core
Note: Correlations are embedded in the resource.
Professional development
Curriki provides webinar support services for educators interested in learning more about integrating OERs into their curriculum. Fees are associated with webinar or in-person workshops - dependent on the number of participants.
Additional Information
An online version of Curriki Geometry with teacher and student access is available at:
Review
Background from OER Project Review Team
Curriki is a non-profit corporation providing a platform for the sharing and creation of free learning resources. This OER Geometry course was designed by teachers and project-based learning specialists. The curriculum has both teacher and student materials with a combination of printable PDF and word files and online activities. The core of the Curriki Geometry learning process is the project-based learning approach and it is designed for teachers to choose any or all of the projects to be taught in any order. This should factor into the viewer's analysis of the review results.
Amount of work required to bring into CCSS alignment (average score): Moderate (2.3)
Comments/Ideal Use:
Overall, I like the scenarios that the publisher uses to generate authentic reasoning in the student. They are very well thought out and articulated. My main concern is that students must be held accountable for their learning every moment of every class. The veteran teacher could make this project run smoothly and very successfully with an honors class. I don't see this curriculum working well with a general population of high school geometry students.
A veteran teacher would be fine in implementing this curriculum. A novice teacher would see many of the classroom management issues that will occur as a result of the nature of project based learning in a classroom environment. As I reviewed this curriculum, I assumed that a teacher has the necessary technology to make this project run smoothly. It is not realistic to think a math teacher can spend weeks in a computer lab.
Challenges:
My main issue with the curriculum is the lack of procedural development by the student.
In my experience as an instructor, and through research I've read, students must see prior products in order to begin forming an idea about how their project will "look".
There is too much left to chance in this curriculum. The final project rubric is too vague in relation to GCO12.
No supplementary material for special needs learners
Suggestions:
I would recommend including some traditional practice problem sets side by side with the pacing guide.
Develop an example project to help teachers and students visually see what the end product "could" look like.
I would suggest listing all or many of the constructions desired and make that list available to the instructor and incorporate them into the final rubric.
I would recommend a more clearly defined list of outcomes that students should demonstrate in their final product. General rubrics are adequate for higher-level students. Teachers must be very specific with lower level learners as to what they need to demonstrate.
Comments/Ideal Use:
I couldn't see myself using this curriculum as a replacement to my current textbook. Some of the CCSS content is missing, and much of what is there is not at the in-depth level required by CCSS. A single one of these projects, however, would provide a great change of pace, and a chance to see what math is required in real-world situations.
This resource would be most useful as a supplemental resource for a seasoned teacher. The group management skills require many tasks and some prior experience/knowledge. A novice would not have as much success in this as a veteran.
Challenges:
The curriculum does not cover all the areas of emphasis provided by CCSS for a geometry course. The curriculum fails in student-written proofs, and has only minimal coverage of coordinate geometry, for example.
The curriculum lacks author-written tests with answer keys and varying formats and forms. The curriculum relies on Kahn Academy's multiple-choice assessments, or Curriki 's multiple choice online test (or a written test with no answer key). Teachers are routinely asked to write their own quizzes.
Suggestions:
Add the areas mentioned above to the product.
Comments/Ideal Use:
I would use this source as a supplement to a unit. I would use it after much of the teaching has been done as a summative assessment. Teachers would need quite a bit of experience with some of the formats used. I would not recommend to a new teacher. Teachers must have a good handle on their kids' levels of learning and type of learning.
Challenges:
Procedural/formative assessments not embedded
Assumes knowledge of Geometer's sketchpad, quizlet, sketch geometry
No support of ELL
Suggestions:
Create and place procedural/formative assessments
Have an instructional aspect for resources like Geometer's sketchpad, quizlet, etc. built in for teachers and students as this will affect the pacing guide
Need to somehow get the ELL kids involved. The problems are rich, but they might not have understanding what certain words are. There is a lot of reading, which will require quite a bit of scaffolding to reach this audience.
Comments/Ideal Use:
This could be used as a supplement to a geometry unit with guidance from the teacher about the important concepts to be included in the presentation project and these should be specifically tied to learning targets aligned with the CCSS. The 'curriculum' consists of six projects for geometry but in fact, the "How Random Is My Life?" project is not aligned to any of the CCSS geometry standards. | 677.169 | 1 |
Information
Mission Statement
The Mathematics Faculty provides an environment for students to achieve their maximum potential and encourages an atmosphere of learning, investigation and co-operation, stimulating activities of varying kinds in order to accommodate students' preferred learning styles and develop enthusiasm and interest in Mathematics.
Why do students study Mathematics
Mathematics is essential because it is one of the most widely used subjects in the world. Every career and pathways needs some sort of Mathematics. It helps the mind to reason and change complicated situations or problems into clear, simple, and logical steps. Students are encouraged to discuss different ways of tackling problems, to explain and justify their explanations to challenge their thinking. The reality is that we live in a society where employers expect some level of numeracy. | 677.169 | 1 |
A Concise Course in Advanced Level Statistics with worked
The mathematics major provides a solid foundation for graduate study in mathematics as well as background for study in economics, the biological sciences, the physical sciences and engineering, as well as many non-traditional areas. Full-time students can complete the degree in four years or 120 credit hours. Only one of these can be a Cognate Course, because the student is not a double major. Education Secretary Richard Riley from more than 200 mathematicians and prominent individuals.
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Calculators
Since many current calculators are now CAS (computer algebra systems) with graphing capabilities, the term calculator can be used interchangeably with math technology.
Calculators: The Good
Here are some reasons why calculators and technology should be used in the classroom. A teacher can focus on these as teaching points in order to make sure the calculator is being used appropriately as a tool instead of a crutch.
Technology can reinforce math skills (order of operations).
Calculators can help you get answers to the problems in your book.
Not sure about the answer for problem 16? Maybe a calculator can
help!
Technology can save us a lot of time: They allow us to focus on the
steps for solving a problem without having to worry about a lot of the
little details.
Graphing calculators can graph most functions quicker and better than
we can.
Technology is useful in testing conjectures.
Technology forces students to learn a new, practical set of skills and
concepts which are important issues in jobs relying on math.
Calculators are a necessary part of the sciences. Physics and Chemistry
have many problems that are too difficult or too time consuming to do
by hand. Any person studying in a science needs to know how to use
a calculator properly.
Technology lets us examine more complicated and/or realistic prob-
lems: For example, most equations and integrals that arise in "real"
world applications can't be solved. Now realistic problems can be stud-
ied because technology can help simplify the difficult parts.
Using technology can make math more interesting to students which will make them more likely to take more math classes.
Calculators: The Bad
Here are some reasons why calculators and technology can be harmful to a student's mathematical maturity. By being aware of the pitfalls, a teacher can make sure the calculator is being used appropriately as a tool instead of a crutch.
All technology uses a finite number of numbers to represent an infinite number of
numbers. This means they are all subject to various problems such as overflow and underflow.
Some calculations/graphs can't be performed on a calculator.
Some calculations are wrong on purpose.
Graphing calculators have bugs like software.
Calculators are great for checking conjectures but can't prove many of them.
The repetoire of problem solving approaches declines because students go to the
calculator first. It becomes a crutch. [Tingyao Zheng]
The efficiency of getting an answer from a calculator may cover a lack of conceptual
understanding of a subject matter. [Tingyao Zheng]
It's difficult to debug the mistakes a student makes when a calculator is used.
[Tingyao Zheng]
Technology may furnish very different meanings and functions to the notations used
in conventional mathematics. [Tingyao Zheng] | 677.169 | 1 |
People study maths at university for many different reasons. For some, it's professional training for a future career as a mathematician in academia or industry, or as a teacher. For others, a maths degree opens the door to a large number of professions where quick-wittedness, clear thinking and an ability to work with numbers are called for. Many graduates go into the financial sector - as accountants, actuaries, investment bankers and financial analysts, for example - and another large group goes into IT and computing. Generally speaking, graduates who opt for one of these possibilities have to receive some training when they begin work, but the top companies compete for graduates with an upper-second or first-class degree, and pay them handsomely, even as trainees.
In the UK there are different types of maths degrees. Besides the three-year BSc (four years in Scotland), most leading universities offer a four-year degree called an MMath. Even though the first M stands for "Master", this is an undergraduate degree. The first two years are more or less the same as the BSc, but the final two years are more demanding, and take students closer to the frontiers of research.
Students entering university on one degree can transfer to the other if their interests change, and since the MMath is tougher than the BSc, students who do not maintain a good average grade in their first two years usually transfer to the BSc in their third year. Many of those who complete the MMath go on to higher degrees. Everyone who thinks they might want to do this should begin their studies on the MMath rather than the BSc, and change later if they find that the MMath does not suit them. Besides these two degrees, many universities offer joint BSc degrees such as maths and economics, maths with business studies, or maths with physics.
Studying maths at undergraduate level is rather different from studying maths at school. It is much more rich and interesting, but for many first-year students the overwhelming impression is that it is much harder. Of course you are expected to be more independent than you were at school, but the main difference is the emphasis on proof, and on solving new and unfamiliar problems. Proof, or rigorous, deductive thinking, is what mathematics is about. When you are studying the geometry of 11-dimensional space, or the factorisation of 1,000-digit numbers, there is very little else to guide you. But it's amazing where rigorous thought will take you, and how exhilarating its subtlety, power and versatility can be, and by the end of their first year, most students begin to feel this.
Of course, the level of difficulty varies from institution to institution. One of the things you have to decide is whether you want to be on a demanding course at a top university (typical entry requirement AAA, or AAB), or whether you might flourish more in a less demanding environment.
Besides the level of difficulty, one of the differences to look out for is the extent to which you can tailor your degree to suit your interests, whether in academia or the financial sector. Although you might see yourself as one or the other, your views may change. If you are ambitious, look for a university with strong research. The Higher Education Funding Council assesses each university department on the strength of its research, and gives it a rating from one (weak) to five (strong). Many departments advertise their rating on their websites.
Departments that actively research are more likely to have passionate and inspiring lecturers, though they will also have other concerns besides their teaching! A research-active maths department will have graduate students who provide additional small-group teaching, and provide a valuable bridge between undergraduates and lecturers. | 677.169 | 1 |
WHY DO HOMESCHOOL EDUCATORS EITHER STRONGLY LIKE OR DISLIKE JOHN SAXON'S MATH BOOKS?
I was online at a popular website for home school educators a while back and I noticed some back and forth traffic about the benefits and drawbacks of John Saxon's math books. One of the homeschool parents had just commented about the benefits of John's books. As she saw them - through their use of continuous repetition throughout the books - she thought the process contributed to mastery as opposed to just memorizing the math concepts in each lesson for the upcoming test.
One reader replied to her comment with the following:
"Or, one can use a math program that makes the mathematical reasoning clear from the outset as a matter of course rather than believing that a child will grasp the mathematical concepts by repeating procedures ad nauseam. I think the Saxon method is flawed."
This reminds me of one of John's favorite sayings when challenged with similar logic. John's reply would be to the effect that "If you are setting about to teach a young man how to drive an automobile, you do not try to first have him understand the workings of the combustion engine; you put him behind the wheel and have him drive around the block several times."
I recall when teaching incoming freshman the Saxon Algebra 1 course that I would first present students with several conditions such as having them all stand up and then asking if they were standing on a flat surface or a curve. Then I explained to them that an ant moving around on the side of the concrete curve of the quarter mile track at the high school would think he was moving in a straight line and he would never realize that, because of his minute size when compared to the enormity of the curve, he thought the curve to be a straight line.
I would then go on to explain that – like the ant's experience in his world - they were standing on an infinitesimal piece of another curve which appears to be a flat surface to them. I would continue by telling the students that in "Spatial Geometry" there are more than 180 degrees in a triangle. It never failed, but about this time someone would put up their hand and – as one young lady did - say "Mr. Reed, I am getting a headache, could we get on with Algebra 1?"
It was a different story when presenting the same conditions to seniors in the calculus class. They would excitedly begin discussing how to evaluate or calculate them. And telling them there were no parallel lines in space did not seem to upset them either. Could it be because the seniors in calculus were all well grounded in the basic math concepts, and they understood the difference between the effects of these conditions in "Flat Land" as opposed to their "Spatial Application?"
Perhaps John and I are old fashioned, but both of us thought it was the purpose of the high school to create a solid educational foundation - a foundation upon which the young collegiate mind would then advance into the reasoning and theory aspects of collegiate academics. Both John and I had encountered what I referred to as "At Risk Adults" while teaching mathematics at the collegiate level. These students could not fathom a common denominator, or exponential growth. They were incapable of doing college level mathematics because they had never mastered the basics in high school.
Students fail algebra because they have not mastered fractions, decimals and percents. They fail calculus - not because of the calculus, for that is not difficult - they fail calculus because they have not mastered the basics of algebra and trigonometry. I recall my calculus professor after he had completed a lengthy calculus problem on the blackboard - filling the entire blackboard with the problem. Striking the board with the chalk he turned and said "The rest is just algebra." I saw many of my freshman contemporaries with quizzical looks upon their faces. Being the "old man" in the class, I quickly said "But sir that appears to be what they do not understand. Could you go over those steps?" Without batting an eye, he replied "This is a calculus class Mr. Reed, not an algebra class."
I firmly believe that what causes individuals to so strongly dislike John Saxon's math books is, not from their having "used" the books, and suffering frustration or failure, but from their having "misused" the books. Or—more importantly—from having entered the Saxon curriculum at the wrong math level assuming the previous math curriculum adequately prepared the student for this level Saxon math book—when in reality it had not!
So when home school parents place the student into the wrong level Saxon math book—and the student quickly falters in that book—it stands to reason they would blame the curriculum, when in reality, their student was not prepared for the requirements at that level.
Why? Because Saxon math books do not teach the test, they require mastery of concepts introduced in previous levels of math to enable the student to proceed successfully at every level of the curriculum.
Taking the Saxon Placement Test before entering a Saxon math book from Math 54 through Algebra 2, will ensure the student and parent can adequately evaluate the student's ability to proceed at a certain level with success based upon what they have previously mastered.
The Placement Tests can be found on this website at the link shown below:
March 2017
WHY USE SAXON MATH BOOKS?
The title of today's news article was the title of my seminar at Homeschool Conventions when I travelled the Homeschool Convention circuit several years ago. What I wanted to convey to homeschool educators at these seminars was factual information on why John Saxon's math books – when properly used – remain the best math curriculum for mastery of mathematics on the market today.
Why did I emphasize "when properly used"? The reason is because improper use of Saxon math books is one of their major weaknesses. The vast majority of students who encounter difficulties in a Saxon math textbook do so, not because the book is "tough" or "difficult", but because they either entered the Saxon curriculum at the wrong math level or because they skipped books and have not properly advanced through the series. Or - for one reason or another - they had been switching back and forth between different math curriculums. Because of switching curriculums, the students had all developed "holes" in their basic math concepts, concepts critical for future success in the math book they were now using. In John Saxon's math books these "math holes" created frustration and failure for the students who were returning to the Saxon curriculum in the upper level math books.
At every convention, there were always a half dozen or more homeschool parents who came to the booth - all facing the same dilemma! Their sons or daughters had recently completed or were currently completing another curriculum of instruction in algebra, and while they said they were happy with the curriculum they were using, they expressed concern that their son or daughter was not mastering sufficient math concepts to score well on the upcoming ACT or SAT tests. I asked each of them to have their student take the on-line Saxon algebra one placement test which consisted of fifty math questions. The test was actually the final exam in the Saxon pre-algebra book (Algebra ½, 3rd Ed).
In almost every case, regardless of which math curriculum the students were using, the answer was always the same. Not one of the students passed the test. It was not a matter of receiving a low passing grade on the test. The vast majority of them failed to attain fifty percent or better. The curriculums the students were using were not bad curriculums. They correctly taught students the necessary math concepts in a variety of ways. But unlike John Saxon's method of introducing incremental development coupled with his application of "automaticity" to create mastery of the necessary math skills, none of these curriculums enabled students to master these concepts. They taught the test!
In those cases where the parents asked for my advice after learning about the failed pre-algebra test, we worked out a successful plan of action to ensure that the failed concepts were mastered and the "math holes" were filled. The plan enabled each of the students to successfully move to an advanced algebra course later in their academic schedule.
Now to address another topic that arose during the seminars. Several attendees asked whether or not they should use the new fourth editions of algebra one and algebra two textbooks as well as the new separate geometry textbook. I told the audience that the new fourth editions were initially created for the public school system together with the company's creation of a new geometry textbook. After all, don't you make more money from selling three math books than you do from selling just two?
I explained that the daily geometry review content as well as the individual geometry lessons had been gutted from the third editions of John's original Algebra one and Algebra two to create the new fourth editions of those books In my professional opinion, I replied to the homeschool educators that they should stay with the current third editions of John's original Algebra one and Algebra 2 two books and not fall into the century old trap of using a separate geometry text in-between the algebra one and algebra two courses.
One homeschool parent commented that I was mistaken because she had called the company customer service desk and they told her there was geometry in the new fourth edition of their Saxon Algebra 1 book. I have a copy of that edition. It was designed to be sold to the public schools along with the company's new geometry textbook, and it does not integrate geometry into the content of the book's one hundred twenty lessons as John's third edition of Algebra one does.
Here are the facts regarding the geometry content in the two books. I will let you draw your own conclusions:
1. In the index of the third edition of John Saxon's Algebra 1 textbook, there are seventeen references dealing with the calculation of total area, lateral surface area, and volume of spheres, cones, cylinders, etc. In the new fourth edition index, there are only four references to area and volume and they are not geometric references. They deal with determining correct unit conversions of measure and the application of ratios and proportions in their solution, all of which are algebraic not geometric functions.
2. In the index of the third edition of John's Algebra 1 book there are nine references to the word "angles." In the index of the fourth edition, there are none. The reference term "angles" does not appear.
3. In the third edition index of John's Algebra 1 book, there are three references to "Geometric Solids." In the fourth edition index, the word "Geometric Solids" does not appear.
4. The only reference to the word "geometry" in the fourth edition index is the phrase "Geometric Sequences" and that term is not a geometry term. It refers to an algebraic pattern determined through the use of a specific algebraic formula.
5. Geometry references, terms, concepts and daily problems dealing with them are found throughout John's third edition of Algebra one. This does not occur in the fourth edition of algebra one created by HMHCO - the new owners of Saxon Publishers.
So why was the homeschool educator told there was geometry in the new fourth edition of algebra one?
Well, let me see if I can explain what I believe the marketing people came up with. I say marketing people because several of us have tried for several years to find out who authored the new fourth edition and no one at the company could – or would – tell us who the author is. Someone commented that it was given to a textbook committee to create the new fourth editions of algebra one and two as well as the new geometry textbook.
At the back of the new fourth edition of algebra one, just before the index, is a short section of thirty-two pages referred to as the "Skills Bank." Within these thirty-two pages are thirty-one separate topics of which only twelve deal with geometric functions and concepts. Each of the concepts is about a half page in length and covers just a few practice problems dealing with the concepts themselves. Since they are not presented or practiced throughout the book, I believe it makes it difficult if not impossible for the student to master any of these concepts encountering them this late in the book – if they are encountered at all.
Here are several examples of how these geometry concepts are presented in the "Skills Bank" of the new fourth edition of algebra one:.
1. Skills Bank Lesson 14: Contains two short sentences explaining how to classify a quadrilateral. The student is then given only three practice problems on the concept.
2. Skills Bank Lesson 16: Contains two short explanatory sentences describing congruency followed by only two practice problems.
3. Skills Bank Lesson 19: Contains five brief statements describing the various terms used to describe a circle and its component parts, immediately followed by two problems asking the students to identify all of these parts.
The "Skills Bank" concept is fine as far as using a brief addendum to define what those geometric terms mean. But when does the student get to work these concepts so that the review creates "mastery" as John's original books were designed? "The "frequent, cumulative assessment" of John Saxon's math program is referenced by the company on page 5 of their new textbook as one of the key elements of the new book. However, those attributes are never developed for the geometry concepts. Additionally, the company's use of colored "Distributive Strands" reflecting the distribution of functions and relations throughout the textbook does not list any geometry functions or relation strands showing up anywhere in the book – at least not in the book they sent me.
The new algebra one fourth edition textbook created by HMHCO - under the Saxon name – may be a good algebra textbook. However, it does not contain geometry concepts on a daily basis as John's third edition of algebra one does. Before you make a decision to use a separate geometry textbook along with the new fourth edition of algebra one and two, please read my September 2015 news article. If you need to discuss the issue further, please do not hesitate to call or email me.
February 2017
SHOULD YOU GRADE THE DAILY SAXON MATH ASSIGNMENTS?
I continue to see comments on familiar blogs about correcting – or grading – the daily work of Saxon math students. That is a process contrary to what John Saxon intended when he developed his math books. Unlike any other math book on the market today, John's math books were designed to test the student's knowledge every week. Why would you want to have students suffer the pains of getting 100 on their daily work when the weekly test will easily tell you if they are doing well?
I always tell homeschool educators that grading the daily work, when there is a test every Friday, amounts to a form of academic harassment to the student. Like everything else in life, we tend to apply our best when it is absolutely necessary. Students will accept minor mistakes and errors when performing their daily "practice" of math problems. They know when they make a mistake and rather than redo the entire problem, they recognize the correction necessary to fix the error and move on without correcting it. They have a sense when they know or do not know how to do a certain math problem; however, when they encounter that all important test every Friday, – as I like to describe it – they put on their "Test Hat" to do their very best to make sure they do not repeat the same error!
In sports, daily practice ensures the individual will perform well at the weekly game, for without the practice, the game would end in disaster. The same concept applies to daily piano practice. While the young concert pianist does not set out to make mistakes during the daily practice for the upcoming piano recital, he quickly learns from his mistakes. Built into John Saxon's methodology are weekly tests (every four lessons from Algebra ½ through Calculus) to ensure that classroom as well as homeschool educators can quickly identify and correct these mistakes before too much time has elapsed.
In other words, the homeschool educator as well as the classroom teacher is only four days away from finding out what the student has or has not mastered during the past week's daily work. I know of no other math textbook that allows the homeschool educator or the classroom teacher this repetitive check and balance to enable swift and certain correction of the mistakes to ensure they do not continue. Yes, you can check daily work to see if your students are still having trouble with a particular concept, particularly one they missed on their last weekly test, which can be correlated to their latest daily assignment. However, as one home school educator stated recently on one of the blogs "Yes, they must get 100 percent on every paper or they do not move on." While this may be necessary in other math curriculums that do not have 30 or more weekly tests, it is a bit restrictive and punitive in a Saxon environment.
John Saxon realized that not all students would master every new math concept on the day it is introduced, which accounts for the delay allowing more than a full week's practice of the new concepts before being tested on them. He also realized that some students might need still another week of practice for some concepts which accounts for his using a test score of eighty percent as reflecting mastery. Generally, when a student receives a score of eighty on a weekly test, it results from the student not yet having mastered one or two of the new concepts as well as perhaps having skipped a review of an old concept that appeared in the assignment several days before the test. When the students see the old concept in the daily work, they think they can skip that "golden oldie" because they already know how to do it! The reason they get it wrong on the test is that the test problem had the same unusual twist to it that the problem had that the student skipped while doing the daily assignment.
In all the years I taught John Saxon's math at the high school, I never graded a single homework paper. I did monitor the daily work to ensure it was done and I would speak with students whose test grades were falling below the acceptable minimum of eighty percent. I can assure you that having the student do every problem over that he failed to do on his daily assignments does not have anywhere near the benefit of going over the problems missed on the weekly tests because the weekly tests reveal mastery – or lack thereof - while the daily homework only reveals their daily memory!
