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ary algebra, branch of mathematics that deals with the general properties of numbers and the relations between them. Algebra is fundamental not only to all further mathematics and statistics but to the natural sciences, computer science, economics, and business. Along with writing, it is a cornerstone of modern scientific and technological civilization. Earlier civilizations—Babylonian, Greek, Indian, Chinese, and Islamic—all contributed in important ways to the development of elementary algebra. It was left for Renaissance Europe, though, to develop an efficient system for representing all real numbers and a symbolism for representing unknowns, relations between them, and operations.
Real and complex numbers, constants, and variables—collectively known as algebraic quantities.
Rules of operation for such quantities.
Geometric representations of such quantities.
Formation of expressions involving algebraic quantities.
Rules for manipulating such expressions.
Formation of sentences, also called equations, involving algebraic expressions.
Solution of equations and systems of equations.
Algebraic quantities
The principal distinguishing characteristic of algebra is the use of simple symbols to represent numerical quantities and mathematical operations. Following a system that originated with the 17th-century French thinker René Descartes, letters near the beginning of the alphabet (a, b, c,…) typically represent known, but arbitrary, numbers in a problem, while letters near the end of the alphabet, especially x, y, and z, represent unknown quantities, or variables. The + and − signs indicate addition and subtraction of these quantities, but multiplication is simply indicated by adjacent letters. Thus, ax represents the product of a by x. This simple expression can be interpreted, for example, as the interest earned in one year by a sum of a dollars invested at an annual rate of x. It can also be interpreted as the distance traveled in a hours by a car moving at x miles per hour. Such flexibility of representation is what gives algebra its great utility.
Another feature that has greatly increased the range of algebraic applications is the geometric representation of algebraic quantities. For instance, to represent the real numbers, a straight line is imagined that is infinite in both directions. An arbitrary point O can be chosen as the origin, representing the number 0, and another arbitrary point U chosen to the right of O. The segment OU (or the point U) then represents the unit length, or the number 1. The rest of the positive numbers correspond to multiples of this unit length—so that 2, for example, is represented by a segment OV, twice as long as OU and extended in the same direction. Similarly, the negative real numbers extend to the left of O. A straight line whose points are thus identified with the real numbers is called a number line. Many earlier mathematicians realized there was a relationship between all points on a straight line and all real numbers, but it was the German mathematician Richard Dedekind who made this explicit as a postulate in his Continuity and Irrational Numbers (1872).
In the Cartesian coordinate system (named for Descartes) of analytic geometry, one horizontal number line (usually called the x-axis) and one vertical number line (the y-axis) intersect at right angles at their common origin to provide coordinates for each point in the plane. For example, the point on a vertical line through some particular x on the x-axis and on the horizontal line through some y on the y-axis is represented by the pair of real numbers (x, y). A similar geometric representation (see the figure) exists for the complex numbers, where the horizontal axis corresponds to the real numbers and the vertical axis corresponds to the imaginary numbers (where the imaginary unit i is equal to the square root of −1). The algebraic form of complex numbers is x + iy, where x represents the real part and iy the imaginary part.
This pairing of space and number gives a means of pairing algebraic expressions, or functions, in a single variable with geometric objects in the plane, such as straight lines and circles. The result of this pairing may be thought of as the graph (see the figure) of the expression for different values of the variable. |
Prealgebra - 5th edition
Summary: Prealgebra, 5/e, is a consumable worktext that helps students make the transition from the concrete world of arithmetic to the symbolic world of algebra. The Aufmann team achieves this by introducing variables in Chapter 1 and integrating them throughout the text. This text's strength lies in the Aufmann Interactive Method, which enables students to work with math concepts as they're being introduced. Each set of matched-pair examples is organized around an objective...show more and includes a worked example and a You Try It example for students. In addition, the program emphasizes AMATYC standards, with a special focus on real-sourced data. The Fifth Edition incorporates the hallmarks that make Aufmann developmental texts ideal for students and instructors: an interactive approach in an objective-based framework; a clear writing style; and an emphasis on problem solving strategies, offering guided learning for both lecture-based and self-paced courses. The authors introduce two new exercises designed to foster conceptual understanding: Interactive Exercises and Think About It exercises This listing is for a paperback book not a DVD set. This is an AIE copy and includes answers. Perfect condition. Great dicounted text. Ships same or next business day. NO INTERN...show moreATIONAL ORDERS PLEASE. ...show less
$20218956883 |
Paul Abbott, a faculty member in the School of Physics at The University of Western Australia, wants to teach his students a tool that they can use to tackle real-world problems—not only in his physics and mathematics courses, but throughout their studies and into their professional careers. For him, Mathematica is that tool.
Abbott uses Mathematica to build all of his courseware, from lecture slide shows and assignments to quizzes and exams. His students use Mathematica to visualize surfaces, explore concepts using interactive examples, hypothesize results, and check their work. He says Mathematica is an "immersive environment" that helps his students reach a higher level of understanding.