NOTE: The upper level Saxon math textbooks from algebra ½ through calculus have a test every four lessons, making it easy to standardize the tests always on a Friday - with a weekend free of math homework. However, from Math 54 through Math 87, the tests are taken after every five lessons which either require a Saturday test or place the test day on a rotating schedule. You can easily remedy this by having the student do the fifth lesson in the test series on Friday morning, then later that day, have them take the weekly test leaving them to concentrate on resolving the one's they missed on the test - with no week-end homework. This places them on the same Friday test schedule as the upper level Saxon math students.
January 2017
SHOULD HOMESCHOOL STUDENTS TAKE CALCULUS?
Calculus is not difficult! Students fail calculus not because the calculus is difficult - it is not - but because they never mastered the required algebraic concepts necessary for success in a calculus course. However, not everyone who is good at algebra needs to take a calculus course.
A number of the students I taught in high school never got to calculus their senior year because they could not complete the advanced mathematics textbook by the end of their junior year. They ended up finishing their senior year with the second course from the advanced math book titled "Trigonometry and Pre-calculus" and then taking calculus at the university level. This worked out just fine for them as they were more than adequately prepared and had an opportunity to share the challenge with likeminded contemporaries on campus.
Some of my students advanced no further than completing Saxon Algebra 2 by the end of their senior year in high school. They were able to take a less challenging math course their first year of college by taking the basic college freshman algebra course required for most non-engineering or non-mathematics students. These students would never have to take another math course again - unless of course they switched majors requiring a higher level of mathematics. And, if they did, they would be adequately prepared for the challenge.
I believe the answer for homeschool students in these same situations is what we in Oklahoma call "concurrent enrollment." In other words, don't take a calculus course at home by yourself. Under the guidelines of "concurrent" or "dual" enrollment - or whatever your state calls it - take the course at a local college or university and share the experience with likeminded contemporaries. If your state has such a program a high school student can also receive both high school and college credit for the course. I would not recommend taking calculus under "concurrent" or "dual" enrollment at a local community college unless you first verified that the college or university your child was going to attend will accept that level credit for the course. Many of them will accept those credits but only as electives and not as required courses in the student's major field of studies. Check with the head of the mathematics department or the registrar's office before you enroll in the local community college.
The concept of "concurrent" or "dual" enrollment was just beginning to take hold in the field of education when I was teaching and there were not many high school students taking these college courses enabling them to receive both a high school and college math credit for their efforts. As we gained experience with the new program, we learned that our high school juniors and seniors who had truly mastered John Saxon's Algebra 2 course could easily enroll at the local university in the freshman college algebra course and could - provided they went to class - easily pass the course. And, if they were English or Art majors, they would never have to take another math course if they so desired.
Students who were eligible and wanted to take a calculus course their senior year looked forward to taking it at the local university and receiving "concurrent" or "dual" credit for the course. Many of these same students went on to become research technicians in the field of bio-chemistry and physics. However, several of them never took another math course in their college careers because they were English or Art History majors. They took the college freshman calculus course because they wanted to prove they could pass the course. They wanted to be able to say "I took college calculus my senior year of high school."
So, what does all this mean? Home school students whose major will require calculus at the college level should adjust their math sequence to complete John Saxon's advanced mathematics textbook (2nd Ed) by the end of their junior year of high school, and then take calculus the first semester of their senior year at a local college or university. Not only will this enable them to receive "concurrent" or "dual" - unless their state prohibits it - but they will enjoy the camaraderie of other likeminded college students taking the course with them.
There is a final serendipity to all of this. When enrolling at most universities, honors freshman and freshman with college credits enroll before the "masses" of other freshman students. This would virtually guarantee the student with college credits the courses and schedule they desire - not to mention the potential for scholarship offers with high ACT or SAT scores and earned college credits in a course titled "Calculus I" recorded on their high school transcript. | 677.169 | 1 |
Exploring Graphs of Exponential Functions
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PRODUCT DESCRIPTION
This is an introductory lesson on the graphs of exponential functions. The lesson provides a guided exploration on the effects of changing the parameters of the equation on the graph. Students will need a graphing calculator to complete the guided exploration. After the exploration, there is a 15 question "Check For Understanding" assignment which allows students to apply what they learned in a variety of ways and enables you to see what they learned from the guided exploration | 677.169 | 1 |
Reminders: 1. There are two quizzes posted on CourseWare. 2. First EMCF will be posted later today. " EMCF " = "Electronic Multiple Choice Forms" EMCF answer sheets are available through CourseWare at And the questions will be posted on the course homepage.
Last time: 1. What are vectors? 2. How to add, subtract vectors? 3. How to multiply vectors by scalars? 4. Parallel vectors? 5. Norm of a vector? 6. Unit Vectors? Today: There are two ways to define product of vectors: 1. Dot Product 2. Cross Product
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Description
In this book David Towers presents a carefully paced and sympathetic treatment of linear algebra, assuming kwledge only of the basic tation and elementary ideas of set theory. He progresses gradually to the more powerful and abstract tions of linear algebra, providing exercises which test and develop the reader's understanding at the end of each section. Full sections are given for most of the exercises to facilitate self-paced study.
Author Biography
DAVID TOWERS is Senior Lecturer in Mathematics at Lancaster University and taught previously at the universities of Sheffield and Leeds. he is also Consultant Editor for the Palgrave Mathematical Guides. | 677.169 | 1 |
GrafEq (pronounced 'graphic') is an intuitive, flexible, precise and robust program for producing graphs of implicit relations. GrafEq is designed to foster a strong visual understanding of mathematics by providing reliable graphing technology.
Learning mathematics can be a challenge for anyone. Math Flight can help you master it with three fun activities to choose from! With lots of graphics and sound effects, your interest in learning math should never decline.
This is an advanced expression and conversion calculator. Vast array of built-in functions, constants and confersion operations that can be extended with your own user-defined functions. Now with graphs.
The Dovada student calculator is ideal for use in the school, home, office or engineering and scientific research centers, anywhere scientific calculator or graphic calculator is continually used or required, great for that homework help. | 677.169 | 1 |
ACADEMICS
Academics
Mathematics
Algebra I (Part 1)
This course integrates algebra and geometry concepts at a slower pace. The course focuses on linear concepts and basic geometry. This course prepares students for Foundations of Algebra I (Part 2). Students should have a scientific calculator. Year course for grades 9-12.
Algebra I (Part 2)
This course is a sequel to Algebra (Part 2) and integrates algebra and geometry concepts. This course covers linear and quadratic equations, graphing, and functions in addition to basic geometry. Students who complete both parts of Algebra will have completed a full Algebra I course with basic geometry. Students should have a scientific calculator. They will be exposed to graphing calculators. This course prepares students for Geometry. Prerequisite: Must have at least a C in Algebra I (Part 1) Year course for grades 9-12.
Algebra I
This course focuses on extensive use of linear and simple quadratic equations, graphing, functions and relationships, and integrates geometry and algebra. Scientific calculators are required. Students are exposed to graphing calculators. Year course for grades 9-12.
Algebra II
Builds upon concepts learned in Algebra I. New topics include complex numbers, quadratic relations, logarithms, and matrices. A graphing calculator is required. Prerequisite: At least a C in Algebra I; At least a C in Geometry. Year course for grades 9-12.
Geometry
This course investigates a range of subjects including Non-Euclidean Geometry, spatial relations, logic, proof, congruence, reflections, polygons, circles, and the dimensions of various figures. Prerequisite: At least a C in Algebra I. Year course for grades 9-12.
Geometry (Part 1)
This course covers the first half of Geometry and investigates Algebra I or Algebra I (Part 2). Year course for grades 9-12.
Geometry (Part 2)
This course is a sequel to Geometry (Part 1) and continues to investigate Geometry, Part 1. Year course for grades 9-12.
Computer Science
The main emphasis is on programming oriented toward solving mathematic problems. The program language is True BASIC. It is strongly recommended that students taking this course (1) enjoy math; (2) have a computer at home or allow for time before or after school to complete assignments; (3) have keyboarding skills. Prerequisite: Algebra I. Second semester course for grades 9-12.
Advanced Mathematics
An elective which follows Algebra I and II and Geometry. It prepares students for college work in mathematics. The structure of the number system is stressed. Topics include sequences and series, mathematical induction, vectors, and trigonometry. A graphics calculator is required. Prerequisites: At least a C in Algebra II and Geometry. Year course for grades 11-12.
Advanced Placement Calculus
Covers differentiation and integration and some of their applications. Limits and analytic geometry also receive quite a bit of attention. Students taking this course may take the Advanced Placement exam and should be able to test out of at least one semester of college calculus. A graphics calculator is required. This is a weighted class. Prerequisite: At least a C in Advanced Math. Year course.
Statistics
The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data by exploring data, planning a study, producing models and confirming models by statistical inference. This academic class prepares students for either college or the world of work. Prerequisite: At least a C in Algebra II. First semester for grades 11-12.
Advanced Placement Statistics
The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, planning a study, producing models using probability and simulation, and statistical inference. Students completing this class will be prepared for the Advanced Placement Statistics Exam. A TI-83 or TI-84 graphing calculator is required. This is a weighted class. Prerequisite: At least a C in Advanced Math. Year course. | 677.169 | 1 |
A wondrously romantic belief is that brilliant thinkers magically produce brilliant ideas: Einstein jostles his hair and relativity falls out. We can enjoy these fanciful visions of leaps of genius, but we should not be fooled into believing that they're reality.
Brilliant innovators are brilliant because they practice habits of thinking that inevitably carry them step by step to works of genius. No magic and no leaps are involved.
Professor Starbird will discuss how habits of effective thinking and creativity can be taught and learned through puzzles and mathematics. Anyone who practices these habits of mind will inevitably create new insights, new ideas, and new solutions.
2.01x introduces principles of structural analysis and strength of materials in applications to three essential types of load-bearing elements: bars in axial loading, axisymmetric shafts in torsion, and symmetric beams in bending.
While emphasizing analytical techniques, the course also provides an introduction to computing environments (MATLAB) and numerical methods (Finite Elements: Akselos)
This course is based on the first subject in solid mechanics for MIT Mechanical Engineering students. Join them and learn how to predict linear elastic behavior, and prevent structural failure, by relying on the notions of equilibrium, geometric compatibility, and constitutive material response.
We are surrounded by information, much of it numerical, and it is important to know how to make sense of it. Stat2x is an introduction to the fundamental concepts and methods of statistics, the science of drawing conclusions from data.
The course is the online equivalent of Statistics 2, a 15-week introductory course taken in Berkeley by about 1,000 students each year. Stat2x is divided into three 5-week components. Stat2.1x is the first of the three.
The focus of Stat2.1x is on descriptive statistics. The goal of descriptive statistics is to summarize and present numerical information in a manner that is illuminating and useful. The course will cover graphical as well as numerical summaries of data, starting with a single variable and progressing to the relation between two variables. Methods will be illustrated with data from a variety of areas in the sciences and humanities.
There will be no mindless memorization of formulas and methods. Throughout Stat2.1x
Statistics 2 at Berkeley is an introductory class taken by about 1,000 students each year. Stat2.3x is the last in a sequence of three courses that make up Stat2x, the online equivalent of Berkeley's Stat 2. The focus of Stat2.3x is on statistical inference: how to make valid conclusions based on data from random samples. At the heart of the main problem addressed by the course will be a population (which you can imagine for now as a set of people) connected with which there is a numerical quantity of interest (which you can imagine for now as the average number of MOOCs the people have taken). If you could talk to each member of the population, you could calculate that number exactly. But what if the population is so large that your resources will not stretch to interviewing every member? What if you can only reach a subset of the population?
Stat 2.3x will discuss good ways to select the subset (yes, at random); how to estimate the numerical quantity of interest, based on what you see in your sample; and ways to test hypotheses about numerical or probabilistic aspects of the problem.
The methods that will be covered are among the most commonly used of all statistical techniques. If you have ever read an article that claimed, "The margin of error in such surveys is about three percentage points," or, "Researchers at the University of California at Berkeley have discovered a highly significant link between ...," then you should expect that by the end of Stat 2.3x you will have a pretty good idea of what that means. Examples will range all the way from a little girl's school science project (seriously – she did a great job and her results were published in a major journal) to rulings by the U.S. Supreme Court.Statistics 2 at Berkeley is an introductory class taken by about 1000 students each year. Stat2.2x is the second of three five-week courses that make up Stat2x, the online equivalent of Berkeley's Stat 2.
The focus of Stat2.2x is on probability theory: exactly what is a random sample, and how does randomness work? If you buy 10 lottery tickets instead of 1, does your chance of winning go up by a factor of 10? What is the law of averages? How can polls make accurate predictions based on data from small fractions of the population? What should you expect to happen "just by chance"? These are some of the questions we will address in the course.
We will start with exact calculations of chances when the experiments are small enough that exact calculations are feasible and interesting. Then we will step back from all the details and try to identify features of large random samples that will help us approximate probabilities that are hard to compute exactly. We will study sums and averages of large random samples, discuss the factors that affect their accuracy, and use the normal approximation for their probability distributions.
Be warned: by the end of Stat2.2x you will not want to gamble. Ever. (Unless you're really good at counting cards, in which case you could try blackjack, but perhaps after taking all these edX courses you'll find other ways of earning money.)Will certificates be awarded?
Yes. Online learners who achieve a passing grade in a course can earn a certificate of achievement. These certificates will indicate you have successfully completed the course, but will not include a specific grade. Certificates will be issued by edX under the name of BerkeleyX, designating the institution from which the course originated | 677.169 | 1 |
Scientific Computing and Differential Equations An Introduction to Numerical Methods Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on aMore...
Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context. This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level. * An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment * Contains an introduction to numerical methods for both ordinary and partial differential equations * Concentrates on ordinary differential equations, especially boundary-value problems * Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course * Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level | 677.169 | 1 |
Grade Levels
Math
what you have learned about rational expressions and their applications, and then consider how you might apply rational expressions to your daily life. Explain this application, and discuss what the equation might be. Did the study of these types of equations help you to understand the application better? | 677.169 | 1 |
MatBasic Desciption:
The MatBasic is the language of mathematical calculations. Strong mathematical base: full complex arithmetic's, linear algebra and operations, nonlinear methods and graphical visualization.
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MatBasic is a calculating, programming and debugging environment using special high-level programming language designed for solving mathematical problems. MatBasic programming language allows execution of difficult mathematical calculations, involving an exhaustive set of tools for the purpose of creation of algorithmic programs. It also allows a user to abstract his mind from the type of working data which can be either real-valued, or complex numbers, or matrices, or strings, or structures, etc. The MatBasic supports both the text and the graphical data visualization.
MatBasic is fast language interpreter and its environment application field is wide: from solving the school problem to executing different engineering and mathematical computations. The MatBasic programming language combines; simplicity of BASIC language, flexibility of high-level languages such as C or Pascal and at the same time turns up to be a powerful calculation tool. By means of a special operating mode, Matbasic it is possible to use as the powerful calculator. Also the MatBasic can be used for educational purpose as a matter of studying the bases of programming and raising algorithmization skills.
Efficient Java Matrix Library or EJML is an Java based linear algebra library designed to help you with the manipulation of dense matrices. Its design goals are: to be as computationally efficient as possible for both small and large matrices and to be...
Differential Equations is a handy application designed to help you solve equations with minimum effort. The program enables you to specify the coefficients by using the keyboard on the main window.It is designed to calculate the solution to homogeneous...
Linear Algebra Decoded is a program designed to assist students in the subject of Linear Algebra, although it has features for professors, including the ability to generate tests where problems are customized and solutions are in the field of integers....
This script defines the Matrix class, an implementation of a linear algebra matrix. Arithmetic operations, trace, determinant, and minors are defined for it. This is a lightweight alternative to a numerical Python package for people who need to do
Diofantos is a library for the solution of equations that arise in physics. It deals with ordinary differential equations (ODE), partial differential equations (PDE), including grid generation, and integral equations.
centralApp Controller was built as a small and useful app that uses Ordinary Differential Equations to find a solution to a body under a central force.centralApp Controller was developed with the help of the Java programming language and can run | 677.169 | 1 |
Overview
Math Talks have become a go-to routine for many math teachers in their response to the new wave of math standards that call for a much greater emphasis on requiring students to justify their solutions, to communicate their mathematical reasoning, to make arguments with math, and to think critically about the mathematical reasoning and arguments of others.
A debate has broken out over the past few years in (and beyond) education circles over whether algebra should be a high school graduation requirement. The controversy in its current iteration was fueled when the Common Core elevated algebra to a privileged position in secondary math education. Then Secretary of Education Arne Duncan made the case for the standards' commitment to algebra in a 2011 speech to the National Council of the Teachers of Mathematics.
In recent years, it has become increasingly clear to the country — not just to you guys as teachers — that algebra is a key, maybe the key, to success in college. Students who have completed Algebra II in high school are twice as likely to earn a degree as those who didn't. Algebra teaches students reasoning and logic leading to academic success not just in math but across the curriculum.
Overview
The Stock Market Sector Scuffle teaches math-based financial literacy using a real-world scenario in which students have to produce and analyze a financial data set in order to build arguments to convince "investors" that their sector-based stock portfolio holds the greatest promise of financial returns.
Argument-Centered Education is working with partner high schools right now on implementing a variation (and somewhat of a simplification) of the Justify & Critique activity for mathematics classrooms.
This version of the argument-based activity has the same warrants for its use as were laid out in a version previously posted here in The Debatafier on algebraic relationships in two variables, and the same alignment with Common Core and NCTM standards that elevate meta-cognition, ability to communicate how math principles work in solutions, and mathematical reasoning process over product.
Current standards in mathematics require that students be able to "construct viable arguments and critique the reasoning of others" (Common Core Standards, Standards of Math Practice 3). Further, "mathematically proficient students . . . justify their conclusions, communicate them to others, and respond to the arguments of others." This activity has students justifying and making arguments for their solutions to higher-order thinking math questions, and it has students questioning or critiquing the solutions of their classmates. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
This second edition of a popular and unique introduction to Clifford algebras and spinors has three new chapters. The beginning chapters cover the basics: vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters, which will also interest physicists, include treatments of the quantum mechanics of the electron, electromagnetism and special relativity. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing among the Weyl, Majorana and Dirac spinors. Scalar products of spinors are categorized by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy's integral formula is generalized to higher dimensions.
Review
"This is certainly one of the best and most useful books written about Clifford algebras and spinors." Mathematical Reviews
Synopsis
This is the second edition of Professor Lounesto's unique introduction to Clifford algebras and spinors.
Synopsis
This is the second edition of Professor Lounesto's introduction to Clifford algebras and spinors.
Synopsis
Here, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. This will interest physicists as well as mathematicians, and includes treatments of the quantum mechanics of the electron, electromagnetism and special relativity with Clifford algebras.
Synopsis
This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras. | 677.169 | 1 |
Problems with Simultaneous Equations
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0.8 MB
PRODUCT DESCRIPTION
Problems with Simultaneous Equations
What's Included
PowerPoint, Notebook, Flipchart Presentations that include a starter, two main activities and a plenary.
Differentiated worksheet with solutions
Interactive question and answer generator
To introduce the idea of equivalent equations the starter involves calculating the common factor between multiple equations in order to determine the odd one out. In the main phase the teacher is provided with progressively more complicated pairs of equations in which to model the idea of making coefficients equal in order for an unknown to be eliminated.
Differentiated Learning Objectives
All students should be able to solve a pair of simultaneous equations with different coefficients using the elimination method
Most students should be able to derive and solve a pair of simultaneous equations by equating two unknowns.
Some students should be able to equate two unknowns from a diagram and solve using the method of elimination | 677.169 | 1 |
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this file type before downloading and/or purchasing.
6 MB
Product Description
This flipbook is perfect for a factoring unit! It is a great practice/study guide or as class notes during a factoring unit. This was created for use as a review in Algebra 2, but could also be used in an Algebra 1 class.
There are five tabs in the flipbook. The tabs are:
• Greatest Common Factor
• Factoring Trinomials x^2+bx+c
• Factoring Trinomials ax^2+bx+c
• Special Factoring Patterns
• Factoring by Grouping
Under each tab, there are examples and practice problems. Examples are meant to be filled in with the teacher, but could also be assigned as practice problems. Photos of a completed flipbook are included. Some of the tabs also include short written descriptions. A version of the flipbook is also included with fill-in-the-blank descriptions.
A presentation file is included. To view the presentation file, you must have Microsoft Powerpoint. The presentation file is included to help facilitate note taking, if desired. Only the problems are given in the presentation file so that the teacher can present the information in whichever way they choose.
Copying and assembling directions are included, with photos. Photos of a filled in flipbook are included as well. Download the preview to see problem examples.
Upon purchase, you will receive a zip file with a Microsoft Powerpoint Show and a pdf file. Help Opening Zip Files | 677.169 | 1 |
Honors Algebra I, Part 1 (MTH124A)
Honors Algebra I, Part 1 (MTH124A)
Quick Overview
This high school course prepares students for more advanced courses while they develop algebraic fluency, learn the skills needed to solve equations, and perform manipulations with numbers, variables, equations, and inequalities. Topics include simplifying expressions involving variables, fractions, exponents, and radicals; and working with integers, rational numbers, and irrational numbers. This course includes all the topics in MTH123, but includes more challenging assignments and optional challenge activities. Each semester also includes an independent honors project.
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Course Overview
K12 High School Honors Algebra I prepares students for more advanced courses while they develop algebraic fluency; learn the skills needed to solve equations; and perform manipulations with numbers, variables, equations, and inequalities. They also learn concepts central to the abstraction and generalization that algebra makes possible. Students learn to use number properties to simplify expressions or justify statements; describe sets with set notation and find the union and intersection of sets; simplify and evaluate expressions involving variables, fractions, exponents, and radicals; work with integers, rational numbers, and irrational numbers; and graph and solve equations, inequalities, and systems of equations. They learn to determine whether a relation is a function and how to describe its domain and range; use factoring, formulas, and other techniques to solve quadratic and other polynomial equations; formulate and evaluate valid mathematical arguments using various types of reasoning; and translate word problems into mathematical equations and then use the equations to solve the original problems. The course is expanded with more challenging assessments, optional exercises, and threaded discussions that allow students to explore and connect algebraic concepts. There is also an independent honors project each semester.
Course Outline
SEMESTER 1
Honors Algebra I A, Unit 1: Algebra Basics
The English word algebra and the Spanish word algebrista both come from the Arabic word al-jabr, which means "restoration". | 677.169 | 1 |
Holt McDougal Larson Algebra 1: Student Edition 2011
Program Overview Active Learning Hands-on games and activities capture the imagination and help your students connect to essential concepts. Flexible Lesson Development Flexible planning tools help you reduce your preparation time and maximize your goals, while giving you the freedom to teach your way every day. Effective Assessment Ongoing, intetegrated assessment gives you the power, flexibility, and feedback to prepare your students for success.
Book Description HOLT MCDOUGAL. Hardcover. Book Condition: New. 0547315155 MULTIPLE COPIES AVAILABLE - New Condition - Never Used - DOES NOT INCLUDE ANY CDs OR ACCESS CODES IF APPLICABLE. Bookseller Inventory # Z0547315155ZN
Book Description HOLT MCDOUGAL. Hardcover. Book Condition: New. 0547315155 OVER 80 IN STOCK 12/29/16 WE HAVE NUMEROUS COPIES. HARDCOVER. School barcode sticker on the back cover. Bookseller Inventory # Z0547315155ZN | 677.169 | 1 |
Detailed Description
The purpose of this module is to show you how the dynamic features of geometry software such as the Geometer's Sketchpad can be used to illustrate theorems, to foster experimentation, to support problem solving, and to encourage conjecture.
Dynamic geometry software such as the Geometer's Sketchpad or Cabri II are very powerful packages that allow you to make accurate geometric constructions and then to manipulate either the initial objects or the constructed ones to examine which relationships in the configuration are coincidental and which are inherent in the constructions.
To be able to exploit these features in the classroom you do not need to be an expert with the software, but you do need some experience with the basic capabilities and you need to see some of the "tricks of the trade" that facilitate the creation of good demonstrations and projects. And, of course, no matter how good the software is, what you don't know you can't illustrate!
This module provides you with a good deal of experience examining and experimenting with dynamic sketches. You will also have the opportunity to imitate some of these and to create examples of your own. This is all done in the context of discussing interesting topics in geometry that are accessible to high school students. Some of them are results that are already standard in the curriculum and others are not.
A brief description of the actual work needed to complete the module follows.
Prerequisite: The module assumes that you are familiar with the Geometer's Sketchpad. You might well have gained this experience from workshops or courses, or just by experimenting yourself. The Using the Geometer's Sketchpad module provides an adequate introduction and there are other on-line tutorials available. Links to some of these electronic resources are provided in the course outline.
Step 1: Begin by getting a feeling for some of the special "dynamic" features of Sketchpad sketches. You will work through several demonstrations and be asked to create your own versions of them.
Step 2: You will gain experience in creating dynamic sketches by working through examples that illustrate some elementary but beautiful theorems in geometry --- in particular, Ceva's Theorem and Monge's Theorem. In the process, you will not only learn some new mathematics, but you will also see some of the techniques for creating attractive and useful dynamic sketches.
Step 3: You will see that a triangle has many, many "centers" besides the ones we already know and love --- circumcenter, incenter, orthocenter --- and you will be given the opportunity to find some new ones of your own!.
Step 4: Select and begin a classroom project that you would like to do for one of the classes that you teach. We will provide you with a file that contains many such projects. You can use these sample projects as a source of ideas for your own project. You can also use these sample projects as a source of inspiration programs that you can copy and modify to suit your own purposes.
All of the ingredients necessary to complete these steps are contained in the files that you will download for this module. Moreover, you can get help when you need it by e-mail to the mentor named in your welcome letter. The next section will explain how to get started. | 677.169 | 1 |
In a physics class, data
collection during several experiments involving oscillating systems will lead
to the development of models through the Stella software package.
These
oscillating systems should produce periodic data.
The physics class will provide various data sets produced
by their models for mathematical analysis.
The data should
encompass at least one full cycle
The precision of the
data should be five to six decimal places
40 to 50 data points
per cycle is recommended.
The physics students will
also submit detailed lab reports to the math students describing the physical
parameters of each model.
Students
will import this data into a specially prepared Excel spreadsheet that will
allow them to determine the specific sine functions that fit the models
developed by the physics students.They
will investigate how the various coefficients of the sine function affect the
mathematical model, and understand how to look at a graph and calculate the
coefficients.
The
mathematics students will then communicate to the physics students the
mathematical models of the data they provided and how the physical parameters
of the experiment relate to the mathematical model.
This unit involves
computational modeling from a systems AND mathematical perspective.Communication between these perspectives
will involve interaction between both physics and math students and require a
deep understanding of the concepts involved.Students will demonstrate this understanding through both ongoing and
summative assessments requiring both technical understanding and an ability to
communicate information clearly. | 677.169 | 1 |
elimination.. elimim. ...
This eBook introduces the topic of inequalities, the meaning of the inequality symbols, how to rearrange and solve inequalities as well as the use of inequalities and number lines and the use of inequalities in graphs.
This eBook introduces the topic of inequalities, the meaning of the inequality symbols, how to rearrange and solve inequalities as well as the use of inequalities and number lines and the use of inequalities in graphs
This eBook introduces the subject of algebra to the student encompassing, inverse operators, equations, the order of precedence, algebraic conventions, BODMAS, expressions, formulae, factorising, rearranging and solving linear, quadratic and simultaneous equations as well as inequalities. | 677.169 | 1 |
Algebra 1 Bundle 2
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599 KB|10 pages
Product Description
This is a collection of five activities (which have also been listed as individual resources) that are useful when learning the basic skills involved with co-ordinates (points), gradients, straight line graphs, writing straight line formulae, intercepts and vectors (if needed).
These activities can be used as starters or review work but they do help to tie the ideas together and provide the variety needed. Being able to handle the tiles adds another dimension to the learning process. I usually ask that students combine the tiles and glue them into their work books - some students have other ways of working with them eg numbering/shading in.
The 3 Level Guide is a favourite as it encourages students to provide reasons or evidence to support their True/False decisions. The 3 levels are based on Bloom's Taxonomy with the lowest level requiring remembering/understanding, the next level requiring ideas to be connected and the final level encouraging a deeper understanding.
The cloze resource is straight forward and helps to "state the obvious" with the process of eliminating some options. It helps to confirm what the students already know or think they know. | 677.169 | 1 |
0_Introduction - Introduction The course is focused on...
1 Introduction • The course is focused on modeling of biological processes at cell and molecular levels. • Good in math is not necessarily good in modeling.- Solving equations vs setting up equations • What is mathematical modeling? • The basic idea of mathematical modeling is to find a mathematical relationship that behaves in the same ways as the objects or processes under investigation. • It is to approximate a real world system, (e.g., cell), using mathematical equations, that the prediction can be tested against observable properties of the system. Therefore, the sophistication of the model depends on techniques that are available for making observations of the system. • A useful mathematical model may give insight about how something really works, and predict new things that cannot be predicted through intuition. ( e.g., blackbox => greybox ) • It can provide a powerful means of integrating several pieces of knowledge at a given level to describe responses at a higher organizational level. ( e.g., molecule => cell => tissue => whole body ) Various Definitions in the literature
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Reinventing Math Class with EquatIO (Chrome Extension)
EquatIO introduces a digital way for students to easily demonstrate and communicate their thinking. What's more, Texthelp is fundamentally about helping individuals understand and be understood, which we can now do across all subjects. EquatIO Features: – Easily create math expressions including equations and formulas – Compatible with Google Docs and Forms* (Sheets and Slides coming soon!) – Input via keyboard, handwriting recognition* (via touchscreen or touchpad) and voice dictation –…
How to build a math expression tokenizer using JavaScript .::. Some time ago I got inspired to build an app for solving specific kinds of math problems. I discovered I had to parse the expression into an abstract syntax tree so I decided to build a prototype in Javascript. While working on the parser I realized the tokenizer had to be built first. .::. coding | 677.169 | 1 |
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Microsoft Mathematics
posted 21 Sep 2011, 06:09 by Jason Zagami
Microsoft Mathematics is an educational programme designed by Microsoft to help students learn, visualize and understand mathematical concepts. Subjects such as algebra, geometry, calculus, physics and chemistry are covered in this program. It is free and easy to install, provides step-by-step learning and powerful visualization tools which can help students to grasp the concepts behind the correct answers.
With Microsoft Mathematics, students can learn step-by-step to solve intimidating math problems and gain better comprehension on math concepts. Teachers can assist students to learn in depth the math concepts they are most interested in.
It must be downloaded and installed on a computer with the Microsoft Windows operating system. | 677.169 | 1 |
ASAssessments
Your AS MEI Mathematics course contains a number of assignments which your dedicated course tutor will mark and give you valuable feedback on throughout your study.
Examinations
Paper 1: Core Mathematics 1 (C1)
Mathematical Processes and Language
Algebra
Co-ordinate geometry
Polynomials
Curve Sketching
72 marks 1 hour and 30 minutes – written paper 33.3% of AS
Paper 2: Core Mathematics 2 (C2)
Sequences and Series
Exponentials and logarithms
Trigonometry
Calculus – Differentiation
Calculus – Integration
Curve Sketching
72 marks 1 hour and 30 minutes – written paper 33.3% of AS
Paper 3: Mechanics 1 (M1)
Mathematical modelling in mechanics
Kinematics of particles
Force
Newton's Law of Motion
Projectiles
Vectors
72 marks 1 hour and 30 minutes – written paper 33.3% of AS
Arranging Your Exams
You are required to arrange and pay for their examinations yourself ( ALL the relevant course text books required to complete this course.
Tutor Support
The most important part of your online AS MEI Mathematics course (apart from you) is your dedicated tutor. All of our tutors have extensive academic experience and have all taught AS AS MEI Mathematics, however we recommend a minimum grade C in GCSE Maths. | 677.169 | 1 |
Mathematics
The Mathematics Department at Kent College aims to provide a supportive, enjoyable and stimulating environment where students are inspired to achieve.
Years 7-11
From Year 7 to Year 11, Mathematics is taught as a core subject. Students are set according to ability but there is a flexibility of movement between sets. Differentiated activities are provided for the more able students and additional support is offered to those who need it.
The department is well-resourced and
every classroom is equipped with an interactive white board. The school subscribes to MyMaths which is a
valuable interactive resource for all students from Year 7 to Year 13.
In September 2014, a new Key Stage 3 Scheme of work was introduced. It will include exciting
new textbooks which reflect the changes in the New Secondary Curriculum in Mathematics.
GCSE Mathematics
At GCSE, students follow the Edexcel Linear Higher Tier
course, taking the examination at the end of Year 11. There are two written examinations, one with a
calculator and one without, each worth 50% of the final mark. For a few students after their Year 11 Mock
Exams, it might be advisable to sit the Foundation Tier to achieve their C grade.
AS/A2 Level Mathematics and Further Mathematics
AS/A2 level Mathematics and Further Mathematics is offered
in the Sixth Form. Students wishing to
study Mathematics at A level are expected to have achieve a grade A or A* at
GCSE.
Studying Mathematics at this level develops skills in
logical thinking and the ability to process information accurately. There are many degree subjects that require
these valuable skills and employers are impressed by this qualification. Mathematics also complements and assists the
understanding of a number of other A level subjects.
The A level Mathematics course comprises of six modules
taken over two years. There are four
compulsory pure mathematics modules and two applied (usually statistics 1 and mechanics
1).
Students wishing to study Further Mathematics take an
additional six modules. Click here for further information. | 677.169 | 1 |
Summer Assignments
2016 Summer Assignments
As the summer approaches check back here to see all summer AP and Honors assignments.
Calculus
Pre-Calculus
This Summer Assignment is for those students who are going into Pre-Calculus in 2016-17.
It consists of: 1. Instructions on how to do the summer assignment and how to self-grade it. 2. The questions come in 2 parts: Part A has 60 questions; Part B has 30 questions. 3. The fully worked solutions to all problems. Do Part A first. After every question, grade it based on the score in the little circles. Partial credit is OK. BE HONEST. Follow the instructions.
Do Part B next. Self-grade it. Work out your grade and change it to a percentage. Follow the instructions.
Do the test in pencil and do all corrections in a colored pen. Your setting out should be at least as good as mine. Show all work.
You will receive full marks for the assignment as long as you have the grade that you got on the test, as a percentage, and all corrections completed.
This Summer Assignment is for those students who are going into AB Calculus in 2016-17. It is due Friday August 12, 2016. It consists of: 1. Instructions on how to do the summer assignment and how to self-grade it. 2. The 36 questions. 3. The fully worked solutions to all problems. After every question, grade it based on the score in the little circles. Partial credit is OK. BE HONEST. Follow the instructions. Work out your grade and change it to a percentage. Follow the instructionsThis Summer Assignment is for those students who are going into BC Calculus in 2016-17. INSTRUCTIONS: Buy Baron's Edition 12 AB Calculus. Second hand online is about $1. You might like to also get a box of the flash cards for the same year. They are cheap. Don't buy the new ones….not good value for this assignment.
Do the first 3 tests for AB Calculus. Self-grade it. Multiple Choice 5 marks each. Free response 30 marks each.
Work out your grade and change it to a PercentAP Physics 1
Students are completing an online course with Mrs. Ferguson. Registration was done through Mrs. Ferguson in May. For questions contact her at fergusonba@pcsb.org
Welcome to our world of words! To explore this world, over the summer we will communicate via our class blog. You will need to create a user name of your last name first initial at: On the homepage, you will notice a space for AP and another for Honors; you will employ the AP section. I posted a variety of forums for you to read and respond to during the summer. You will create an original thread for each of the forums and respond to two other posts by a classmate for each forum. We will read TheDevil in the White City by Eric Larson. We will blog about the writing style, elements of text, voice, vocabulary, tone, rhetorical triangle, and other fun aspects of language. You will be graded on your participation in the summer blogs. | 677.169 | 1 |
Study Guide for College Algebra and Trigonometry is a supplement material to the basic text, College Algebra and Trigonometry. It is written to assist the student in learning mathematics effectively. The book provides detailed solutions to exercises found in the text. Students are encouraged to use these solutions to find a way to approach a problem.... more...
Sets: Naïve, Axiomatic and Applied is a basic compendium on naïve, axiomatic, and applied set theory and covers topics ranging from Boolean operations to union, intersection, and relative complement as well as the reflection principle, measurable cardinals, and models of set theory. Applications of the axiom of choice are also discussed, along with... more...
The Puzzler's Dilemma explores the world of classic logic puzzles, and tells the amazing stories behind them, from the Lighthouse of Alexandria to code-breaking with the Enigma machine. Here are brain teasers that even maths whizzes have never seen explained by a mind as nimble and playful as Derrick Niederman's, the author of Number Freak and the... more...
The book targets undergraduate and postgraduate mathematics students and helps them develop a deep understanding of mathematical analysis. Designed as a first course in real analysis, it helps students learn how abstract mathematical analysis solves mathematical problems that relate to the real world. As well as providing a valuable source of inspiration... more...
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results... more...
This book constitutes the refereed proceedings of the 9th International Workshop on Security, IWSEC 2014, held in Hirosaki, Japan, in August 2014. The 13 regular papers presented together with 8 short papers in this volume were carefully reviewed and selected from 55 submissions. The focus of the workshop was on the following topics: system security,... more...
Like its wildly popular predecessors Cabinet of Mathematical Curiosities and Hoard of Mathematical Treasures , Professor Stewart's brand-new book is a miscellany of over 150 mathematical curios and conundrums, packed with trademark humour and numerous illustrations.In addition to the fascinating formulae and thrilling theorems familiar to Professor... more... | 677.169 | 1 |
Minimal prerequisites make this text ideal for a first course in number theory. Written in a lively, engaging style by the author of popular mathematics books, it features nearly 1,000 imaginative exercises and problems. Solutions to many of the problems are included, and a teacher's guide is available. 1978 edition.
Very informative book but not enough examples worked out
Elementary Number Theory: Second Edition is a relatively short mathematics book that deals a lot with prime number theory. The topics covered in this book are senior college level topics, making the name "Elementary" in the title somewhat deceptive. While topics they talk about in an intro to proofs class focus on the basics, this book focuses on the applied basics. The book is short and has many examples for the student to work out, but it is limited in that there are few examples that the author worked out. Because of the level of this book, many steps are also removed, however, even for a math student, some of the steps skipped left me stumped, and many topics are still out of grasp through independent study. There is a nice section of the book that has some induction problems, which is geared towards those who have already done proofs and now are working on number theory. This book is solid for the $10 it cost, but there is a reason other math texts run from $100-200, and that's because of the extensive amount of problems worked out in those texts. (You get what you pay for)
Undergrad math and phys major review
I picked up this book after taking a course in set theory/math logic.It was my first experience with proof based math and I found it very challenging and rewarding.I decided over the summer I would teach myself number theory as well.So far I am about 3 or 4 weeks into the summer and I've chopped down sections 1-6.Keep in mind I am also doing undergrad physics research and a directed study astrophysics course as well, you could easily progress further.I really have enjoyed this book thus far. I often get so caught up in it that I am up until morning toying with problems.The author did a fantastic job of finding the fine line between too difficult and elementary.It seems just short of a graduate text but a little above a common undergraduate text. Thanks to this text I am becoming much more confident in my ability to set up and execute proofs.I don't want to spoil the methods- but it seems MOSTLY up until this point all proofs are found in the same manner.I have not been able to execute a variety of proof methods (e.g. deduction, mathematical induction, contrapositive, and contradiction.)I would have liked to be able to switch it up some. However, I am no expert and this may be my own doing.
If that is the best "CON" I can come up with for this book, that says a lot.I HIGHLY recommend ANY student who enjoys thinking to pick up this book and complete it in it's entirety. I feel deprived that I wasn't given this opportunity sooner.
I am a 3rd year math+physics major.This book changed me from physics and chemistry to math and physics student and possibly from a physics grad student to a math grad.
Excellent on Elementary Number Theory
Excellent text on number theory.Topic coverage is extensive: quadratic reciprocity, linear diophantine equations, Lagranges's 4-square theorem, Pell's equation and more.Proofs are very good and plenty of exercises.
Good overview to basic number theory
This is a great book for the mathematically-interested layman, non-math-major undergraduate, and people in other fields (such as computer science) who want a fairly quick read on the basics of this fascinating field.It would also serve well as a a precursor/warmup for more advanced treatments of the subject.
It is a book that has aged very well
Published in 1978, this book suffers very little from the illness of being dated. Of course, Fermat's last theorem has been proven and computers have grown much more powerful. However, those advances have little affect on the value of the book. Done well, basic number theory is timeless, and Dudley does it very well. The explanations of the fundamentals are sound and solved exercises are scattered throughout. Solutions to most of the odd numbered problems at the end of the chapters are also included.
The coverage is fairly typical, so the book can still be used as the text for a course in beginning number theory. Chapter 23 contains a set of 267 additional problems, a set for each of the other chapters in the book. Solutions to most of the odd problems in this set are also included. I commend Dudley for including so many solutions; I have little time for authors of books who do not provide solutions to at least some of the exercises. If I ever teach a course in basic number theory, this is the book that I would use.
... Read more
Written by an distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
Classic Number Theory Text
This is one of the classic texts on Number Theory.It is a challenging book for anyone.The problem sets range from easy to hard.There are some hints, but those are few and far between.Like most Dover math books, it's dry and concise.There are better books on the market, but not for this price.
An incredible text in elementary number theory
Despite the deceptively small size of the text compared to many of its type, be sure to carry at least twice as many sheets of paper to fully get all you can out of it. George Andrew's pedagogical style of using combinatorics (basic gambling probability) to explain advanced concepts in number theory is executed brilliantly, and leaves even first-year undergraduates like me without a doubt in the world.
It is essential to do the problems in this book! Do not skip them thinking writing down the definitions and theorems will be enough-- some of the problems will kill you if you go in only knowing the written theorems, without any proper thought into the subject. Like any mathematical subject, it requires rigorous thinking and hours of reading before even considering going on to more advanced topics, like algebraic number theory, abstract algebra, or residue theory.
Breaking down the book into parts, I find it slightly disconcerting that despite the small nature of the book, the concept of quadratic congruences are only introduced in a less-than-introductory fashion, in comparison to other number theory books. It may be true that the author's main research was based off partition theory (the largest section in the book), but quadratic congruences have large applied mathematical influences, and should be considered to be read on, after the book as been finished.
Despite that, this text is an incredible foray into elementary number theory, and is a recommended buy for all those interested in the mathematical world.
Essential Number Theory
This book is great for the price and if you can handle the terseness of a Dover book I would say it is great in general. The back of the book indicates it would be good for liberal arts majors. That is just crazy. However, you don't need much more than a solid foundation in mathematics through the Calculus of sequences and series. To get the most out of this book, you should do as many of the exercises as you can, even the ones without answers. Also, plan on supplementing the text with some online research. A general review of generating functions may be useful. Chapter 3 is a bit out of place and easy to lose patience with. Perhaps it can be read following Part 1. With that said, you can get a lot out of this book with regard to number theory (which arguably may not be generally useful).
best bang for the bucks in number theory books
Price is a factor and Hardy is the classic text.
This one by George E. Andrews is well written has good examples and exercises
and doesn't cost an arm and leg used.It has a good prime section and a good quadratic section. I found stuff I hadn't seen before here.
It is going to take me a while to get everything out of this one!
Good
The author tries to make things easy, and he succeeds in most parts. However, some proofs seem to be simple, but they actually involve complicated reasoning. My suggestion is that the author should not try to hide these difficult parts by reformulating abstract things into simple objects because it doesn't really help. I'd rather see difficulties in proofs than follow them with no idea why they have to be like that.
... Read more
Product Description An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory.
Updates include a chapter by J. H. Silverman on one of the most important developments in number theory - modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader.
The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists. ... Read more
Customer Reviews (16)
There is no such thing as 'number theory'!
I'm not as impressed as the other reviewers here with this book, despite it's being in some sense a 'classic'.
I take it some people - I have no idea what proportion of the population - now and then are struck by properties of numbers. For example, if a number AB is added to BA, the result always divides by 11. If the difference is worked out, this is always a multiple of 9.(E.g. 75 minus 57 is 18, a multiple of 9). Or (e.g.) Any number cubed, less the number, will always divide by 6 and is also the product of three consecutive numbers.(e.g. 5 cubed is 125; less 5 gives 120, which is 4x5x6).This sort of thing is the basis of 'number theory'.
There are at least two problems with this book. Firstly, there is in fact not yet such a thing as 'number theory'. This book is a ragbag of techniques and things which have been identified and passed down by lecturers. But it is NOT a coherent 'theory' in any sense. Perhaps I might compare it with a book on 'chess theory'. Chess books have accounts of such things as opening gambits, sacrifices, end games - including some with extremely precise techniques needed for victory. And there are things like 'zwischenzug' and assorted events which are rare, but have some interest. But does this make up a body of 'theory'? I'd say not. Anyone looking to this book for insight into the Pythagorean mystery of number will in my view be more or less disappointed.
Now, what follows from this is my second point, which perhaps is to do with human psychology, or the capacity of the human brain. What is it that makes some people fix on a certain type of problem? For example, this book, like most or maybe all on number theory, starts with prime numbers - probably discovered as a result of packaging and division of actual objects. This of course had practical applications, such as the Babylonian 360 degrees, and our 12 inches, 14 pounds, 1760 yards, and so on. A collection of techniques (e.g. Eratosthenes' sieve), formulas, limits and other results has accumulated. Looking at Euclid's proof of the infinity of primes, his method was to multiply all the primes, and add 1. This function in effect is designed to use the properties of primes to generate a new prime. However Hardy and Wright don't attempt to generalise this process. Maybe Fermat's Last Theorem could be proved elegantly by inventing some ingenious function which combines the properties of addition, multiplication, and powers - repeated multiplication by the same number? What is it that makes some problems (so far) insoluble - and many of them are very trivial to state?
So we have here a collection of results, embodied in symbolism which is far enough from the actualities to (perhaps) look more impressive than it really is. Integration, for example, is basically simple enough, but the long s and the notation removes the reader from the real world...
And there's a related problem, which is that the connective material, explaining why the next bit is there and what it is supposed to illustrate, is completely missing. The result is like a tour of museum exhibits, where the tourist is expected to infer the significance of all the specimens. Or like a concert, where one sample piece of music is played after another, from which the auditor is presumably left to infer a theory of music. In fact, I've just decided to demote the book to two stars!