After talking with community college educators recently at the national AMATYC conference in Boston, I'm reminded, once again, that time is the most valuable commodity in a teaching setting.
It takes time to plan a lesson for students, time to refine this lesson such that it has the most impact, and time to plan what technology will accompany a lesson and how to guide students through the process of using that technology. Any wrinkles with using the technology will greatly distract students from the course concept at hand.
As a concrete example, community college faculty are used to explaining to students the four menus, and roughly eight steps, to visualize a function and its derivative using a calculator, which is a significant time investment. (The examples are from my own TI calculator I've kept all these years.)
It seems that most community college educators know how powerful and useful Mathematica can be to support lectures or individual student projects. But this year, more than anything else, we talked about how Mathematica 8′s new free-form input will reduce or eliminate a teacher's preparation time and will help students who are new users access Mathematica's powerful functionality immediately.
"We have a real problem with math education right now," is how Conrad Wolfram starts his TEDGlobal 2010 talk in Oxford, in which he reasons through what's wrong, why, and how we can fix it.
Central to Conrad's argument is the role of calculating—that for the mainstream subject it's not an end in itself, but a means to an end, and therefore should be wholeheartedly computer based. As he puts it, "Math ≠ Calculating, Math >> Calculating".
He's optimistic about what's possible. "We have a unique opportunity to make math both more practical and more conceptual simultaneously," and to get people to "really feel math".
It's back-to-school time in the U.S., and we're starting our trips to meet with educators ranging from the high school to post-graduate level. Many schools will be hearing about Mathematica for the first time, while others have requested specialized training to expand Mathematica usage in their work and in the classroom. Several schools are taking advantage of a program created in response to a recent domestic focus on science, technology, engineering, and mathematics (STEM) education called the STEM Education Initiative.
When I attended this year's National Council of Teachers of Mathematics conference in San Diego, I met many "math coaches". All teachers are coaches of their classrooms, but I'm referring to teachers whose titles are "coach". These coaches spend time with at-risk or struggling students, trying to help the students gain further success in their education.
Coaches spend time working one on one or in small groups with these students to help them achieve a higher level of knowledge. They are looking for interactive ways to get students excited about all of their homework as well as to prepare them for standardized tests—especially in math—in new ways, relevant to the students and the topics.
However, very few of these math coaches have computer programming backgrounds. Quite often, their main technology tool has been the basic calculator. These coaches were interested in a tool that would not cost them hours of time to learn.
Mathematica and Wolfram|Alpha are revolutionizing education. Teachers and students are pretty pumped and starting to envision the possibilities. That was the chatter at our Joint Mathematics Meetings (JMM) 2010 booth in San Francisco this month, as we listened to Mathematica enthusiasts voice their opinions on technology and education.
There are lots of things going on at Wolfram Research these days. October 22–24 is our annual International Mathematica User Conference, and October 21 is the first-ever Wolfram|Alpha Homework Day! Homework Day is a groundbreaking, marathon live interactive web event that brings together students, parents, and educators from across the United States to solve their toughest assignments and explore the power of using Wolfram|Alpha for school, college, and beyond. You can read more about it in the Wolfram|Alpha Blog post.
Mathematica and Wolfram|Alpha are great resources for both teachers and students. Using the two together is a good way to explore topics in more depth. This video shows a few examples of how you can utilize Mathematica and Wolfram|Alpha in your own classroom.
As a fan of cars, I find that even when I am perfectly happy with my vehicle, I check car lots and classifieds and car-dealer ads. This began in college when I had to drive a car that, let me just say, was not a high-performance vehicle. It got me from point A to point B most of the time, but it always needed work and I never knew when it would break down and leave me stranded. I always dreamed of driving a really nice automobile.
Working at Wolfram Research, I have many times heard the analogy of Mathematica as a high-performance computational engine. The high-performance phrase takes me back to cars and I wondered, what kind of car would Mathematica be? In my mind, it would clearly be something very fast that has a great engine under the hood but is easy to drive. A car I would've liked to have had in college. Then I thought about how many students have access to Mathematica, which is much like a college student driving a brand-new sports car. It has more than enough power for most applications, and using it can make you look good.
I just visited Washington, DC, and I find myself returning with a renewed sense of enthusiasm. Did this have something to do with the progression from mild rain to what could be the first sunny, summer days of the year? Or seeing the nation's capitol in person?
I've attended five NCTM conferences over my ten years with Wolfram Research, and I always find the teachers' enthusiasm contagious. They constantly look for new ways to inspire their students, while at the same time building a strong foundation in mathematics. Teachers usually have clever ways to share information and spend countless hours trying new ideas and new presentation styles.
Mathematica has long been used by university-level faculty and researchers for work in math, physics, engineering, and many other fields. Good at everything from creating class documents and lab assignments to analyzing and visualizing data collected during experiments, Mathematica has become the software of choice for millions of academic researchers, faculty, and students because it is an all-in-one system that combines powerful computing and visualization capabilities with sophisticated documentation and presentation tools.