Easy read
This book provides a gentle presentation to many subfields of number theory: including analytic, algebraic, and elementary. It discusses generating functions in everyday language. The book's section on the zeta function is incredible. I would recommend this gem to anyone who taken calculus.
awesome book on number theory
I am an undergrad student in computer engineering. I bought this book after I looked at the table of contents and found some topics which I interested in. This is by far the best book on number theory I ever came across. It is very readable, fairly free of errors (the ones that are there are easy to spot and do not cause confusion). In comparison to another number theory book I read before. This one has the charm of making previously confusing concept clear. Different proofs are often given on major theorems. I do not really have a good way to describe it, but this book really "flows". The logic is clear and easy to follow. If I read this one to start with, it would save me a lot of time and I would have a much better understanding of the subject by now. I know, this review is totally uninformative, you have to see it for yourself to be sure, but I totally recommend this one.
The only downside is the price dropped by like 20$ since I bought it.
Number Theory
The book was an excellent accumulation
of Number Theoretic ideas. However, it
failed to produce applications or clearcut
examples of the theorems.
A Mathematical Classic Reviewed
Even though I have only read a small portion of this book, I can already tell that it deserves its "classic" label. I have been accumulating some mathematical classics, mostly purchased through Amazon, and this one certainly fits in with the rest. Like Euclid's Elements, it has a timeless appeal even as mathematics advances. And, judging by the table of contents, it goes well beyond a mere "introduction" to number theory, like H. S. M. Coxeter's "Introduction to Geometry."
... Read more
Product Description Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps readers explore key concepts and push their understanding to new heights. Computational exercises and computer projects are also available. Reflecting many years of professors' feedback, this edition offers new examples, exercises, and applications, while incorporating advancements and discoveries in number theory made in the past few years. ... Read more
Customer Reviews (12)
half truth
The book itself is a fine book. However, the book is not in good shape. It was marked as in good condition and it is falling apart. I am very disappointed and will think twice about buying books on here again.
So obvious, it's difficult
Great book! Rosen explains tough concepts well and the homework problems really drive it home. The computational homework for programmers is especially nice. However, some of the problems are worded in such a way that it obscures the intent of the question. Then again, this IS number theory.
Moderately Helpful
For a good number of the odd problems the solution manual is good at working out the problem and coming to an answer. However, some of the answers are identical to what is in the back of the Number Theory textbook.
ODD PROBLEMS ONLY
The description is misleading. The solutions manual only contains the solutions to odd problems. The same 'answers' that are available at the back of the book are explained in a little bit more detail in the solutions manual. If you are looking for solutions to even numbered problems as well then don't buy this.
Omits obvious visual and intuitive ways of looking at concepts.
This book is wordy, but less clear than I think it could be.It moves slowly, yet omits helpful ways of looking at concepts in the interest of being elementary.Also, it does not pave the way for future study of the material, nor does it pave the way for later study of connections to algebra, analysis, or combinatorics.
This book overlooks intuitive, visual ways of representing basic concepts.For example, lattice/Hasse diagrams helped me understand divisibility and GCD's, but this book does not even mention this way of looking at divisibility.Congruence relations can be visualized in a number of ways, but this book only treats them using basic algebra.A book that moves as slowly and is as elementary as this one should really explore these sorts of visual presentations of concepts.
Since this book is elementary, it does not explore any connections to groups, rings and ideals, fields, or lattices, and I think this is a shame because these structures make number theory make more sense.I think the book would do better to introduce a few of these structures in a very basic way.The book also passes up the opportunity to introduce generating functions, a critical and fairly elementary topic in number theory, which are only touched in one exercise.The first few chapters of Wilf's Generatingfunctionology and Newman's "Analytic Number Theory" show that generating functions can be presented at an elementary level.
There are blurbs of history interspersed throughout the text, and I like the idea, but the history focuses almost exclusively on biographical information, with a tiny bit of history of famous problems and conjectures.There is little discussion of how the core mathematical ideas in the book were discovered and evolved over time.This book would do well to cut out the biographies and replace them with richer discussion of the historical development of the subject itself.
I like the idea of a number theory book that focuses on applications, but this book does so at the expense of other things: its treatment of truly fascinating topics (such as continued fractions) is so weak that I do not think it's worth the trade-off.The book does nothing to pave the way towards the study of either analytic or algebraic number theory.The Zeta function only gets a token mention.
This book is usable as a textbook or for self-study, but it is not outstanding for either of these goals, nor is it useful as a reference foradvanced students.Studying from this book alone won't help one develop a good sense of intuition in number theory.Stillwell's thin book is about as easy to follow as this one, and yet it slowly introduces ideals and other algebraic concepts by the end of the book.My favorite book on number theory is Apostol's "Analytic Number Theory".It is considerably more advanced than this one, but I think that students with a strong background will actually find it easier to learn from.I have not yet found a truly elementary book on number theory that I liked; I think students would be better off to first acquire enough background and mathematical maturity to dive right into some of these more advanced texts, than to spend their time working through a book like this.
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Product Description This book gives an elementary undergraduate-level introduction to Number Theory, with the emphasis on carefully explained proofs and worked examples. Exercises, with solutions, are integrated into the text as part of the learning process. The first few chapters, covering divisibility, prime numbers and modular arithmetic, assume only basic school algebra, and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics. Elementary ideas about groups and rings (summarised in an appendix) are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third year students, uses ideas from algebra, analysis, calculus and geometry to study more advanced topics such as Dirichlet series and sums of squares. The last chapter gives a concise account of Fermat's Last Theorem, from its origins in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles. ... Read more
Customer Reviews (15)
The knowledge I had expected, but too out of place, and does not help in solving basic questions.
I originally bought this book to gain the knowledge and have an advantage in competing in Math Olympiads, but this book deters from that purpose.
The book skips many important subjects, (such as qualities of divisors, essential qualities of prime numbers). Also, it is not that straightforward. Although I have learned a few tricks from this book, the book skips many steps in proving theorems, which, although may be filled by a teacher or student, the skipped steps are beyond the level of an average person reading this book.
Also, it is not very clear in its approaches, since it assumes the reader has learned many mathematical notations (such as cyclotomic polynomials, derivatives from Calculus, etc, etc), which can be confusing for the average high schooler.
Also, the exercises in this book are not very consistent with the topics of the book, such as proving theorems beyond the scope of the already learned knowledge, as well as the lack of problems actually consistent with the topics of the book (such as find the gcd(21390, 123, or 1290x+9233y=1, find solutions to x and y, if any). This book only gives me 1 or 2 of those problems, and then moves on. Many times I have found myself to have the need to re-read the materials from the book because of its lack of review sections. I have even seen online notes from people about number theory more consistently put together than this book, which also have firmly emplaced their knowledge into my mind.
Another realization I have is that this book does not fit the skill level of a high schooler, or even an undergraduate. Many times the exercises and the proofs in the book give either very easy problems, or very hard problems. Such problems include (find gcd(234, 123), then skipping to proving if 2^m+1 is prime, then m is prime as well, as well as proving Eintstein's criterion for polynomials).
They do not provide many "in between" problems, and so, part of the learning becomes defunct, or people might even be discouraged by the book.
However, I do realize that this book may be useful for undergraduates taking cryptography, this is however, not useful for anyone who is studying for math competitions.
Probably the best maths book I've ever read
This is a great little book thats packed full of great number theory results. It is well written.
I'm a real fan of the SUMS books (I've bought 4 of the titles in the series), because all of the books I've bought are well written, they're jammed full of useful information and they're relatively cheap!
The book strikes a good balance between keeping focused on number theory (there are chapters requirng a knowledge of rings and groups, but these structures only support the numbers, not abstract them away) and not being trivial (I've read too many number theory books that are 'bitty', in the sense that there is too much breadth and not enough depth).
Nice book with some flaws
"Elementary Number Theory" by Jones and Jones is a nice book, easily accessible to the average undergraduate math major. I used this book as a text for the junior level number theory course at my university. The price is very attractive, especially for students on a budget. The text is for the most part very readible. There are a few flaws with the book that prevent it from truly being an excellent text:
1) Complete (or nearly complete) solutions are given for every exercise. While this is good if you are trying to learn the material yourself, it makes it difficult to assign problems from the text.
2) Non-intuitive steps are often left out of proofs. While the instructor or a mature student can usually fill these in, some of the omissions are (in my opinion) beyond that of the average undergraduate.
With its excellent price point, I would recommend the book as a supplement to another text.
A Satisfactory Text for Elementary Number Theory
I've recently received my copy of Elementary Number Theory by Jones and Jones, and I'm (thus far) satisfied with the textbook. Although I'm not a professional mathematician, I have worked toward a degree in math and still love to study it. For me, the current textbook for number theory is a challenge to master, but with all the solutions to problems provided, I find it quite palatable to work toward an understanding of number theory, using this text.
In view of my current experiences with this textbook, I would recommend it to a mathematical hobbyist like myself, or to a professional student of mathematics -- or anyone wishing to tackle number theory.
An almost perfect square
That the book's almost square is easily gathered from the photo. That it's almost perfect must be verified by reading it. And what an enjoyable verification indeed awaits those who take on the challenge! Not that reading it is a challenge - on the contrary, the Joneses take every effort to ensure your learning experience be as painless as possible. Every proof is complete, all exercises are solved. The proofs are always selected for their instructional merit, rather than for their mathematical "elegance" (read: brevity and algebraic gimmickry). As one Amazonian reviewer put it: you could read it through, lying in a bubble bath.
Another Amazonian reviewer commented that "Number theory is like the cement on your driveway. Real and Complex analysis are the Porsche and Ferrari you drive home every night." I disagree. In any case, in my opinion the book's weak spots are those sections where the discussion forays into the realm of real and complex analysis, namely 9.4-6 ("Random Integers", "Evaluating Zeta(2)", "Evaluating Zeta(2k)"), 9.9 ("Complex variables"), 10.2 ("The Gaussian Integers"), a part of 10.6 ("Minkowsky's Theorem") and 11.9 ("Lame and Kummer"). "Sums of two squares" (Section 10.1) could also use improvement, but this is compensated by the excellent, independent treatment this topic receives in the "Minkowsky's Theorem" chapter.
On several occasions, from the very beginning, the book assumes familiarity with single-variable polynomials (particularly the division algorithm and the x^n-y^n expansion). Be prepared.
If it weren't for the forays mentioned above, the book would have been a straight fiver. But even as it stands, it'sa tour-de-force of pedagogy and expository mathematical writing.
One last quibble. The book doesn't have a homepage, nor is there any indication of a way to contact the authors. Textbook publishers should learn from their colleagues in the applied computer science publishing industry (such as O'Reilly, Wrox, Apress, etc.) and always make a homepage available for every book, with, at the minimum, a link to an errata page, and a forum where readers of the book can discuss it, (preferably with the involvement of the author(s)).
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Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition.
Crystal clear
Samuel's book is a classic. It is a bit "antique", certainly not the most modern introduction to algebraic number theory. The topics covered in the book are algebraic and integral extensions, Dedekind rings, ideal classes and Dirichlet's unit theorem, the splitting of primes in an extension field and some Galois theory for number fields. So the range of topics is quite small (and the book is short, ~100 pages).
And yet I love this book. It is crystal clear, well written and well structured; it is quite dense (especially the last chapter) and makes the beginning student of algebraic number theory think a lot, but without ever getting too heavy to digest. The list of problems is fantastic: there are many very concrete problems which sharpen your understanding of the material considerably. And last but not least, it is ridiculously cheap.
I recommend this to anyone who wants to learn the basic material about number fields. Without any hesitation.
Samuel Knows Numbers
It's a little dense, and some proofs are lacking detail, but otherwise a great book.Extensive subject covered in one semester's worth of reading.
Good service
Never got shipping confirmation email but customer service was very quick to respond to my question about the shipping status.
A gem of a book
This is a lovely, lovely book -- the first I ever read on algebraic number theory. It is spare and direct, and a great introduction to the field.
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Product Description Number Theory: A Lively Introduction with Proofs, Applications, and Stories, is a new book that provides a rigorous yet accessible introduction to elementary number theory along with relevant applications.A unique feature of the book is that every chapter includes a math myth, a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exercise sets include in-depth Explorations, in which a series of exercises develop a topic that is related to the material in the section. ... Read more
Genuinely funny!(Not to mention clear and well-written.)
This is an extraordinary book.A model of clarity, painstaking attention to detail, and all of it in a light-hearted, engaging manner.With cartoons!That are actually funny!
I compared this book's TOC to the catalog description of the Number Theory course at my school.It contains every topic in our syllabus.So it passes my first test.
Every dozen pages or so, one comes across a real gem.For example, the book discusses the AKS primality test and notes the significant contributions of undergraduates to that breakthrough.The illustrations of pineapples exhibiting Fibonacci numbers are both beautiful and illuminating.
Do not skip the "Math Myths"!They are not mere add-ons.They introduce the topics well, via engaging and well-thought-through analogies, and they are genuinely entertaining.The puns are of Daily-Show-headline calibre.It is one thing to ask a class for their ideas on how to solve the linear Diophantine equation aX+bY=1.It is another thing altogether to introduce the topic by asking the class to help Diophantus the "farmer" weigh potatoes using only a balance scale and the bricks he has on hand.The context provided by the latter provides the traction needed for students to *think* about the question for themselves.
I think this book would be especially well-suited to schools that offer Number Theory as a sophomore-level course, where students have not yet had experience with writing abstract proofs.No other book on this subject will soften that shock nearly as well, helping students make the transition to advanced mathematics by spelling out in detail the habits of mathematical thinking that we practioners of math tend to simply perform without explanation as autonomously as tying our shoes.
I will certainly be using this book for my class the next time I teach Number Theory.
One of the most helpful guides I have read.
Though it starts out at a nearly absurdly fundamental level, the authors do a fantastic job at guiding the reader through the material, guaranteeing that almost no prior knowledge is necessary to get the full experience. The stories and historical anecdotes, true or not, are almost a reason to read the book by themselves. Like one of the other reviewers said, an advanced middle-schooler would be able to go through this book and understand it, as would any undergrad who has yet to take number theory. The examples and exercises are fun and engaging even to someone who has learned the subject.
Be warned, however, that the book is oriented at those who want to learn the subject, and who are willing to take the time for a deep understanding. The lack of answers is not an accidental omission, it is meant to force readers to think through the problems and come up with their own solution. The book teaches not only number theory, but mathematical reasoning and logic as well.
monumental work of patience and love
When I first started reading this book, I was almost brought to tears at the appallingly elementary level that the book starts at: is the average American College Student so ignorant, unprepared, and childish to the point that one must start by teaching them material that would be covered in primary school in Asia and Europe, in a tone appropriate for kindergarten?However, as I kept on reading, I was amazed at the care and thought that the authors put into this book to keep the reader entertained and engaged, while at the same time making sure that no intermediate step, however small, was ever overlooked so that even the most unprepared students could be brought up to speed (as long as they work through the book diligently).
Starting from the Pythagorean theorem and the irrationality of the square root of 2, by the end of the book the reader will be able to understand the proof of Fermat's Last Theorem for the case n=4. Proofs of theorems are always preceded by numerical examples to give the reader a feel of the logic being used.Detailed instructions on how to perform proofs (including some basic English grammar) are also provided so that the reader can write proofs themselves.Various real world applications of the material are provided showing the reader the relevance of it all.
The problems are also very entertaining. The lack of solutions is not a drawback since for most problems one can easily tell whether the solution is correct or not by simply checking to see if one's solution satisfies the condition provided in the problem.Also, the joy of math is in trying to figure out the solution by oneself.If you cannot figure out an answer, just keep on thinking. You will learn nothing by trying to peek at the answer and trying to memorize it.
The authors' patience and their love of the field emanates from every page. The book is so well written that I would say that a gifted 6th or 7th grader will be able to understand it.This is a monumental piece of work that all future textbooks in math should be judged against. If you are interested at all in number theory, this book is a must have.
Postscript: as is often the case with first-editions, there are a few unfortunate typos which may be immensely confusing to the reader:
page 25, second equation: the left-hand-side should be x
page 29, first equation: the left-hand-side should be 2
page 275, table: the numbers in the second row under 5 and 8 should be 2
Hope these will be corrected in the second printing.
No answers
I've only covered the first couple of chapters so I can't comment on the overall effectiveness of this text. However, I can say that I am disappointed that there are no answers to the exercises. Most texts provide answers for at least the odd numbered exercises. The author alludes to a Student Companion on a web site but gives no link. On the Wiley site there is a page associated with this text, but it is a pay site. How lame.
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This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.
Key features:
* Contains problems developed for various mathematical contests, including the International Mathematical Olympiad (IMO)
* Builds a bridge between ordinary high school examples and exercises in number theory and more sophisticated, intricate and abstract concepts and problems
* Begins by familiarizing students with typical examples that illustrate central themes, followed by numerous carefully selected problems and extensive discussions of their solutions
* Combines unconventional and essay-type examples, exercises and problems, many presented in an original fashion
* Engages students in creative thinking and stimulates them to express their comprehension and mastery of the material beyond the classroom
104 Number Theory Problems is a valuable resource for advanced high school students, undergraduates, instructors, and mathematics coaches preparing to participate in mathematical contests and those contemplating future research in number theory and its related areas.
Great book but some solution can be simpler
It is a nice book.Some solution can be solved in different ways that is little simpler.
Number Theoretic Gem
I think that the only way for description of this book is buying it.
This book is as usual another gem, and this time in Number Theory, from
great math problemists Titu Andreescu and his colleagues Dorin Andrica and Zuming Feng.
If you would like to have fun and exciting in number theory, I highly recommend this fabulous book to you.
Congratulations to Titu Andreescu and his colleagues for their excellent books and attempts!!!
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Product Description Elementary ... Read more
Customer Reviews (13)
Low price, good book
The book condition is still good although its bought used. There are a few writings on the pages but its fine. However, there are some missing pages probably from printing error of the book.
Very clear and interesting
Got the book for free in electronic format. The prices for these books are criminal. Intellectual property is the fraud of frauds.
The book itself is excellent. I had not had any formal study of proofs when I started reading, but this book guides you very gently and clearly through the process. Number theory is NOT boring, and going through this book will make you feel enlightened. It's not easy, but very doable for anyone of average intelligence.
All the starting stuff is here
Most of this stuff I found in different books,
but usually not as well presented as this.
This book is a perfect one for someone starting in on number theory.
It even has some neat tables at the end.
I wish I had had this book ten years ago!
an excellent introductory book
before finally selecting this book for reading i 've spent a few hours in the library browsing through some number theory books. Coming from a a different background electical & computer engineer, I had no notion at all of number theory. I like his way of writing with the embedded historical notes and furthermore the proofs of the theorem and their chronological order particularly in the second chapter. I have to admit that I comment on the previous version but new versions are supposed to improve. It is not time consuming to go through the proofs while you understand the theorems and the techniques used behind. The flow is very coherent and solidly written. Overall an excellent introductory book as cited in a previous review.
Rigorous and not too hard
This is a textbook about Elementary Number Theory, where "elementary" does not
mean "simple" or "beginning", but rather those portions of the mathematics of
integers that do not rely on analysis (infinitesmal calculus).
Number theory allows many different orderings of topics, without omitting
proofs.I found Burton's order to be easy to follow. Many results in number
theory follow easily from results in abstract algebra or linear algebra.
The author does not depend on results beyond elementary algebra, but some
degree of mathematical maturity is required.Readers with a math degree will
still have to work to absorb the material.
There are many problems. Those with numerical answers are answered in the back
of the book. About half of the others are answered in an answer guide,
available separately.Almost everything is proved. I only recall two cases
of "left to the reader" except for the problems, of course. None of the
problems are used for future developments in the main text.
The author has a separate text about the history of mathematics.Most of the
chapters in this book start with a section about the history of the material
in the chapter and about the people that developed it. This is interesting
extra material, or padding that makes the book even more expensive than it
should be, depending on you.
This is the 6th edition. The only error I encountered was a consistent misspelling
of one name in chapter 10.I could not find any reported errors on the WWW.
I've used several other number theory books over the years. This one seems the best
for me.Perhaps that is due to Burton's skill, or perhaps it is because I finally
worked through one from front to back, instead of searching for the information
I needed just then.
From Ore with love: old but instructive introduction to number theory.
Pros:
1. The book could teach basic number theory to a wide range of readers, from mathematically inclined high-school students to much more advanced lovers of mathematics. 2. It is enlivened by nice historical allusions.
3.The author shows and shares his fascination with the subject in the writing.
4. On a less lofty side, the font is large enough to avoid eye strain.
Cons:
1. First published 59 years ago, the book has to be dated. For example, many beautiful applications of number theory had been unknown at the time of writing.
2. Not all exercises require creativity, many of them are routine drills.
Bottom line:
If number theory is not your fortress, the book could strike a balance between enjoyable reading and learningHamony?
A noted conjecture of the author's on the harmonic mean of the divisors is tucked unobtrusively in this pleasant reader: "Every harmonic number is even." See problem B2 in Richard K. Guy's Unsolved Problem's in Number Theory.
A good book (but not a great book). Very basic. For the more advanced historical approach, Andre Weil's Number Theory: An approach through history" is to be recommended. Or even Guy's book mentioned above.
Excellent theory interspersed with history
This book goes into detail on number theory, but it is often hard to follow with the history mingled with the theory.More advanced material is referenced without proofs.Two readers will especially like this book: those who want an introduction to number theory and those who want a good introduction to the history of number theory.
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Starting with nothing more than basic high school algebra, this volume leads readers gradually from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. Features an informal writing style and includes many numerical examples. Emphasizes the methods used for proving theorems rather than specific results. Includes a new chapter on big-Oh notation and how it is used to describe the growth rate of number theoretic functions and to describe the complexity of algorithms. Provides a new chapter that introduces the theory of continued fractions. Includes a new chapter on "Continued Fractions, Square Roots and Pell's Equation." Contains additional historical material, including material on Pell's equation and the Chinese Remainder Theorem. A useful reference for mathematics teachers.
Great for mathematicians who have not studied number theory..!
I think its a brilliant introduction to someone like myself, who teaches high school maths to some very able students who may well go on to undergraduate maths courses.
My first degree was in engineering, so I havent had the priviledge of a second level number theory course.. Its ideal! I love the conversational style.. and there are recommendations of books with more rigour, but dont be fooled into thinking this is easy.. Its a demanding read, at least I think so.
Useless piece of garbage
Okay, so I used this book in a semester-long course in elementary number theory. It's totally useless. Aside from the fact that the writing style is too chatty and to some extent patronizing, here's my main problem with this book:
The text gives minimal explanations of things -- basically it states a theorem, gives a few practical examples of why the theorem is true, then gives a chatty proof of said theorem. That'd be fine, but when you get to the exercises, you're left thinking, "huh?" The problems are either mind-numbingly routine or they are insanely beyond the scope of the text, requiring proofs of things that are MAJOR THEOREMS IN ELEMENTARY NUMBER THEORY with absolutely no context, hints, or help. Granted, the instructor of the course gave hints/direction for a lot of these problems, but without a good professor's guidance, good luck trying to prove major theorems all on your own for homework!
Yeah, don't use this book. It's just not very helpful to the student and should only be used if the course requires it AND you have a knowledgeable instructor who can give good guidance.
Great for a casual exploration of the topic
I can understand much of the criticism that I read here from frustrated math majors.I just want to say that, as an engineer who took a number theory course for fun, this was a great introduction to the subject.I found it very readable and easy to understand.It got me interested in number theory - enough so that I would consider reading a bit of it on my own time as I pursue further education in science.It seems that engaging non-mathematicians is the intent, so I have to consider the book a success.
P.S.Can you really complain about the style of the book after reading the title?You certainly can't claim false advertisement.
Pretty good!
I used this book for my Introduction to Number Theory class.I enjoy Silverman's writing style, but I wish there were some more examples and a little bit more theory involved.
It seemed to me as though there were a LOT of topics covered in a short about of time, but I would have liked to have seen some more of the actual meat behind it.
Not bad though!
For its intended audience, this is a gem....
I am a working oceanographer with a physics background who is interested in browsing through various areas of mathematics, particularly ones like number theory which are not a common part of a physicist's background. I picked up and read Dr. Silverman's "Friendly Introduction to Number Theory" and was thoroughly charmed. The book presented many of the basic results of number theory in a clear, concise fashion, and also gave a bit of context and background to the results. Basis computations for "non-experts" are stressed, and the reader for whom this book was intended goes away with a nice feeling of having picked up a bit of knowledge of a new topic. I would also add my voice to those who chided the math majors for panning this book. There are plenty of high level "theorem-proof" books out there for mathematicians, and to criticise a book that popularizes mathematics is both snobbish and counterproductive. We should heartily applaud and value good popularizations of science and technology. This book is a first rate popularization.
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Product Description This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus.Jeffrey Stopple pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs, as well as to the important open problems.The culmination of the book is a brief presentation of the Riemann zeta function, which determines the distribution of prime numbers, and of the significance of the Riemann Hypothesis. ... Read more
Customer Reviews (4)
A Readable Delightful book
This is definitely one of the delightful math books to read.The material is so well organized that it flows very nicely.This book provides a very gentle introduction to such topics as Zeta function and Prime Number Theory.
One of my favorite math books
A little background on me. I have just finished my freshman year of high school, and this was my first book on number theory. However, I have read many other math texts. In the beginning of the book there are some new concepts introduced, but they are not too hard to understand. The middle is refreshing as it involves a lot of calculus, which the student is most likely familiar with. The latter part consists of a variety of new ideas, and the theorems can get quite lengthy. I do not fully understand all of them myself. The book is well written and also includes the history of many mathematical problems.
For the senior math undergraduate
A great book for senior undergraduates in mathematics or anyone with some background in calculus and complex numbers.Proofs are at a level where a careful reading makes them clear, and the author tells the reader when he is not being rigorous.Historical background and logical development of topics makes this a good read too.Most surprising to me was how the author tied in topics from prior chapters into later chapters--he didn't just jump from one topic to the next willy-nilly, but made the book flow as a whole.Problems given to the reader were helpful though sometimes too hard for me, a math major.
Do you like primers? ...and number theory? Well here you go!
There usually seems to be a pretty big gap between the math background needed to understand books on elementary number theory and what's needed to understand most books dealing with analytic number theory, and this book does a good job of making that gap seem smaller.The writing feels a bit like Silverman's "Friendly Introduction to Number Theory" and Derbyshire's "Prime Obsession."There are plenty of experiments for Mathematica and Maple.I could see this book being used in an undergraduate number theory class.The book doesn't assume any familiarity with complex variables. If you can integrate and aren't too afraid of series or logarithms, this book should be no problem.
The book goes over multiplicative functions, Mobius inversion, the Prime Number Theorem, Bernoulli numbers, the Riemann zeta function (and its value at 2n, its analytic continuation, its functional equation, and the Riemann Hypothesis), the Gamma function, Pell's equation, quadratic reciprocity, Dirichlet L-functions, elliptic curves (including their L-functions and the Birch and Swinnerton-Dyer conjecture), binary quadratic forms, and an analytic class number formula for imaginary quadratic fields.
I recommend this book to anyone who can read; and for those who can't read, this book is good motivation to become literate.
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A good and brief introduction
The book covers main topics of elementary number theory. The book is very short (120 text pages) but not at cost of clarity: almost all theorems are proven in the text and many examples are given.
Not many problems have answer in the back, which is not good thing for self-studying.
The text does not require much mathematical background (I believe highschool is enough), and I can recommend the book to anyone interested in number theory. The book is very well worth its price. Buy this and if you still like number theory, buy one of those heavy books over $100 :-).
Readable, clear, but needs an errata page
As others have said, this is a fairly easy read.For me it's actually fun and I'm working through it for that reason.But:
- I don't normally use a highlighter, but found it necessary to highlight symbols where they were defined, because some of them come up only once in a while and it's easy to forget where the definition is.Symbols are not indexed.I have started my own symbol index in the back of the book.
- There are some annoying errors.The theorem to be proven in section 1-3, problem 2 is false for n=1.The decimal expansions in the chapter on continued fractions (page 75) are wrong (for example 1.273820... should actually be 1.273239...).It seems to me if you're going to give 7 digits they should be the right 7 digits.
On the other hand, these errors don't affect the overall flow of the text, and I'm having a great time working through this book on my own.I've read through the whole thing over the summer, and I'm going back through doing problems and writing programs.I was a math major 40 years ago, and haven't done much with it since, to give a context for that remark.
Very good
Very good book.First to comment on the fact that LeVeque has 2 dover books that cover basically the same topics (this one, and Fundamentals of Number Theory).I have looked at both, and this one is the better of the two.The other one uses slightly different definitions that have an Abstract Algebra twist to it.But the other book still doesn't use the power of abstract algebra so the different/akward definitions and explanations just make it hard to read.
An elementary number theory book should use elementary definitions and concepts (abstract algebra is meant for ALGEBRAIC number theory books).So avoid his other book, which is good, but not as easy to read as this one.
This book is very easy to read and concepts are introdced very clearly.Things come in small chunks which are easily digested.The thing about this book is, you can go through it faster than normal textbooks but you still end up learning everything you would by going slowing through hard-to-read texts (not like The Higher Arithmetic by Davenport, that book can lull you into reading it like a story book, but you end up learning nothing).
Good Introduction to Key Topics and Proofs of Number Theory
William J. LeVeque's short book (120 pages), Elementary Theory of Numbers, is quite satisfactory as a self-tutorial text. It should appeal to math majors new to number theory as well as others that enjoy studying mathematics.
Chapter 1 introduces proofs by induction (in various forms), proofs by contradiction, and the radix representation of integers that often proves more useful than the familiar decimal system for theoretical purposes.
Chapter 2 derives the Euclidian algorithm, the cornerstone of multiplicative number theory, as well as the unique factorization theorem and the theorem of the least common multiple. Speaking from experience, I recommend that you take the time necessary to master Chapter 2, not just because these basic proofs are important, but more critically to reinforce the skills and discipline necessary for the subsequent chapters.
Two integers a and b are congruent for the modulus m when their difference a-b is divisible by the integer m. In chapter 3 this seemingly simple concept, introduced by Gauss, leads to topics like residue classes and arithmetic (mod m), linear congruences, polynomial congruences, and quadratic congruences with prime modulus. The short chapter 4 was devoted to the powers of an integer, modulo m.
Continued fractions, the subject of chapter 5, was not unfamiliar and yet, as with congruences, I quickly found myself enmeshed in complexity, wrestling with basic identities, the continued fraction expansion of a rational number, the expansion of an irrational number, the expansion of quadratic identities, and approximation theorems.
I have yet to tackle the last two chapters, the Gaussian integers and Diophantine equations, but my expectation is that both topics will also require substantial effort and time. LeVeque's Elementary Theory of Numbers is not an elementary text, nor a basic introduction to number theory. Nonetheless, it is not out of reach of non-mathematics majors, but it will require a degree of dedication and persistence.
For a reader new to number theory, LeVeque may be too much too soon. I suggest first reading Excursions in Number Theory by C. Stanley Ogilvy and John T. Anderson, another Dover reprint. It is quite good.
Some caution: LeVeque emphasizes that many theorems are easy to understand, and yet this very simplicity is a two-edged sword. Simple theorems often provide no clues, no hints, on how to proceed. Discovering a short and elegant proof is often far from easy.LeVeque also stresses that a technique ceases to be a trick and becomes a method only when it has been encountered enough times to seem natural. A reader new to number theory may initially be overwhelmed by the variety of techniques used.
A nit: The Dover edition of LeVeque's Elementary Theory of Numbers would benefit from a larger font size. I occasionally found myself squinting to read tiny subscripts and superscripts.
Contents of this Book
1. Introduction 2. The Euclidean Algorithm and Its Consequences 3. Congruences 4. The Powers of an Integer Modulo "m" 5. Continued fractions 6. The Gaussian Integers 7. Diophantine Equations
Plus the sample problems and solutions in the above area.
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Product Description Who were the five strangest mathematicians in history?What are the ten most interesting numbers? Jam-packed with thought-provoking mathematical mysteries, puzzles, and games, Wonders of Numbers will enchant even the most left-brained of readers. Hosted by the quirky Dr. Googol--who resides on a remote island and occasionally collaborates with Clifford Pickover--Wonders of Numbers focuses on creativity and the delight of discovery. Here is a potpourri of common and unusual number theory problems of varying difficulty--each presented in brief chapters that convey to readers the essence of the problem rather than its extraneous history. Peppered throughout with illustrations that clarify the problems, Wonders of Numbers also includes fascinating "math gossip." How would we use numbers to communicate with aliens?Check out Chapter 30. Did you know that there is a Numerical Obsessive-Compulsive Disorder? You'll find it in Chapter 45. From the beautiful formula of India's most famous mathematician to the Leviathan number so big it makes a trillion look small, Dr. Googol's witty and straightforward approach to numbers will entice students, educators, and scientists alike to pick up a pencil and work a problem. ... Read more
Customer Reviews (18)
Another Great Book on Recreational Mathematics
If you enjoy Recreational Mathematics and have enjoyed other books by the author, then you will like this book as well. A few things to keep in mind about this specific book:
1. Chapters are VERY short, some less than 1 page. Author covers a lot of ground. It may not be detailed enough for some, but for the most part, I though there was enough background history and examples to sufficiently introduce each topic. It is better to know something exists than to never be exposed to it, and this book will expose you to a lot!
2. Answers and followup discussions are not at the end of the chapter where I think they should be, but in a separate section toward the end of the book. I don't like this style as it requires you to use 2 bookmarks and constantly go back and forth. One star penalty for this.
3. Many of the great problems posed in the book are answered, but some are specifically left out. I think it should be up to the reader to decide how much they want to spoil the fun.
Summed up, a good book well worth getting and reading.
I love Mathematics
I am still reading the book.
It is elementar, but very interesting.
A delightful collection of mathematical puzzles
This book contains a delightful collection of mathematical puzzles in the tradition of Martin Gardner. There are Klingon Paths, Hexagonal Cats, Messages from the Stars, and Doughnut Loops. If you liked the puzzles in Pickover's "Alien IQ Test", you will like the puzzles in this book.
The book is not all numbers. There are historical anecdotes and stories about mathematicians told by the author's alter-ego, Dr. Googol. Are all mathematicians insane? The answer is not clear. However, the author describes the five strangest. Did you know that Pythagoras believed that it was sinful to eat beans?
There are a number of interesting top ten lists. As one who thinks that the proper role of mathematics is to solve the problems of the physical world, I was happy to note that Dr. Googol chose equations of physics for six of the ten most important mathematical expressions, e.g. Gauss' law and Newton's law of gravitation. Dr. Googol must have some physicist friends.
This is just one in a series of wonderful books that Dr. Pickover has written. I also recommend "The Science of Aliens, or Time: A Traveler's Guide", and his new book "A Passion for Mathematics".
Mind blowing !!
The book provides very valuable information about mathematics.The language is simple and any leyman can understand it well.The book also provides brain teasers to refresh your mind.And DEFINATELY this book will generate your interest in Mathematics.Thanks Clifford Pickover. KB.
More unusual mathematics from a master
Narrated by the outstanding and eccentric mathematician Dr. Francis Google, this book is a collection of unusual mathematics problems, from those involving very large numbers to those defined by applying operations. For example, the Leviathan number (10^666)! is used to demonstrate that it is not necessary to compute a number to learn some of the properties that it has. Sets of numbers such as apocalyptic numbers, those that involve 666, the number of the beast, appear several times. One of my favorites are the Schizophrenic numbers, defined by the formula f(n) = 10 * f(n-1)+n, f(0) = 0, which is a set of integers demonstrating a simple pattern. However, the action starts when the square roots of the numbers are taken. These roots exhibit an unusual, repeated pattern in their digits. Some incidents of mathematical history that are interesting trivia are also used. The number 365, 365, 365, 365, 365, 365 is supposedly the largest number that was ever squared in the head of a human. Other segments were based on surveys, where people answered questions such as, "Which would have had the greatest impact on the world as we know it today: `If Albert Einstein had lived another twenty years with a clear mind?', `If mathematician Srinivasa Ramanujan had lived another twenty years with a clear mind?", If Steven Hawking was not afflicted with Lou Gehrig's disease?'."A ranking of the top eight female mathematicians of all time, a listing of the five greatest scandals in mathematics history, the ten most important unsolved mathematical problems, the ten most influential mathematicians of all time, the ten most influential mathematicians alive today and the ten most difficult areas of mathematics to understand provide additional intellectual fodder. Every time I read a Pickover book, the number of ideas used as the seeds to generate the text astounds me. He always seems able to come up with new twists on old problems and sometimes new problems that set your brain moving in circular motions as you try to comprehend the consequences of the statements and attempt to follow the logical consequences of the transformations. While some of the best books keep you reading from page to page without stopping, others cause you to read a little, process a lot and then read some more. That is what this book did to me, and I am sure that it will do the same to you.
Published in the recreational mathematics e-mail newsletter, reprinted with permission.
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Product Description This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. Part I introduces some of the basic ideas of the theory: number fields, ideal classes, ideles and adeles, and zeta functions. It also contains a version of a Riemann-Roch theorem in number fields, proved by Lang in the very first version of the book in the sixties. This version can now be seen as a precursor of Arakelov theory. Part II covers class field theory, and Part III is devoted to analytic methods, including an exposition of Tate's thesis, the Brauer-Siegel theorem, and Weil's explicit formulas. This new edition contains corrections, as well as several additions to the previous edition, and the last chapter on explicit formulas has been rewritten. ... Read more
Customer Reviews (1)
Classic
Awesome text.For the more well-versed reader in Algebraic Number Theory.Great resource for a variety of topics.
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Product Description Traditionally, elementary number theory is a branch of number theory dealing with the integers, but without use of techniques from other mathematical fields. In this concise and elegant book, the author has sought to pare away all material that might be considered extraneous to a three-hour-per-week, twelve-week semester course in elementary number theory. The author presents in natural sequence the basic ideas and results of elementary number theory, laying a strong foundation for later studies in algebraic number theory and analytic number theory. The only background knowledge required of the reader is of some simple properties of the system of integers. Elementary Number Theory begins with a few preliminaries on induction principles, followed by a quick review of division algorithms. Then in the second chapter, the author touches upon the usage of divisors, the greatest (or least) common divisor (multiple), the Euclidean algorithm, and linear indeterminate equations. This foundation supports discussions in the subsequent chapters concerning: prime numbers; congruences; congruent equations; and, finally, three additional topics (comprising cryptography, Diophantine equations and Gaussian integers). Each chapter concludes with exercises that both illustrate the theory and provide practice in the techniques. Answers to even-numbered problems are given at the end of the book. ... Read moreProduct Description The ... Read more
Customer Reviews (4)
good book
This book (5th edition) cover the topics of undergraduate number theory well. The chapters are - (1)divisibility (2)congruences (3)quadratic reciprocity and quadratic forms (4)some funtions of number theory (5)some diophantine equations (6)farey fractions and irrational numbers (7)simple continued fractions (8)prime estimates and multiplicative number theory (9)algebraic numbers (10)partition funtion (11)density of sequences of integers. It also contains basic cryptography, basic group theory and basic elliptical curves in some of the chapters. The authors give notes on the end of each chapter about some research results, which I enjoy reading.
However, the author give too much hints spoling the fun of solving the problems. Eg 32-36, 40-3, 59-53, 108-36, 136-17, 312-8, and most of the problems in chapter 8. The author should put these hints at the back of the book. I suggest you look up IMO (imo.math.ca) for problems suitable for chapter 1-7 because IMO is well-knowned for its excellent number theory problems (especially 1990-3).
Overall this is an excellent book. I give it a rating of 4.5/5, I don't give it 5 because of the author give too much hints to problems instead of putting hints at back of the book.
Comprehensive
This is a fantastic book on number theory. It covers far more ground than most introductory text (comparable to Hardy and Wright in depth with much less concern for the big O). It covers material usually only available in separate texts: Rational points on elliptic curves, the partition function, and Dirchlet series.Quite readable chapters, well motivated theoretically, although the historic motivation for the subject matter comes largely in the end-of-the-chapter notes.It's an excellent refresher and reference for non-specialist who find themselves using an algorithm or formula they've forgotten(number theory now playing a role in physics and CS, like never before). It is well cross-referenced with regards to methods of proofs the can be accomplished in different section by different methods - this again making it an excellent reference.
Alas, it is pre-FLT. So you'll have to look elsewhere for that.
The best intro to the subject!
I have started my studies in Number Theory reading this book from thepreface to the last word. It is amazing! I think it is a betterintroduction to the subject than the classical Hardy and Wright...it is"more objective" and almost 100% elementary...a good high schoolreader could do well with it. The chapter of diophantine equations has somedivine proofs, very clever and very beautiful. And there is an easy proofof the irracionality of Pi. The only negative point is the existence ofsome points where the authors could be less concise and a bit clearer,stating the theorems before giving the demonstrations, instead of saying atthe end of the paragraph "we then have proved the theorem of..."Its a good book for self-study. It has many exercises.
I've found a marvellous proof...
It's a excellent book. Guide you through the simplest proofs until the great ones. If you can follow the book since start until end you'll be prepared for beginning research in this incredible world.
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"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS
Introduction to Analytic Number Theory
The reason I bought this book was to understand an elementary proof of the prime number theorem. Actually, it contains only an outline of an elementary proof. But the book introduces methods for the proof with awesome clarity. It must have been much greater if we could see the detailed elementary proof of the prime number theorem written by Apostol. He gives a reference to An Introduction to the Theory of Numbers by G.H. Hardy and E.M. Wright for the detailed proof, but the reader may be required to do unnecessary guessing (which is believed to be good in learning math, but seems to be nothing but trouble for me) to go through it.
Amazing
This book is absolutely incredible.The topics covered range from some very elementary topics on the theory of certain basic arithmetic functions, to much more advanced topics such as the theory of Dirichlet L-Functions.I have never seen a clearer explanation of the characters associated with finite Abelian groups, and the L-functions associated with Dirichlet Characters, than that provided by this book.Apostol makes even the most difficult concepts seem clear and simple.As an added bonus, the end-of-chapter exercises range from moderately difficult to almost excruciatingly so (but still very fun to work on) and give the reader excellent experience in solving problems in this field.With all this said, it should be pointed out that, as another reviewer stated, this book should not be read until the reader has already had a good deal of previous exposure to number theory.I myself would recommend the book of Hardy and Wright.As a second text on number theory, and an introduction to the aspects of number theory related to function theory and analysis, I believe that Apostol's book is the best that anyone could possibly hope for.
Exceptional readability
You normally dont talk so much about readability of a book on Math, but of all the other books on number theory that I've seen, this isquite a page turner. Strikes just the right ballance between theory, proofs and examples. As mentioned somewhere in the book, one of the aims of the author is to arouse reader's interest in number theory..which this book will certainly do..especially since its main emphasis is on prime numbers.
Unsurpassed SECOND text on number theory
The amazing positives of this book are accurately described in the other reviews so I will skip them.There is no negative, but the other reviewers assert that the reader needs no prior exposure to number theory.I completely disagree.
While this book does quickly cover elementary number theory, a reader new to this field will quickly feel lost.Without more exposure and a good prior feel for elementary number theory, the use of analytic techniques will seem ad hoc instead of following a logical pattern.By way of example, three areas covered in this book that are not part of analytic number theory and for which the reader would do better to learn from a less sophisticated text are the Fermat-Euler Theorem, Diophantine equations, and quadratic reciprocity.
Excellent texts for a first exposure to number theory are, from simpler to more difficult:
1. Elementary Number Theory by Underwood Dudley
2. An Introduction to the Theory of Numbers by Niven, Zuckerman and Montgomery
3. An Introduction to the Theory of Numbers by Hardy and Wright
Apostol's book on analytic number theory is a classic that may never be surpassed.It is a marvelous second book on number theory.
well presented, delightfully written
I think that there will be little harm if the title of the book is changed to 'Introduction to elementary number theory' instead. The author presumes that the reader has not any knowledge of number theory. As a result, materials like congruence equation, primitive roots, and quadratic reciprocity are included. Of course as the title indicates, the book focusses more on the analytic aspect. The first 2 chapters are on arithmetic functions, asymptotic formulas for averaging sums, using elementary methods like Euler-Maclaurin formula .This lay down the foundation for further discussion in later chapters, where complex analysis is involved in the investigation. Then the author explain congruence in chapter 4 and 5. Chapter 6 introduce the important concept of character. Since the purpose of this chapter is to prepare for the proof of Dirichlet's theorem and introduction of Gauss sums, the character theory is developed just to the point which is all that's needed. ( i.e. the orthogonal relation). Chapter 7 culminates on the elementary proof on Dirichlet's theorem on primes in arithmetic progression. The proof still uses L-function of course, but the estimates, like the non-vanishing of L(1) , are completely elementary and is based only on the first 2 chapters. The author then introduce primitve roots to further the theory of Dirichlet characters. Gauss sums can then be introduced. 2 proofs of quadratic reciprocity using Gauss sums are offered. The complete analytic proof, using contour integration to evaluate explicitly the quadratic Gauss sums, is a marvellous illustration of how truth about integers can be obtained by crossing into the complex domains. The book then turns in to the analyic aspect. General Dirichlet series, followed by the Riemann zeta function, L function ,are introduced. It's shown that the L- functions have meremorphic continuation to the whole complex plane by establishing the functional equation L(s)= elementary factor * L(1-s). The reader should be familiar with residue calculus to read this part. Chapter 13 may be a high point of this book, where the Prime Number Theorem is proved. Arguably, it's the Prime Number Theorem which stimulate much of the theory of complex analysis and analyic number theory. As Riemann first pointed out, the Prime Number Theorem can be proved by expressing the prime counting function as a contour integral of the Riemann zeta function, then estimate the various contours. The proof given in this book , although not exactly that envisaged by Riemann , is a variant that run quite smoothly. As is well known , a key point is that one can move the contour to the line Re(s)=1, and to do this one have to verify that zeta(s) does not vanish on Re(s)=1.The proof , due to de la vale-Poussin, is a clever application of a trigonometric identity. Unfortunately, the method does not allow one penetrate into the region 0The last Chapter is of quite differnt flavour, the so-called additive number theory. Here the author only focusses on the simplest partition function ---the unrestricted partition. However interesting phenomeon occur already at this level. The first result is Euler's pentagonal number theorem, which leads to a simple recursion formula for the partition function p(n). 3 proofs are given. The most beautiful one is no doubt a combinatorial proof due to Franklin. The third proof is through establishing the Jacobi triple product identity, which leads to lots of identites besides Euler's pentagonal number theorem. Jacobi's original proof uses his theory of theta functions, but it turns out that power series manipulaion is all that's needed. The book ends with an indication of deeper aspect of partition theory--- Ramanujan's remarkable congrence and identities ( the simplest one being p(5m+4)=0(mod 5) ). To prove these mysterious identites, the "natural"way is to plow through the theory of modular functions, which Ramanujan had left lots more theorem ( unfortunately most without proof). However an elementary proof of one these identites is outlined in the exercises. This book is well written, with enough exercises to balance the main text. Not bad for just an 'introduction'.
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Product Description A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject. ... Read more
Customer Reviews (3)
Great book for computational aspects
I bought this book for the math course I had taken having the same title. This is an excellent book, but only if you are really interested in its content. It's not a casual read, since it's graduate text. Also, a background in number theory will be of great help - being a CS major, I had a little tough time in the beginning, but things turned out just fine. As for content, it has excellent coverage of the subject, and I would highly recommend this as a reference in this subject. Remember, though, that this book deals COMPUTATIONAL aspects, for only number theory, look for other books like Ireland-Rosen.
Definitely belongs on the shelf of all number theory lovers
This book is an excellent compilation of both the theory and pseudo-code for number theoretic algorithms. The author also takes the time to prove some of the major results as background to the algorithms, in addition to sets of exercises at the end of the book. The book is too large to do a chapter by chapter review, so instead I will list the algorithms in the book that I thought were particularly useful:
1. Most of the algorithms on elliptic curves. The author reminds the reader that number-theoretical experiments resulted in the famous Swinnerton-Dyer Conjecture and the Birch Conjecture. (a) the reduction algorithm, which for a given point in the upper half plane, gives the unique point in the half plane equivalent to this point under the action of the special linear group along with the matrix that maps these two points to each other. (b) The computation of the coefficient g2 and g3 of the Weierstrass equation of an elliptic curve. (c) The computation of the Weierstrass function and its derivative. (d) Determination of the periods of an elliptic curve over the real numbers. (e) The determination of the elliptic logarithm. (f) The reduction of a general cubic (f) The Shanks-Mestre algorithm for computing the order of an elliptic curve over a finite field F(p), where p is prime and greater than 457. (g) The reduction of an elliptic curve modulo p for p > 3. (h) The reduction of an elliptic curve modulo 2 or 3. (i) Reduction of an elliptic curve over the rational numbers. (j) Determination of the rational torsion points of an elliptic curve. (k) Computation of the Hilbert class polynomials and thus a determination of the j-function of an elliptic curve.
2. A few of the algorithms on factoring. (a) The Pollard algorithm for finding non-trivial factors of composites. (The author does not give the improved algorithm due to P. Montgomery, but does give references) (b) Shanks Square Form Factorization algorithm for finding a non-trivial factor of an odd integer. (c) Lenstra's Elliptic Curve test for compositeness.
3. Primality tests (a) The Jacobi Sum Primality Test for a positive integer. (b) Goldwasser-Killian elliptic curve test for a positive integer not equal to 1 and coprime to 6.
The author gives an overview of the computer packages used for number theory, including Pari, which was written by him and his collaborators. I have not used this package, but instead use Lydia and Mathematica for most of the number theoretic computations I need to do.
Excellent!
Cohen (the world renowned expert) starts with the most basic of algorithms(i.e. Euclid & Shanks). He moves seamlessly into Linear Algebra &Polynomials (bedrocks of most CAS). Although meant to be concise, heproves, or sketches a proof of the important results. Finally, the meat ofthe book, C.A.N.T. One important problem is finding the "classnumber" (has to do with unique factorization, which we are allaccustomed to in Z). A detailed description of the continued fractionalgorithm (for finding the fundamental unit), and others made it veryenlightening. He then deals with primality testing and factoring, two veryimportant problems, the latter because of RSA. First, a description of thealgorithm, then the theory behind it. He covered everything, from TrialDivision (Dark Ages) to Pollard Rho to NFS (cutting-edge). Also includedare some useful tables. | 677.169 | 1 |
"CliffsQuickReview" course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. "CliffsQuickReview Math Word Problems" gives you a clear, concise, easy-to-use review of the basics of solving math word problems. Introducing each topic, defining key terms, and carefully walking you through each sample problem gives you insight and understanding to solving math word problems. You begin by building a strong foundation in translating expressions, inserting parentheses, and simplifying expressions. On top of that base, you can build your skills for solving word problems.This title helps you to: discover the six basic steps for solving word problems; translate English-language statements into equations and then solve them; solve geometry problems involving single and multiple shapes; work on proportion and percent problems; solve summation problems by using the Board Method; use tried-and-true methods to solve problems about money, investments, mixtures, and distance."CliffsQuickReview Math Word Problems" acts as a supplement to your textbook and to classroom lectures.
Use this reference in any way that fits your personal style for study and review - you decide what works best with your needs. Here are just a few ways you can search for information: view the chapter on common errors and how to avoid them; get a glimpse of what you'll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapter; use the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to know; test your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource Center; and, use the glossary to find key terms fast. With titles available for all the most popular high school and college courses, "CliffsQuickReview" guides are a comprehensive resource that can help you get the best possible grades.
Author Biography - Karen L. Anglin
Karen Anglin, a mathematics instructor at Blinn College in Brenham, Texas, since 1990, regularly presents workshops to teachers on best practices for teaching math word problems. She holds an MS in Statistics and a BS in Mathematics from Texas A&M University. | 677.169 | 1 |
Publisher: University of California, San Diego 2010 Number of pages: 261
Description: In this book, four basic areas of discrete mathematics are presented: Counting and Listing (Unit CL), Functions (Unit Fn), Decision Trees and Recursion (Unit DT), and Basic Concepts in Graph Theory (Unit GT). At the end of each unit is a list of Multiple Choice Questions for Review. | 677.169 | 1 |
Oxford Mathematics Study Dictionary
Barbara Lynch, R. E. Parr
This is a unique and comprehensive reference book for secondary school mathematics students. The 'Dictionary' contains an extensive list of mathematical words and their meanings, organised into topic sections typically included in mathematics syllabi around the country: arithmetic, number, complex numbers, matrices, circles, symmetry and transformations, functions and relations, coordinate geometry, differential calculus, vectors… Specific words can be found through the index; the actual entries contain appropriate definitions, theorems, formulae, diagrams and worked examples of major applications designed to make the meanings clear. | 677.169 | 1 |
The National Curriculum for Mathematics aims to ensure that all students:
Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that students develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately..
At both Key Stage 3 and Key Stage 4, the Mathematics programmes of study are centred around the five main areas of mathematics: Algebra(20%), Number (25%), Ratio, proportion and rates of change (25%), Geometry (15%) and Probability and Statistics (15%).
Key Stage 3
At Key Stage 3, the department aims to focus on developing skills that students have gained in KS1 and 2 and improving the students' thinking and problem-solving skills by integrating activities and investigations with real life problems. Students are given opportunities to work collaboratively in pairs and as members of a team, where it is hoped they will gain confidence in setting their own challenges, posing their own questions and thus extend themselves as fully as possible. Problem solving is integrated into everything they do.
Key Stage 4
At Key Stage 4, students continue to develop and build upon their mathematical knowledge gained at Key Stage 3, where all students are entered for the Edexcel GCSE examination. Due to the challenge of the new specification, we do not enter students for the GCSE examination in Year 10. Instead, the more able students will study GCSE Statistics and sit the examination at the end of Year 10 and then study Additional Maths in Year 11 and will sit GCSE Mathematics and Additional Maths at the end of Year 11. This provides our most able Year 11 students the opportunity to stretch and challenge their mathematical understanding . In addition to this, depending on the academic profile of the year group, we would also enter one or maybe two groups for GCSE Statistics with the aim of gaining two Mathematics qualifications. The assessment of Mathematics at GCSE involves three examinations (one non calculator and two calculator papers) which are sat at the end of the course. The department also offers revision workshops after College on Monday for Year 11 students only and on Thursday afternoons which are available to all Key Stage 4 students.
Intervention
Using assessment data we identify students that have fallen behind their expected levels of progress and we provide support. One of the ways is small group intervention where students are removed in groups of 3-5 from lessons and given specialist support, thereby allowing more focussed attention. Another way that support is given is during registration. Students go to intervention during the registration period and work on improving number skills. The targeted students are monitored regularly and the list is updated according to need.
Key Stage 5
Mathematics at Advanced Level is a very popular subject, where different combinations of units including Pure Mathematics, Mechanics, Statistics or Decision Mathematics (or combinations of these) are combined to gain AS or A2 Mathematics. For gifted mathematicians there is an opportunity to gain a double award at A Level in both Mathematics and Further Mathematics. Use of Mathematics is also offered at AS and A2 Level. This is a more practical approach to mathematics where the students study mathematical topics in real-life scenarios and develop confidence in using their Mathematics. Transferable skills are acquired that can be a useful support to those studying Business Studies, Geography, Biology and Psychology.
Enrichment
The Mathematics Department is committed to providing as many opportunities as it can to enrich the education of our most able students in all year groups. The different activities that we encourage our students to participate in are designed to promote their interest in Mathematics, to enhance their problem-solving abilities and to develop their ability to work as part of a team.
For several years the Mathematics Department have invited Key Stage 3 students to attend Masterclass sessions after College in a variety of topics from Fibonacci to Fractals. These always prove very popular. In the Spring term the most able Year 8 students are invited to attend 8 weeks of Saturday sessions at Surrey University where they learn about topics such as code breaking and curves. Those who attend also get the opportunity to go to a Maths lecture in London at the end of the Summer term. This year teams of students from Years 7, 8 and 9 were entered for the SHAPE Inter-school Maths competitions in November, March and June which they all thoroughly enjoyed and some were very successful. Teams from Years 12 and 13 and Years 8 and 9 took part in the UKMT Senior and Junior Team Maths Challenges. They were impressed by the standard of the competition and especially enjoyed the problem-solving and the teamwork aspect of the events.
We entered over 200 students for the UKMT Individual Maths Challenges, significant numbers of students achieved Bronze, Silver or Gold certificates and several students qualified for and participated in the prestigious follow on rounds, reserved for the top few percent of mathematicians in the country.
In September a small group of Year 11 students were selected to visit Three in Maidenhead to learn about Mathematics involved in the work place and in the data industry. The students thoroughly enjoyed the day out and have had the opportunity to be student ambassadors, feeding back to their peers in College.
In October the Maths Department took a group of 15 Year 9 students to Windsor Racecourse to investigate how Maths is used in the racing industry. The students thoroughly enjoyed their day out and appreciated seeing how the topics studied in class relate to real life.
In October, February and April we took groups of Years 10 and 11 students to Maths Inspiration events held at Wellington College, the Hexagon Theatre in Reading and Surrey University in Guildford, where they were motivated by speakers including Matt Parker and were able to learn about different and often unexpected applications of Mathematics. These events enable students to see beyond classroom Mathematics and encourage them to study Mathematics at A Level and beyond.
In March a team of our most able Year 10 students entered a Maths competition at Sandhurst school.
In July some of our most able Year 10 students were able to go to Brooklands Museum to work alongside Primary School students, helping them to build parachutes and solve problems, enabling our students to develop their leadership skills and build on their mathematical communication. | 677.169 | 1 |
The Ultimate Math Text
I have a new ambitious project for myself. I am going to create a math text that covers every subject of math from high school algebra, geometry, trigonometry, to calculus, boolean algebra, probability and statistics, linear algebra, differential equations, complex analysis, Fourier analysis, and whatever else I can think of. Oh, and I want to make it available online. For free.
I have some ideas about the structure of this text.
Derivations: I will have derivations of useful theorems, formulas, and known problem solving strategies as the main part of the text. Each will be self contained, and will have links to the prerequisite material found in other parts of the text.
Note I said "other parts of the text" and not "previous parts of the text." The text itself will not follow page numbers like ordinary books that are physically limited to them. Certain areas of mathematics can be learned without knowing about certain other areas of mathematics. For example, you can learn all about elementary linear algebra without knowing any calculus, but you do have to know how to do basic algebra. Likewise, you can learn calculus without knowing any linear algebra. The subjects are simply "independent." Now, if you want to learn how to solve systems of linear differential equations, then you have to know both calculus and linear algebra, and that will be reflected on the page for that.
Exercises and practice problems: These will consist of a few easy exercises that can serve as definition checks and concept checks. They will be followed by more comprehensive problems designed to combine multiple topics together. I would also like to include some open-ended long term type questions, but I'm not sure how to do that yet. Since this will be available online (and for free!) I would like to have some interactive animations to help illustrate some of the topics. I will include "historical problems of interest" to give the reader an idea of how these things came up in the first place, and some of the challenges that arose in the initial attempts to solve them. Finally, I will include a list of open problems in the subject, to show the reader that there is always more to be done in a given field of study.
As I develop the text, I'm sure some of this will be modified greatly, and I would appreciate input from others on this project. My ultimate goal is to provide a free resource for anybody who wants to learn any subject in math (and hopefully, eventually this format can be extended to any number of other subjects in the future.) Right now it's just me doing this, although there are others who have created amazing online resources such as the stack exchange . I don't know how long this is going to take, either, but considering I spend a good chunk of my free time doing math problems for my own amusement anyway, I may as well amuse myself to someone else's benefit.
3 Responses to "The Ultimate Math Text"
Maybe the outlines of your project could be even more clearly seen if you state what will NOT be included, such as (possibly) statistics, or statistical mechanics (which my exposure to in my junior year at Cal tipped me over the edge from being a physics major to a public health major), vectors, n-dimensional anything, quantum anything, etc. Or will this expand to contain the universe? Just asking…
Hi Alex,
Ron sent me this, and I think it is, indeed, an ambitious project; good luck. Among the fields not listed are number theory and group theory; do you plan to include these as well as the ones you listed?
Yours,
Bill
Bill,
I should absolutely put those topics in. Thanks! I am trying to figure out how to organize everything, and I feel like those are topics that can be introduced with little prerequisite material (really only basic algebra is needed), especially group theory. Well, as long as we're talking finite groups. A lot of number theory meshes nicely with other topics, so I would like to somehow develop it in parallel with calculus and linear algebra. Any input on how to do this would be amazing. | 677.169 | 1 |
AP Physics 1 & 2 Math Review
Although this is a science lesson, math will be half of what you learn in this course on top of the physics concepts so be sure to have mastered your algebra for this course. Luckily, the math in this physics course won't be as challenging as that in your mathematics classes, however some topics like trigonometry will be used ad nauseam, so it's best to be ready for the challenges ahead.
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Math Review
The SI system is a system of units based on the metric system designed to standardized measurements across the world.
The fundamental units of the SI system are the meter, kilogram, second, ampere, candela, Kelvin, and mole.
Significant figures represent a manner of showing which digits in a number are known to some level of certainty.
Scientific notation provides an efficient way to describing very large and very small numbers.
Accuracy is how close a measurement is to the actual value. Precision describes the repeatability of a measurement.
Math Review
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
Transcription: Math Review
Hi folks, and welcome back to educator.com. What I'd like to do now, is take a few minutes to go through a review of some of the math skills we are going to need to be successful in this course.0000
In our outline, we are going to talk about the metric system and the system international, or SI units, which is the unit system that we use in physics.0010
We will talk about significant figures, scientific notation, and finally, the difference between accuracy and precision, and why they are so important.0019
The objectives are: convert and estimate SI units, recognize fundamental and derived units, express numeric quantities with correct significant figures so we understand how accurate and how precise our measurements are going to be.0028
We will use scientific notations to express physical values efficiently, and finally, differentiate between accuracy and precision.0043
So, why do we need units? Well physics involves the study of prediction and analysis of real world events and real world events have quantifiable numbers.0052
In order to communicate these to other people accurately, we need to have some sort of standards. Whether it be a sound was this loud, or this quiet. We need to put a number on that so we can communicate to people. The light was this bright, or this dim.0062
How do we put numbers around that? We have to decide on a set of standards and physicists have agreed to use what is known as the system international, which is a subset of the metric system.0080
You will also sometimes see it referred to as the MKS system because the basic units include meters, kilograms, and for time, seconds0090
Let's talk about it. The system international is comprised of seven fundamental units. It is based on powers of 10 because it is a subset of the metric system and all other units are derived from these basic seven.0109
The fundamental units are the meters, the kilograms, the second, hence the MKS system, the ampere, the candela, kelvin and the mole, which you may be familiar with from chemistry.0122
So let's start with the meter. The meter is a measure of length similar to the yard in the English system. For measurements smaller than the meter, use a centimeter which is about the width of your pinky finger perhaps. A millimeter is 1/10 of that, micrometer which is often times written μm, and nanometer, nm.0137
For measurements larger than a meter, typically we use kilometers, kilometers, 1000 meters.0158
The kilogram on the other hand, is roughly equivalent to 2.2 English pounds. For measurements smaller than a kilogram, we often times use grams or milligrams. A gram is about a paperclip.0166
For measurements larger than a kilogram, we could use things like a megagram, also known as a metric ton. That is 1000 kilograms.0179
In time, and everyone is probably familiar with this one, the base unit of time is a second. And unlike the rest of the metric system, time is a little funny. It is not based on units of 10. We have, instead, things like minutes, which is 60 seconds. Hours, which is 60 minutes. Days, which is 24 hours, and years, 365¼ days. But most of us are so familiar with this, it is not really a big deal.0189
For shorter times, we go back to base 10. For example, things like milliseconds, microseconds, and nanoseconds and so on...0212
We can take and we can make other units from these fundamental units. A unit of velocity or speed, for example is a meters per second, or if we take that further, could be a kilometer per hour. In the English system it might be a mile per hour.0219
Acceleration is a meter/second2 which is really just a meter per second every second.0237
Force is measured in newtons. But a newton is really just a kilogram times a meter divided by a second, divided by a second. That is kg×m/s2.0244
These are derived units. They are comprised of combinations of those seven fundamental units.0253
As we talk about the metric system and these powers of ten, we need to look at the prefixes. 0260
If we talk about something like a kilogram, a kilogram gets the symbol k in front of the g, for gram, kilogram would be 103 grams.0267
A gigagram would be 109 grams. Micrometer would be 10-6 meters, and this table is awfully helpful for converting units.0276
Let's talk about how we convert fundamental units. If we have something like 2,480 meters and we want to convert it to kilometers, here is a nice and easy way to convert these.0282
Even if you can do it in your head, it is probably pretty good to learn this method because later on, when the units get more complicated, it will still work out for you.0302
Let's start off with what we have right now. 2,480m, and I am going to write that as a fraction so it is 2480/1.0310
I want the meters to go away, so I am going to multiply by something where I have meters in the denominator on the right hand side.0320
The units that I want are kilometers. To fill in the rest of this, what I have to realize, is that I can multiply anything by 1 and I get the same value.0328
If I multiply 3,280 by 1, I get 3,280. If I multiply 6 pigs by one, I get 6 pigs. The trick is, I can write 1 in a bunch of different ways.0341
I could write 1 as 0.5/0.5, that is equal to 1. I could write 1 as 3 apples/3 apples, that is still equal to 1.0353
So, I am going to use this math trick and I am going to multiply this by 1, but I am going to pick how I write 1 very carefully.0363
To do this, what I am going to do, is, I am trying to convert to kilometers, k. So I go over to my table of prefixes and I find k for kilo.0370
I see that it means 103, so I am going to write 103 over here on the bottom because on the bottom, there is no prefix in front of the unit.0380
If I put 103 here, I am going to put 1 on the other side. What I have now made is a ratio 1km/103m and 1km is 1000× - 103m. 0392
What I have really written here is 1 but I've written it in a special way so when I multiply this through, my meters make a ratio of 1. 2,480×1km/103 is going to leave me with 2.48 and my units that are left are kilometers.0405
2,480m is 2.48km. It is a nice, simple way of converting units. Let's try another one.0428
5.357kg. Let's convert that to grams. I start by writing what I have. 5.357kg, and I write it as a ratio over 1, 5.357kg/1 ×,I want kg to go away so I will write kg in the denominator and I want grams in the numerator.0439
Now, I go to my prefix table and look up kilo, k, again is 103. I am going to write that on this side that does not have a prefix. So that goes on the top this time and put a 1 on the bottom.0460
Now kg and kg make a ratio of 1, or cancel out. What I'm left with is 5.357×103g/1. So 5.357×103;is just going to be 5,357 grams.0476
There we go, converting fundamental units. Let's take a look at a 2 step conversion. Sometimes you have to do this in a couple of different steps.0499
We want to convert 6.4×10-6milliseconds to nanoseconds. I start by writing what we have. 6.4×10-6ms/1. I want ms to go away.0509
I put ms on the bottom and I will convert to my base unit, seconds on the top. I look up what milli, m, means and it means 10-3. Again, I write that on the side that does not have a prefix.0526
So 10-3 up there and 1 on the other side. Milliseconds would make a ratio of 1 and we are left with seconds but I do not want just seconds. I want nanoseconds, so I need to do another step.0541
Multiply by, I want seconds to go away, so I will put that in the denominator and I want units of nanoseconds.0556
Now I go look up nano, n, 10-9. That again goes on the side without a prefix. I put a 1 on the other side and when I go look back here, seconds are going to cancel out.0562
When I multiply this through, 6.4×10-6×10-3/10-9 and the units I'm left with should be nanoseconds. I come up with 6.4 nanoseconds.0578
Let's go back the other way just to verify we have got this down. We already know what the answer should be here because we just did this problem, just in the other direction. Let's verify that it works.0604
6.4ns/1 and we are going to multiply. We want nanoseconds to go away so we are going to put that on the bottom and we'll go to seconds.0616
I look up nano, which means 10-9 so I write 10-9 over here on the side that does not have a prefix. I put 1 on the other side.0628
Now I'm left with seconds, but I want milliseconds so I do it again. If I want seconds to go away, I want milliseconds so I go to my table and look up milli which is 10-3.0640
It goes on the side without a prefix, I put a 1 on the other side, and as I look here, nanoseconds cancel out, seconds will cancel out, and I should be left with milliseconds.0654
So I multiply through. 6.4×10-9/10-3 gives me 6.4×10-6 and the units I'm left with are milliseconds.0666
There is my answer. It is exactly as we expected. Let's do one with some derived units.0682
We have 32m/s and we want to convert that to something like kilometers per hour. We are going to follow the same basic path again. We are going to write 32m/s as a fraction and if I want to convert to kilometers per hour, I can convert either the meters or seconds first, it does not really matter.0690
Let's start by converting the meters into kilometers. I want meters to go away, so that goes into the denominator and I want kilometers in the numerator.0710
I go to my handy dandy table over here and find that kilo means 103. That goes on the side without a prefix and 1 goes on the other side.0719
Now I'm going to be left with kilometers per second but I want kilometers per hour. So I have another step. The seconds here in the denominator, I need those to go away so I put seconds up here and it would be nice to put hours down here but I do not really know how many seconds are in an hour, but I know how many seconds are in a minute.0730
So I will do this first. I will say that there are 60 seconds in 1 minute. Now when I look at my units, my seconds will cancel out and I'm down to kilometers per minute.0750
I had best do another step here. So if I want minutes to go away, I will put that in the numerator. I want hours and I know that there are 60 minutes in 1 hour. I check my units again and minutes make a ratio of 1 and what I should be left with for units is going to be kilometers in the numerator per hour.0761
I am all set to go do my math. 32×60×60/103should give me about 115.2 kilometers per hour. A derived unit conversion problem.0782
Let's take a look at a multi-step conversion. One last unit conversion problem. Let's see how many seconds are in one year. I have no idea but it is kind of a fun problem to take a look at.0804
Let's start with 1 year, we will make that as a ratio. I do not know how many seconds are in a year but what I do know is that there are 365¼ days in 1 year. Years make a ratio of 1 and I am left with units of days.0816
We are still not to seconds but what I happen to know is if the days go away, there are 24 hours in 1 day. Days will make a ratio of one and I am down to hours. We are still not to seconds. 0836
So in another step, I want hours to go away so I will convert to minutes. I know there are 60 minutes in 1 hour. Hours will make a ratio of 1 and I am down to minutes. We are getting closer.0853
I want minutes to go away so I will put minutes in the denominator. I want seconds and there are 60 seconds in 1 minute. Minutes will make a ratio of 1 and I am left with my units of seconds.0867
When I go through and I do all of this math, 1×365¼×24×60×60, I come out with about 3.16×107seconds. That is a lot of seconds in 1 year.0880
Another useful tool or skill is being able to estimate some of these units. For example, estimate the length of a football field. Well that is pretty big but just a rough ballpark figure is maybe about 100 meters.0901
If you are familiar with the English system, 100 yards and 100 meters are roughly the same thing. Or the mass of a student is maybe 60-70kg for a typical student. 0919
The length of a marathon is somewhere in the ballpark of about 40, 42km or the mass of a paperclip, I think we mentioned this one previously is somewhere in the ballpark of about one gram.0931
So as you walk around and see different objects see if you can take an estimate of what their mass, their length, their time is in various units. It is a useful skill.0946
Let's talk about significant figures. Significant figures represent the manner of showing which digits in a number you know with some level of certainty. 0959
For example, If you are walking along and see a garden gnome in someone's yard, significant figures can help you understand to what exactness you know the height of that garden gnome.0970
14cm, 14.3827482cm, or 14.0cm? These three numbers are all telling you slightly different things. What do they mean? Well, the key to significant figures is following these rules: Write down as many digits as you can with absolute certainty.0982
Once you have done that, go to one more decimal place, one more level of accuracy and try to take your best guess. The resulting value is your quantity in significant figures.1003
Now reading the significant figures, you start with the value in scientific notation and we will talk about that here very shortly. All non zero digits are significant. All digits that are in-between non zero digits are significant.1015
Zeros to the left of significant digits are not significant but zeros to the right of significant digits are significant.1031
As an example, how many significant digits are in the value 43.74km? Well we have 1,2,3,4 non zero digits so we must have 4 significant figures. We know at for certainty to 43.7 and that 4 is our best guess on the next level of accuracy.1040
How many significant figures are in the value of 4,302.5 grams? Well we have 4 non-zero digits and zeros between significant figures are significant so we have a total of 5 significant figures.1062
How many significant figures are in the value of .0083s? Well those are significant but zeros to the left of significant figures are not significant so here we have 2 significant figures.1081
How many significant figures are in the value 1.200×103kg? Zeros to the right of significant figures are significant so we have 1,2,3,4 significant figures.1094
Having gone through this, let's talk now about scientific notation. The need for scientific notation has to do with the tremendous variation in units, in magnitudes of these units, and their sizes.1111
For example, when we talk about length, we could talk about something like the width of a country, like the United States, which is probably a pretty big number, but we also have to talk about the thickness of human hair, all with the same base measurement of meters.1126
Even smaller, how about the transistor on the integrated circuit. Those are getting so small, it is smaller than a wavelength of light. So small that there is no optical microscope in the world that can ever see some of those features.1142
Huge ranges in orders of magnitude for these different measurements. Scientific notation can helps us express these efficiently and make it much easier to read.1154
For example, which of these numbers is easier to read. 4000000000000 or 4×1012. That is obvious, that is a lot easier to read and there is much less chance of making a mistake.1167
Or, which is easier here .0000000001m or 1×10-9m? I think it's easy to see that those are a lot more accurate and less error prone. It is almost tough to read these numbers with all of the zeros because it's so easy to lose your place in them.1182
So, using scientific notation. First off, show your value using the correct number of significant figures. Then, move the decimal point so that one significant figure is to the left of the decimal point.1200
Finally, show your number being multiplied by 10 to the appropriate power so that you get the same quantity, the same numerical value.1214
And finally let's talk about accuracy and precision. There is a difference between these two and in everyday speech, we often times use them interchangeably but in the world of physics, the world of science, There is an important distinction.1223
Accuracy is how close a measurement is to the target value. Precision, on the other hand, is how repeatable your measurements are. I like to look at these from the metaphor of target practice with a bow and arrow.1236
If we are aiming over here towards our first target and we are kind of all over the place here with our arrows and, by the way, they are nowhere close to the target and nowhere near each other, we have low accuracy and low precision which is typically not what you are after.1248
Over here, however, we have pretty high accuracy, we are starting to get close to the target but we are still not repeatable. We are accurate, close to the target but not repeatable therefore we have high accuracy and low precision.1262
Over here we are nowhere close to the target but we can hit that same spot nowhere close to the target every time. We are extremely precise, but our accuracy is off. High precision and low accuracy.1277
Finally, the nirvana of measurement, we have high accuracy, we are very near the target and we are repeatable, we have high precision. We can get near the target and we can get near the target every time.1291
With that, let's take a look at a couple more examples. Let's show this number 300,000,000 in terms of scientific notation assuming we know 3 significant figures.1303
We will find that 3 significant figures and I want to show this in scientific notation, I have one digit, one number to the left of the decimal place and I know 2 more significant figures so I write that as 3.00 to give me my 3 significant figures and I multiply it by 10 to the appropriate power which would be 1,2,3,4,5,6,7,8. 3.00×108.1316
How about showing this number, .000000... There is no way I can read this whole thing... 282 in scientific notation. Well, we have 3 significant figures so this must be 2.82×10 to some power. What power is that going to be? Well we have to move the decimal place 15 places to the right. So it would be 10-15. Isn't that a lot more efficient and easier to read?1343
How about here? Express the number .000470 in scientific notation. We have 3 significant figures, so 4.70×, and the power is going to be, 1,2,3,4 to the right, so 10-4.1387
And one last one, let's see if we can expand 1.11×107. We have 1.11 and we need to move the decimal place 7, so 1,2,3,4,5,6,7. So I would write that as 11,100,000. 11 million, 100 thousand.1408
Hopefully this gets you a good start on some of the basic math skills we are going to need here in physics especially around scientific notation, significant figures, units, converting units, and accuracy and precision. Thanks for watching educator.com, we will see you next time and make it a great day!1434
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Robert Ghrist from University of Pennsylvania wrote in to tell us about his new, free Coursera course in single-variable Calculus, which starts on Jan 7. Calculus is one of those amazing, chewy, challenging branches of math, and Ghrist's hand-drawn teaching materials look really engaging.
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include:
the introduction and use of Taylor series and approximations from the beginning; signed up for this course, rather than another introductory calculus course offered through Coursera, because Ghrist's approach seems radically different than the industry standard. His Funny Little Calculus Textbook starts off with functions, but immediately jumps to Taylor series, assuming the reader knows how to take the derivatives of simple polynomials. In other words, it seems more like a course about understanding calculus than doing calculus.
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your child will…
These
learning targets are found in the following High School California Common Core
Standards from the domains and subdomains listed below
Number and Quantity
Quantities
Use units to make sense of problems
and solutions.
Define appropriate quantities.
Choose and interpret appropriate
units.
Choose and interpret the scale in
graphs from tables.
Use appropriate quantities for
descriptive modeling.
Algebra
Seeing Structure in Expressions
Interpret expressions.
Interpret the parts of quadratic
functions.
Identify ways to re-write quadratic
functions.
Factor and complete the square to
identify key features.
Use factoring to identify zeros in
quadratic functions.
Complete the square to find maximum
and minimum values in quadratic functions.
Arithmetic with Polynomials and
Rational Expressions
Use properties of equality to
maintain equivalent systems of equations.
Solve systems of equations
graphically and algebraically.
Understand that the point of
intersection on a graph is common solution to the system.
Graph systems of linear inequalities
(linear programming).
Creating Equations
Create equations and inequalities
(including absolute value) in one variable.
Rearrange formulas to highlight
variables.
Create equations in two variables to
model relationships.
Represent constraints for equations
and inequalities (set-builder and interval notation).
Reasoning with Equations and
Inequalities
Explain steps in solving equations.
Understand that a graph of a two
variable relationship is a picture of all solutions.
Solve quadratic equations using the
best method: for example by taking square roots, completing the
square, the quadratic formula or factoring.
Functions
Interpreting Functions
Identify domain and range.
Use function notation and evaluate
functions.
Recognize patterns in sequences
which are sometimes recursive.
Recognize recursive sequences may
form linear and exponential functions.
Calculate the average rate of change
over an interval.
Graph functions and identify key
features.
Sketch the graphs and interpret the
key features when given a verbal description. | 677.169 | 1 |
Algorithms on Graphs
Algorithms on Graphs
University of California, San Diego, Higher School of Economics
Об этом курсе: If you have ever used a navigation service to find optimal route and estimate time to destination, you've used algorithms on graphs. Graphs arise in various real-world situations as there are road networks, computer networks and, most recently, social networks! If you're looking for the fastest time to get to work, cheapest way to connect set of computers into a network or efficient algorithm to automatically find communities and opinion leaders in Facebook, you're going to work with graphs and algorithms on graphs.
In this course, you will first learn what a graph is and what are some of the most important properties. Then you'll learn several ways to traverse graphs and how you can do useful things while traversing the graph in some order. We will then talk about shortest paths algorithms — from the basic ones to those which open door for 1000000 times faster algorithms used in Google Maps and other navigational services. You will use these algorithms if you choose to work on our Fast Shortest Routes industrial capstone project. We will finish with minimum spanning trees which are used to plan road, telephone and computer networks and also find applications in clustering and approximate algorithms.
Graphs arise in various real-world situations as there are road networks, computer networks and, most recently, social networks! If you're looking for the fastest time to get to work, cheapest way to connect set of computers into a network or efficient algorit 1: Decomposition of Graphs
WEEK 2
Decomposition of Graphs 2
This week we continue to study graph decomposition algorithms, but now for directed graphs. 2: Decomposition of Graphs
WEEK 3
Paths in Graphs 1
In this module you will study algorithms for finding Shortest Paths in Graphs. These algorithms have lots of applications. When you launch a navigation app on your smartphone like Google Maps or Yandex.Navi, it uses these algorithms to find you the fastest rou... 3: Paths in Graphs
WEEK 4
Paths in Graphs 2
This week we continue to study Shortest Paths in Graphs. You will learn Dijkstra's Algorithm which can be applied to find the shortest route home from work. You will also learn Bellman-Ford's algorithm which can unexpectedly be applied to choose the optimal wa... 4: Paths in Graphs
WEEK 5
Minimum Spanning Trees
In this module, we study the minimum spanning tree problem. We will cover two elegant greedy algorithms for this problem: the first one is due to Kruskal and uses the disjoint sets data structure, the second one is due to Prim and uses the priority queue data 5: Minimum Spanning Trees
WEEK 6
Advanced Shortest Paths Project (Optional)
In this module, you will learn Advanced Shortest Paths algorithms that work in practice 1000s (up to 25000) of times faster than the classical Dijkstra's algorithm on real-world road networks and social networks graphs. You will work on a Programming Project b 354 отзывам
sv
Great course, loved it! Maybe a bit easier than the previous ones in this specialization, or maybe it's just because I started using python(compared to java and c in previous courses). Anyways the course was fun. :)
AM
Great content! And explained very well. I was asked a question on graphs in my amazon interview. Wish I had taken the course earlier. Thanks! | 677.169 | 1 |
Fun Self-Discovery Tools
Basics of Parent Functions Part 1
Rating:
Description:
In this lesson, we will go over several different parent functions, what their table and graphs look like; and how to annotate their domain and range.
MAKE SURE YOU FILL OUT THE NOTES THAT GO WITH THIS LESSON! - THOSE WHO HAVE IT DONE, WILL HAVE SOME FUN TOMORROW. (Any students who don't work through this lesson will have several worksheets to do.)
We will be using these pages of notes several times as we work through Unit 1.
Additionally, you will want to keep the completed notes in your composition notebook for a reference. If you loose it, then you can always come back here and fill it out again! You will want to have this as you work on your final project in May.
You will fill out the rest of the information about these parent functions in lesson 2Parent Function Checklist Notes
Notes you received in class. If you misplaced your copy, then print it up and fill it out as you work through this lesson. You will need to cut out the graphs on the last 3 pages and tape them on top of the corresponding functions.
Basic Algebra Notes
You received these in class. You do not need to print this up if you left your notes at school. For this lesson you really only need the last page which goes through set and interval notation for domain and range. You probably could just read over it before you start the tutorial and then refer back to it as needed. | 677.169 | 1 |
ornotes1 - Introduction to Mathematical Programming AGEC...
Introduction to Mathematical Programming AGEC 7100 (Notes, Set 1) Mathematical programming problems generally involve the allocation of scarce resources to achieve some objective. Because economics is often defined in similar terms, mathematical programming models have been used extensively in economic applications, such as: 1) Maximizing the profit of a business 2) Minimizing the cost of producing a given level of output 3) Finding the "best" (least cost or least time) transportation model 4) Analyzing producer responses to policy incentives or constraints In general terms, mathematical programming models will include a set of 1) DECISION VARIABLES (variables whose values can change), 2) an OBJECTIVE FUNCTION , to be maximized or minimized by changing the level of the decision variables, and 3) a set of CONSTRAINTS that limit the decision process in some way. Operations Research involves a systematic and scientific approach to decision making. There are several different types of mathematical programming models including: Linear Programming Models, Integer Programming Models, Quadratic Programming Models, Nonlinear Programming Models, and Dynamic Programming Models. Each type of model involves different assumptions about the nature of the objective function, the decision variables, or the restrictions. Some History Although some of the mathematical theory underlying much of mathematical programming can be traced back to earlier origins, it is generally agreed that the modern approach to programming began during the World War II era. Hence, mathematical programming is a recent development in mathematics. Because of the complexity of problems during World War II and the pressing need to allocate scarce resources to various military operations in the most efficient way, teams of scientists and mathematicians from various backgrounds were brought together first in Great Britain and then in other countries.
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Because the focus of their work was on military operations, the emerging discipline became known as "operations research." The efforts of these teams were credited with the success of several important allied military campaigns. At the end of World War II, those involved in the industrial boom saw the possibility of using these military operations research methods for other purposes. Also, many of the scientists who started the work in this field during the war were interested in continuing their work. In particular, in 1947, George Dantzig developed the simplex method for solving linear programming models. Many of the standard tools of operations research were developed before the end of the 1950s. Without the advent of the "computer age" operations research applications would have remained limited in size and complexity. High speed computing has allowed us to solve larger, more complicated problems using the theories and techniques developed by Dantzig and his colleagues (much of the following material is modified from Dr. McCarl's lecture notes)
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This note was uploaded on 11/15/2011 for the course AGEC 7100 taught by Professor Duffy,p during the Fall '08 term at Auburn University. | 677.169 | 1 |
Pre-Calculus: Part 3
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PRODUCT DESCRIPTION
Starr Books offers Part 3 (of 4) of Quantum Scientific Pre-Calculus covers trigonometry. Unit 1 lays out the basics of trigonometry, including angle measures, the unit circle, the trigonometric functions, and solving right triangles. Unit 2 presents the graphs of the trigonometric functions as well as a look at some applications of the functions. In Unit 3, the focus is on trigonometric identities. The Law of Sines and the Law of Cosines are also described along with applications of these laws. (Please see thumbnails for the full table of contents and some sample pages.)
Each part of this pre-calculus series is broken into three units with 15 lessons each for a total of 45 lessons per part. The four books in the series offer 180 lessons for a full year's study. Lessons include examples and practice exercises. (Be sure to download the free Exercise Answer Key for each part of the series.) The individual lessons can be used as study guides, test preparation materials, and review of previously-learned content. The exercise sets can also be used as worksheet, quizzes, and tests8.00. | 677.169 | 1 |
Book Description
BestBook Details
Amazon Sales Rank: #1249308 in Books
Published on: 1996-09-08
Original language: English
Number of items: 1
Dimensions: 9.00" h x 1.00" w x 7.50" l, 1.15 pounds
Binding: Paperback
332 pages
Editorial Reviews
From the Publisher Best-selling author Delores Etter provides an up-to-date introduction to MATLAB. Presenting a consistent five-step problem-solving methodology, Etter describes the computational and visualization capabilities of MATLAB and illustrates the problem solving process through a variety of engineering examples and applications.
From the Back Cover BestCustomer Reviews
Most helpful customer reviews
0 of 0 people found the following review helpful. Eh, just a text book. By Melissa Garza This textbook is pretty good, I just wish it were more descriptive than it is. It expects a tad of background knowledge on your part which I did not have, so I had to be asking my professor about it constantly. This ws terrible because I can't learn well asking questions directly. On most topics however, its very explanatory and amazing. It can be great but it can make you hate yourself for not knowing things.
4 of 4 people found the following review helpful. Clear presentation - an excellent textbook By Lauren Elizabeth The layout of this text is very helpful for keeping the material straight. It is written with clarity. The real-world sample problems are interesting. I have just one concern, which kept me from giving it 5 stars: there are errors in some of the answers to practice problems. I don't see why these would not have all been carefully checked. (For reference, I have the international edition.) Nonetheless, a great text!
0 of 0 people found the following review helpful. somebody needs to write a good Matlab By Josh Widener outdated. somebody needs to write a good Matlab instructional | 677.169 | 1 |
Integration Practice for AP Calculus BC
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this file type before downloading and/or purchasing.
99 KB|3 pages
Product Description
This three-part worksheet contains practice for all types of integration methods in AP Calculus BC. The three parts are as follows:
- Practice with mental u-substitution: When the derivative of u is a constant
- True/false: Identifying and correcting common mistakes
- Multiple methods: Do the same problem using two different methods. | 677.169 | 1 |
Your Guide to Choosing A-Level Maths Study Aids
Advanced level, or A-level mathematics, is a qualification for further education. Those who have reached adulthood following a two-year course at a sixth form or college traditionally take it. A-level maths consists of six modules; the best-achieved score in each module, after necessary retakes, contributes to your final grade.
Module
Many study aids, such as "A-level Mathematics: The Complete Course for Edexcel", include multiple textbooks. Each textbook is specifically tailored for one of the six modules as indicated on the front cover. The four standard, or core modules, include Edexcel C1, Edexcel C2, Edexcel C3, and Edexcel C4; either you or your school chooses the other two modules. The core modules incorporate major topics in maths, including logarithms, differentiation, integration, and geometric and arithmetic progressions. Still, the two chosen modules, while ultimately a matter of personal preference, often include S1 and M1, or statistics and mechanics, respectively. Edexcel A-level Maths features easy to comprehend notes and step-by-step examples on all course topics covered. It also includes a series of practice questions to test reader understanding as well as reviews and exam-style questions at the end of each section. An answer guide is located at the back of the book for quick reference. In addition to the text, the Edexcel maths book also comes with a CD-ROM that contains two complete practice-exam papers.
Format
Many A-level study aids come in textbook form, while others are completely digitised. Still, others offer a mixture of the two. Choosing the right format is ultimately a matter of personal preference. Many students prefer the convenience of textbooks; these study aids can be easily taken on the go. On the other hand, computerised study aids, often in the form of CD-ROM programmes, diminish the need to carry around cumbersome books; these study aids help students reinforce their math skills through a series of interactive exercises. If planning to invest in the latter, ensure that the A-level maths study aid is compatible with your computer's operating system.
Graphics and Content
Consider A-level maths study aids that feature high-quality graphics; these books help you stay interested and on topic. Textbooks such as "Challenging Mathematics: Bridging GCSE and A-level Maths" help you fully prepare for A-level maths with content tailored for both visual and auditory learners. Written by an experienced A-level author, this student textbook suits both classroom and independent study. For ease of learning, the GCSE maths book is divided into an explanation section and a practice section. Text boxes with worked-out examples further aid in understanding. An answer guide to practice questions is located at the back of the book for quick reference. Additionally, the removable practice exams can help you test your comprehension. | 677.169 | 1 |
This project aims to develop a pen-based software tool that will assist in the process of doing mathematics by providing structured manipulation of handwritten mathematical expressions.
The tool will be used to support the teaching of the dynamics of problem solving in a way that combines the advantages of the traditional blackboard style of teaching with the flexibility and accuracy of computer software. It will provide not only a simpler way to input mathematics – by allowing the recognition of handwritten mathematics -but also enhance students' understanding of the calculational techniques and facilitate the process of doing mathematics – by providing structure editing. Some of the most important features of this tool are the accurate selection and copy of expressions, the automatic application of algebraic rules and the use of gestures to apply them, and also the combined writing of mathematics and text. These features will have a major impact on writing, doing, and presenting mathematics.
This project includes the required technical developments and also the application and testing of the tool in concrete situations, namely in mathematics and computing science courses. | 677.169 | 1 |
Helpful resources
7 Places To Check Looking For Free Homework Answers For Algebra
Most students find it hard to solve algebraic problems. This is because most of them are not "mathematic geniuses" and to them, mathematics is extremely complicated. Others are often too busy to even create enough time for their algebra homework. If you are a student facing such minor problems, algebra homework should not make you scratch your head anymore because there is a solution. Basically, there are several places that you can look for algebra homework answers. Here they are-
Yahoo Answers
Yahoo Answers is a place where people come and ask questions. There are answers for each and every field and algebra is one of them. This is one of the most convenient places to get credible answers for your algebra homework for free. It's also very reliable.
Forums
There are several online forums that are dedicated to helping students with their maths problems. It's simple to join, ask questions and then wait for an answer. They are a great place to look for assistance with algebra homework.
School Libraries
Most school libraries have relevant materials concerning algebra. They include algebra textbooks, journals, magazines etc. There are also past papers with questions and answers; all in one booklet. It's a great place to look for algebra solutions.
Bookstores
Most bookstores are well-stocked with the latest mathematical books that are well-revised and provide students with answers for their mathematical problems. These materials contain updated materials that are easier to understand and get answers from.
Math Tutors
A good teacher will always help his/her students with homework. A maths teacher is in a better position to provide you with relevant materials and also offer you guidance and the know-how of how to handle algebra problems.
Fellow Students
The fact that you are poor in solving algebraic equations doesn't necessarily mean that the student next to you is. Asking for help from these students can really help you get through with your homework. Likewise, joining study groups can be very helpful too.
Maths Websites
The internet is a great source for obtaining mathematics help. There are several websites offering algebra questions and answers and the good thing is that most of them are genuine. You don't have to spend a dime; you only need to click and get your answer fast and easy. They are also very reliable | 677.169 | 1 |
MathMath Skills & Knowledge
Skills and knowledge you may gain from your program:
Provide a core foundation across a broad range of mathematical disciplines, including Analysis, Algebra, Probability and Statistics
Learn and understand definitions and the importance of fundamental concepts such as assets, functions, vector spaces, and limits
Master the fundamentals of abstract logical reasoning including "if and only if" statements, converse, contrapositive, negation, and universal quantifiers
Learn and apply techniques for deduction to be able to prove and disprove mathematical statements and conjectures, including direct application of axioms, proof by contradiction and induction
Build upon previously studied concepts and ideas in order to generalize and for further understanding
Learn methodologies for solving various types of mathematical problems with emphasis on their limitations and understanding of the underlying concepts
Perform computations accurately and relate them back to theory
Learn about and master versatile mathematical and statistical software tools
Communicate mathematical concepts and research Math | 677.169 | 1 |
Mathematics for Computing
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
— John von Neumann
One of the hardest topics for software engineers to teach themselves is the mathematical foundations of their work. They may use sets, logical operations and graphs every day, but without some background in set theory, logic, graph theory and so on, there is a limit to how effective they can be with their tools.
This course is designed as a first formal look for practicing software engineers at the discrete math topics typically covered at the early undergrad level. It also briefly visits a handful of topics outside of discrete math that may be of interest to software engineers.
Since early in the 20th century, most math education has become exceedingly rigorous, which may have been important to the development of the field, but unfortunately an impediment to the practical, intuitive understanding sought by non-mathematicians. Our course eschews the proof-centric methodology, instead focusing on problem solving and intuition building.
Classes
Counting
Probability
Logic and proof
Induction and recurrences
Graph theory
Linear algebra crash course
Number theory for cryptography
Revision and problem solving practice
Projects and exercises
The practical component of this course predominately involves solving small math and programming problems to consolidate your understanding of the content.
Schedule and price
This course is next scheduled to run in July 2017, for 24-27 total hours of classes over evenings and weekends. Apply or enquire now to be notified when the class schedule is finalized. The total price is $1,800. | 677.169 | 1 |
Trigonometry Function Look-up Table
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I teach Algebra 2. My curriculum is divided up into 4 classes, each with 3 units. The students that take my Algebra 2 classes generally need the extra time to process the content. For my Trigonometry Unit, I have found that the Trigonometry Function Look-up Table is a successful tool. This table essentially takes the three basic trigonometric functions (sine, cosine and tangent) in right triangles and solves for all possible variables. Students fill in their own blank sheet (included). Discussions that follow involve identifying patterns in the table; deciding which function should be used for a specific problem; and, of course, why is this table more work than it really needs to be | 677.169 | 1 |
This handbook contains information on courses and components (majors, minors, streams and units) at Curtin in 2017.
Information for the previous year's courses and units is available at Courses Handbook 2016.
MATH1010 (v.1) Advanced Mathematics
The tuition pattern provides details of the types of classes and their duration. This is to be used as a guide only. Precise information is included in the unit outline.
Lecture:
1 x 2 Hours Weekly
Tutorial:
1 x 1 Hours Weekly
Workshop:
1 x 2 Hours Weekly
Equivalent(s):
7062 (v.6)
Mathematics 101
or any previous version
Anti Requisite(s):
10926 (v.5)
Mathematics 103
or any previous version
AND
MATH1004 (v.1)
Mathematics 1
or any previous version
UNIT REFERENCES, TEXTS, OUTCOMES AND ASSESSMENT DETAILS:
The most up-to-date information about unit references, texts and outcomes, will be provided in the unit outline.
Syllabus:
This unit is designed for those students who have passed WACE Mathematics 3C/3D: Specialist or equivalent with a mark >65%. Students will learn skills, to an advanced level, that are needed to solve such problems that arise in science, engineering and business related fields. To build a solid foundation, we start with logic and through it arrive at mathematical proof, including direct proof: proof by contradiction and induction. We review calculus with rigour, including functions, limits, differentiation, integration. We study linearity in the context of solving systems of linear equations, introductory linear algebra (including eigenvalues and eigenvectors), and linear difference equations and by analogy methods for solving linear differential equations. Finally, we review complex numbers, focussing on geometrical aspects.
Field of Education:
010101 Mathematics
Result Type:
Grade/Mark
Availability
Availability Information has not been provided by the respective School or Area.
Prospective students should contact the School or Area listed above for further information | 677.169 | 1 |
Maths Practice & Tests Years 9/10
$24.95
Stock: Available
Product Code: 978-1-876580-04-9
Maths Practice & Tests has a comprehensive range of exercises for extra practice arranged by topic for Years 9 and 10 as well as a series of whole tests for practice and revision including sample School Certificate tests.
Part One of Maths Practice & Tests contains a variety of challenging exercises organised by topic, covering all topics studied in Years 9 and 10. These exercises are intended to be used by students who need extra practice in a topic.
Part Two contains a series of practice tests of increasing difficulty. Each has two parts:
Part A consists of short answer questions,
Part B includes multi-part questions requiring longer answers. In addition, there are two sample School Certificate tests.
As well as testing the student's content knowledge over a range of topics, the tests are valuable in helping students deal with the procedures, format and time limits of formal tests.
economical - includes a lot of material and practice for a very affordable price
versatile - can be used at school or at home; can be used by a whole class or individuals with particular needs
practice - for School Certificate tests; for Year 9 scholarship and selective school entry examinations
Maths Practice & Tests can be used:
in the classroom as a source of extra material
as a source of homework exercises
George Fisher is an experienced maths teacher who has taught at both state and private schools and is the author of a number of maths texts for schools. He is currently teaching at Taylor College.
Maths Practice & Tests for Years 9 - 10 is complemented by Maths Practice & Tests for Years 7 – 8 which contains a comprehensive range of exercises and practice examination papers for each topic in Years 7 and 8. | 677.169 | 1 |
Abstract:"Converts" to geometric algebra often find it difficult to return to traditional methods after experiencing its advantages. It provides a single, consistent language for representing a wide variety of geometric entities and operations; it is practical and efficient to calculate with; it often provides the most compact and elegant formulations of problems. And yet the penetration of geometric algebra in the undergraduate mathematical curriculum (to say nothing of the high school one) has up until now been modest. In this workshop we want to explore this situation by sharing our experiences and visions for the future. We invite contributions including but not limited to the following topics:
• The use of geometric algebra to teach elementary euclidean (and/or noneuclidean) geometry.
• Comparison of geometric algebra with traditional vector + linear algebra approach for "doing geometry".
• Comparison of models of geometric algebra (vector, homogeneous, conformal) with regard to their appropriateness for the general curriculum.
• Case studies of how particular problem settings can be handled with geometric algebra in a pedagogically sound way.
• Recommendations and strategies for introducing geometric algebra into the curriculum: challenges, concept-building, software support, etc.
• How can geometric algebra be adapted for the high school curriculum?
Registration: You can register for the workshop when you register online for ICCA 10. Please provide a title and an abstract for your presentation in the space provided there. Or if you have already registered and wish to participate in the workshop, contact the organizers directly at the email addresses provided above. The organizers will contact you to confirm that your contribution fits into the framework of the workshop. Deadline is June 22, 2014. | 677.169 | 1 |
SECTIONA1A Brief Review of AlgebraThere are many techniques from elementary algebra that are needed in calculus. Thisappendix contains a review of such topics, and we begin by examining numberingsystems.An integeris a "whole number," either positive or negative. For example, 1, 2,875, ±15, ±83, and 0 are integers, while , 8.71, and are not.Arational numberis a number that can be expressed as the quotient of twointegers, where b±0. For example, and are rational numbers, as areEvery integer is a rational number since it can be expressed as itself divided by 1.When expressed in decimal form, rational numbers are either terminating or in±nitelyrepeating decimals. For example,A number that cannot be expressed as the quotient of two integers is called anirrational number.For example,are irrational numbers.The rational numbers and irrational numbers form the real numbersand can bevisualized geometrically as points on a number lineas illustrated in Figure A.1.FIGURE A.1The number line.If aand bare real numbers and ais to the right of bon the number line, we say thatais greater thanband write a.b.If ais to the left of b, we say that ais lessthanband write a,b(Figure A.2). For example,5²2±12³0and±8.2³±2.4FIGURE A.2Inequalities.aba >bbaa <bInequalities–5–4–3–2–1054321π–2.5–√322±2²1.41421356and´²3.1415926558µ0.62513µ0.33 . . .and1311µ1.181818 . . .±612µ±132and0.25µ25100µ14±4785,23,ab±223The Real Numbers642❘APPENDIX A❘Algebra Review❘A-2hof51918_app_641_670 10/17/05 3:28 PM Page 642
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A-3❘SECTION A1❘A Brief Review of Algebra❘643Moreover,as you can see by noting thatThe symbol±stands for greater than or equal to,and the symbol²stands forless than or equal to.Thus, for example,³3±³4³33³4²³3and³44A set of real numbers that can be represented on the number line by a line segmentis called an interval.Inequalities can be used to describe intervals. For example, theinterval a²x´bconsists of all real numbers xthat are between aand b, includingabut excluding b. This interval is shown in Figure A.3. The numbers aand bareknown as the endpointsof the interval. The square bracket at aindicates that aisincluded in the interval, while the rounded bracket at bindicates that bis excluded.Intervals may be ±nite or in±nite in extent and may or may not contain eitherendpoint. The possibilities (including customary notation and terminology) are illus-trated in Figure A.4.Intervals67µ4856and78µ495667´78abxFIGURE A.3The intervala²x´b.abbxxxxClosed interval: a≤x≤bOpen interval: a<x<bHalf-open intervala≤x<bInfinite intervalx≥aInfinite intervalx>aInfinite intervalx≤bInfinite intervalx<bHalf-open intervala<x≤baababbxxxxaabEXAMPLEA1.1Use inequalities to describe these intervals.
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This note was uploaded on 01/21/2012 for the course MA 22300 taught by Professor Staff during the Spring '08 term at Purdue. | 677.169 | 1 |
Maple is a powerful symbolic and numeric computation program which incorporates a large library of mathematical functions — over 2,000 in all — including those for equation solving and integration at all mathematical levels.
Maple provides both 2D and 3D graphics, and can differentiate, integrate, and solve equations, as well as manipulate matrices and perform a host of other mathematical operations.
There are various places on internet where you can look for help on Maple. Here there are some of them:
MATLAB is a computer program for numerical computation. It began as a "MATrix LABoratory" program, intended to provide interactive access to the libraries Linpack and Eispack. It has since grown well beyond these libraries, to become a powerful tool for visualization, programming, research, engineering, and communication.
Matlab's strengths include cutting edge algorithms, enormous data handling abilities, and powerful programming tools. Matlab is not designed for symbolic computation, but it makes up for this weakness by allowing the user to directly link to Maple. The interface is mostly text-based, which may be disconcerting for some users.
A comprehensive source of help on MATLAB can be found at Mathworks. To get started with MATLAB it might be useful for you to check the ACS tutorial.
Xess is a full-functioned engineering and science spreadsheet program which contains full Xwindow support in a spreadsheet, plus special built-in functions for scientific computation, such as matrix operations and Fourier transforms. The program also supports high quality graphics reports, C and Fortran programming interfaces, and more.
There is a sample grade sheet available that can be saved as a .xs4 file and then opened in Xess. You can also see how the file looks without opening the file in Xess. More information on Xess you can access by typing man xess in a UNIX window. Copies of The Xess User's Guide are available on reserve in the Folsom Library, as well as via the ACS Help Desk in the VCC.
LaTeX is a document preparation system built on TeX, a typesetting language designed especially for math and science. LaTeX is extremely popular in the scientific and academic communities, and it is used extensively in industry. Because LaTeX is available for just about any type of computer and because LaTeX files are ASCII, scientists send their papers electronically to colleagues around the world in the form of LaTeX input.
Most LaTeX commands are "high-level" (such as chapter and section) and specify the logical structure of a document. The author rarely needs to be concerned with the details of document layout; the document class determines how the document will be formatted. LaTeX provides several standard document classes from which to choose. | 677.169 | 1 |
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Mark Daniels
Mark Daniels
College of Natural Sciences, Department of Mathematics, UTeach Natural Sciences
Discovery Precalculus: A Creative and Connected Approach
Students in this course will learn to deepen and extend their knowledge of functions, graphs, and equations from their high school algebra and geometry courses so they can successfully work with the concepts in a rigorous university-level calculus course. This course engages students in the "doing" of mathematics, emphasizing conceptual understanding of mathematical definitions and student development of logical arguments in support of solutions. Major emphasis is placed on why the mathematics topics covered work within the discipline, as opposed to simply the mechanics of the mathematics.
Project Highlights
Inquiry-Based Learning (IBL) pedagogy, which engages students in the educational process and stresses the importance of the active construction of learning
Demonstrates mathematics as a creative endeavor, which is reinforced through connecting themes and processes to the field of visual art
Emphasizes the "big picture" connections between important mathematical concepts | 677.169 | 1 |
Introduction to Algebra
Second Edition
Peter J. Cameron
Description
Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics.
Introduction to Algebra
Second Edition
Peter J. Cameron
Author Information
Peter Cameron has taught mathematics at Oxford University and Queen Mary, University of London, with shorter spells at other institutions. He has received the Junior Whitehead Prize of the London Mathematical Society, and the Euler Medal of the Institute of Combinatorics and its Applications, and is currently chair of the British Combinatorial Committee.
Introduction to Algebra
Second Edition
Peter J. Cameron
Reviews and Awards
"This clearly written exposition is accompanied by well-chosen exercises. This book should be useful as a textbook for most undergraduates courses on algebra"--EMS Newsletter
"Altogether this is a concise but solid introduction into algebra and linear algebra."Internationale Mathematische Nachricheten | 677.169 | 1 |
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Show More algebra, ordinary and partial differential equations, and complex variables. The emphasis of the book is a working, systematic understanding of classical techniques in a modern context. Along the way, students are exposed to models from a variety of disciplines. It is hoped that this course will prepare students for further study of modern techniques and in-depth modeling in their own specific discipline | 677.169 | 1 |
Saturday, April 15, 2017
Here is question 3 from the January 2017 New York Regents Exam in Algebra I (Common Core),
This question shocked me when I first saw it.
To get a taste of what such a correlation coefficient is, I suggest you take a look at Wolfram. New York State's EngageNY has an "introduction" to correlation coefficients (find it here) that says "It is not necessary for students to compute the correlation coefficient by hand, but if they want to know how this is done, you can share the formula" and then shows
It should be noted that this formula the bounds of summation and variable subscripts are omitted, so it is a meaningful formula only for those "in the know", and I suspect that very few Algebra I students fit that description.
Is this a case of presenting a "magic button" on a calculator as a key to answering a complex question? Is that how math should be taught?
New York's modules include the following:
Take note of the phrase "use technology". That essentially means the student should plug in the numbers, hit the necessary buttons, and find a result. It is more like following a recipe, and most people recognize that a recipe becomes unnecessary after it has been followed a number of times: not because it is not being followed and not because it is understood, but because it is remembered.
Here is a question from the August 2016 Algebra I Regents;
I would suspect that after enough repetitions of the recipe some students might have caught on and realized that the choices offered make this question a bit easier than it would have been had the data been a bit different and the choices involved some seemingly random 4-digit decimals. Perhaps that might be why questions such as this have, over the years, been categorized as "cookbook" problems.
The next question here is from the Algebra I Regents exam from August 2015:
There is absolutely no way any student will successfully answer this question without following a recipe on their graphic calculator. I do not know why NYS left all the space on the page as all that is asked of the student is to write down one equation and then a two digit decimal together with one word.
Here is a similar question from the January 2015 Algebra I exam:
The big difference here is the 60% increase in time entering the data (16 values instead of 10) and the explanation of part (b). But again, it's enter two columns of data, hit a couple more keys on the calculator, and read off a result.
A similar process is involved in the next question, the big difference is that it asks the student to pick an item from a different line in the calculator's display:
Do all these questions belong in Algebra I?
Are these items here only because of the lobbying efforts of the companies that sell the graphic calculators?
I would much rather see students get the flavor of least squares analysis by using FREE software such as GeoGebra. For an example, check out the Least Squares Demonstration here.
While correlation coefficient seems to be an easy testable item (when proper calculator is present), it should be recognized that it is merely a measurement of how well a regression line actually "fits" the data. The true mathematical questions begin with the regression line itself: what it is, why it is, why it is useful, when is it useful, how we know it is the "best" fit, what do we do when this is not useful, and many others. For a sense of the current state of regression analysis, just visit Wikipedia.
Please take note: correlation coefficients and a slew of its tag-a-longs could fit in high school mathematics, but not in Algebra I. Dynamic geometric approaches to concepts such as least squares could be well developed in an Algebra I course, using software such as Desmos or Geogebra or other equivalent packages.
The biggest problems with high school mathematics occur when students are expected to know and do things mindlessly. Recipes need to be avoided. Magic buttons on calculators need to be avoided like poinson needs to be avoided.
The true value and meaning of the quadratic formula comes only to one who tires of completing the square. Completing the square obtains its true value and meaning when one tires of trying to find factors (especially when they do not exist!). The real meaning of factoring comes to one who is fed up with constantly having to guess and check. There is a hierarchy to the knowledge and skills of mathematics. Jumping too quickly to a higher level does a disservice to students.
Imagine what would happen if we limited single variable quadratics to finding intersections with the x-axis on a graphic calculator, and skipped over everything mentioned in the previous paragraph! It makes just as much sense as tossing regression analysis into Algebra I only because it can be done on a graphic calculator. Jumping too quickly to a higher level does a disservice to students, especially when that jump takes place largely do to the mere availability of a handheld calculator.
Tuesday, March 28, 2017
Here is a very simple dynamic graph, showing a point sliding down a radius in the same amount of time that it takes the circle to do one rotation around its center. Simple to see and explain.
It is the explanation part that makes this valuable. No matter what grade level, it could be used. From simple use as an introduction to the words circle, radius, rotation, and speed (imagine if children started learning these words in kindergarten) to a PreCalculus class being asked to generate parametric equations so that they could continue the graph on their graphic calculators.
Sunday, March 26, 2017
Here is a sketch that could basically be used with any grade, from a visual with elementary students, to a "can we make it ourselves" with middle school students, to a model for exploration for upper levels.
With an elementary class, I would leave out all the text, and create a step-by-step show, from first circle to tangent line to second circle to midpoint to trace, but not using sophisticated language. With middle school students I would use the basic geometric language and do a step-by-step as well. Upper students who are familiar with Geogebra could be shown the graphic and asked to recreate it. Those unfamiliar could be guided through it. Precalculus students could be challenged to determine an equation that could be graphed on a graphic calculator.
Adjustments to the file are easily made.
The main point is that this technology should not just be used as crutch with old curricula, but should also be used as an avenue for new approaches to mathematics education.
Tuesday, March 7, 2017
It is not necessary for students to compute the correlation coefficient by hand, but if they want to know how this is
done, you can share the formula for the correlation coefficient given below.
It demonstrates, in a nutshell, a massive hypocrisy in the implementation of Common Core math here in NY. What starts out, in the lower grades, as a powerful attempt to make students consciously aware of what they are doing, has morphed into the old and disastrous "give them a formula or a calculator and they will be happy." When doing basic arithmetic the emphasis on understanding by expecting multiple methods sometimes seems like overdoing it. Here, understanding is just tossed aside.
What really bugs me is that using a calculator to compute the Pearson correlation coefficient bypasses any attempt to teach understanding. No student will come out of this with any knowledge other than "this is what they told me in school". That is exactly the situation that "teaching for understanding" was supposed to avoid.
Why not let students actually get the opportunity to explore topics such as least-squares regression using software such as GeoGebra? Here is a small visual example of what GeoGebra can do. The labeled points can be dragged and the sliders control slope and y-intercept of the line. The best fit is the line that gets the sum of the squares as small as possible.
We should keep in mind that there is no need to have a line of best fit if we can see all the data plotted in front of us. A best fit line can help us if it can be understood as a model of prediction. If that is the goal, then it would make sense to have some strong connection between the modelling line and the correlation coefficient. Check out what New York State students experience and see if that connection is solidly made.
Wednesday, March 1, 2017
The January 2017 New York regents exam in Algebra I (Common Core) contains a question with a model response that I do not get.
Here are the directions:
Here is the question and the model response:
The student has shown in 2 steps how to convert one equation into slope-intercept form, and you can see that the equation ends up identical to the first equation in the question. In answer to "Is he correct?" the student answers "No." In explanation, he states that the two equations are for the same line.
The model response scoring states: Score 1: The student wrote an incomplete explanation.
Mathematically, this model response nailed it. For some reason it only gets half credit. Was it not verbose enough? Is there a minimum number of words required?
Tuesday, February 28, 2017
You might ask, so what about these words? In answer, I can state with conviction that the knowledge of these terms, their meanings, and their usages, was key in the development of my personal understanding of our language.
Even though I spent years teaching and learning mathematics, I still use the concepts of adjective and noun when discussing fractions. Many of you might remember the terms "numerator" and "denominator", which are fancy words for the ideas of "how many?" (adjective) and "of what?" (noun).
I found that atrocious. How can one even discuss the "art" of language without involving its grammatical structure?
Basing an entire curriculum on grammar would be a waste of time, just as doing nothing but arithmetic under the name of mathematics would be useless drudgery. But to totally ignore grammar amounts to designing a skyscraper while ignoring the hidden structure that holds it up.
Here is question from the New York regents Comprehensive Exam in English from August 1978:
How would students react in this day and age?
I guess it won't matter too much, as long as the gun is around to take care of the grizzlies. | 677.169 | 1 |
many branches of physics, mathematics, and engineering, solving a problem means solving a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The emphasis in this text isMore...
In many branches of physics, mathematics, and engineering, solving a problem means solving a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The emphasis in this text is on how to find and use the symmetries; this is supported by many examples and more than 100 exercises. This book will form an introduction accessible to beginning graduate students in physics, applied mathematics, and engineering. Advanced graduate students and researchers in these disciplines will find the book a valuable reference.
Malcolm MacCallum is Director of the Heilbronn Institute at the University of Bristol and is President of the International Society on General Relativity and Gravitation.
Preface
Introduction
Ordinary differential equations
Point transformations and their generators
One-parameter groups of point transformations and their infinitesimal generators
Transformation laws and normal forms of generators
Extensions of transformations and their generators
Multiple-parameter groups of transformations and their generators
Exercises
Lie point symmetries of ordinary differential equations: the basic definitions and properties
The definition of a symmetry: first formulation
Ordinary differential equations and linear partial differential equations of first order
The definition of a symmetry: second formulation
Summary
Exercises
How to find the Lie point symmetries of an ordinary differential equation
Remarks on the general procedure
The atypical case: first order differential equations
Second order differential equations
Higher order differential equations. The general nth order linear equation
Exercises
How to use Lie point symmetries: differential equations with one symmetry
First order differential equations
Higher order differential equations
Exercises
Some basic properties of Lie algebras
The generators of multiple-parameter groups and their Lie algebras
Examples of Lie algebras
Subgroups and subalgebras
Realizations of Lie algebras. Invariants and differential invariants
Nth order differential equations with multiple-parameter symmetry groups: an outlook
Exercises
How to use Lie point symmetries: second order differential equations admitting a G[subscript 2]
A classification of the possible subcases, and ways one might proceed
The first integration strategy: normal forms of generators in the space of variables
The second integration strategy: normal forms of generators in the space of first integrals
Summary: Recipe for the integration of second order differential equations admitting a group G[subscript 2]
Examples
Exercises
Second order differential equations admitting more than two Lie point symmetries
The problem: groups that do not contain a G[subscript 2]
How to solve differential equations that admit a G[subscript 3] IX
Example
Exercises
Higher order differential equations admitting more than one Lie point symmetry
The problem: some general remarks
First integration strategy: normal forms of generators in the space(s) of variables
Second integration strategy: normal forms of generators in the space of first integrals. Lie's theorem
Third integration strategy: differential invariants
Examples
Exercises
Systems of second order differential equations
The corresponding linear partial differential equation of first order and the symmetry conditions
Example: the Kepler problem
Systems possessing a Lagrangian: symmetries and conservation laws
Exercises
Symmetries more general than Lie point symmetries
Why generalize point transformations and symmetries?
How to generalize point transformations and symmetries
Contact transformations
How to find and use contact symmetries of an ordinary differential equation
Exercises
Dynamical symmetries: the basic definitions and properties
What is a dynamical symmetry?
Examples of dynamical symmetries
The structure of the set of dynamical symmetries
Exercises
How to find and use dynamical symmetries for systems possessing a Lagrangian | 677.169 | 1 |
200 Addition Worksheets with 3-Digit, 1-Digit Addends: Math
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