But in my years of working with universities as Wolfram Research's Academic Program Manager, I've come to realize that many students who will become future high school teachers aren't using Mathematica in their math and science education classes. Why is that? Some have told me that they heard somewhere along the line that Mathematica was too difficult to learn and use. Others had assumed that it was too powerful for their needs, or not completely applicable to the subjects they would be teaching. But those that do take a closer look at Mathematica are usually amazed by what they see. |
The new 9th edition of Elementary Differential Equations and Boundary Value Problems, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. The 9th edition includes new problems and examples, as well as expanded explanations to help motivate students.
The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for reading the book is a working knowledge of calculus, gained from a normal two- or three-semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
Chapter 4 Higher Order Linear Equations
4.1 General Theory of nth Order Linear Equations
4.2 Homogeneous Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients
4.4 The Method of Variation of Parameters
Chapter 5 Series Solutions of Second Order Linear Equations
5.1 Review of Power Series
5.2 Series Solutions Near an Ordinary Point, Part I
5.3 Series Solutions Near an Ordinary Point, Part II
5.4 Euler Equations; Regular Singular Points
5.5 Series Solutions Near a Regular Singular Point, Part I
5.6 Series Solutions Near a Regular Singular Point, Part II
5.7 Bessel's Equation
A Flexible approach to content. Self-contained chapters allow instructors to customize the selection, order, and depth of chapters.
A Flexible approach to technology. Boyce/DiPrima is adaptable to courses having various levels of computer involvement, ranging from little or none to intensive. More than 450 problems are marked with a technology icon to indicate those that are considered to be technology intensive.
Sound and accurate exposition of theory. Special attention is made to methods of solution, analysis, and approximation.
Applied Problems. Many problems ask the student not only to solve a differential equation but also to draw conclusions from the solution, reflecting the usual situation in scientific or engineering applications.
Historical footnotes. The footnotes allow the student to trace the development of the discipline and identify outstanding individual contributions. |
NumericalMethods in Engineering with MATLAB® is a text for engineering students and a reference for practicing engineers. The choice of numericalmethods was based on their relevance to engineering problems. Every method is discussed thoroughly and illustrated with problems involving both hand computation and programming. MATLAB M-files accompany each method and are available on the book website. This code is made simple and easy to understand by avoiding complex book-keeping schemes, while maintaining the essential features of the method.
This book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation.
This is a unique monograph on numerical conformal mapping that gives a comprehensive account of the theoretical, computational and application aspects of the problems of determining conformal modules of quadrilaterals and of mapping conformally onto a rectangle. It contains a detailed study of the theory and application of a domain decomposition method for computing the modules and associated conformal mappings of elongated quadrilaterals, of the type that occur in engineering applications.
This book presents an introduction to MATLAB and its applications in engineering problem solving. The book is designed as an introductory course in MATLAB for engineers. The classical methods of electrical circuits, control systems, numericalmethods, optimization, direct numerical integration methods, engineering mechanics and mechanical vibrations are covered using MATLAB software.
This book enables readers to quickly develop a working knowledge of HTML, javascript and PHP. The text emphasizes a hands-on approach to learning and makes extensive use of examples. A detailed science, engineering, or mathematics background is not required to understand the material, making the book ideally suitable for self-study or an introductory course in programming. Features: describes the creation and use of HTML documents; presents fundamental concepts of client-side and server-side programming languages;
Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numericalmethods and shows how to develop, analyze, and use them.
STATISTICAL METHODS FOR ENGINEERS offers a balanced, streamlined one-semester introduction to Engineering Statistics that emphasizes the statistical tools most needed by practicing engineers. Using real engineering problems with real data based on actual journals and consulting experience in the field, users see how statistics fits within the methods of engineering problem solving. The book teaches users how to think like an engineer at analyzing real data and planning a project the same way they will in their careers.
Key Message: This book aims to explain physics in a readable and interesting manner that is accessible and clear, and to teach readers by anticipating their needs and difficulties without oversimplifying. Physics is a description of reality, and thus each topic begins with concrete observations and experiences that readers can directly relate to. We then move on to the generalizations and more formal treatment of the topic. Not only does this make the material more interesting and easier to understand, but it is closer to the way physics is actually practiced. |
Mathematics
Mathematics is the foundation of the sciences, and the technology largely responsible for our present standard of living. Mathematics is one of the most productive tools yet discovered for unraveling the mysteries of our universe. In some instances, it is the only language in which some ideas can be expressed.
Many Options
Degrees
LSSU offers several options for a student interested in the study of mathematics, including a traditional mathematics major, along with a mathematics program that emphasizes actuarial and business applications, programs in mathematics for education at both the elementary and secondary levels, and a program emphasizing computational mathematics applications.
The Computer and Mathematical Sciences program provides a solid background in both mathematics and computer science. Many graduates from this program who work in the computer industry have stressed that the mathematics foundation gained from this degree gave them a distinct advantage in the work place.
Professor Explores Technology as Teaching Aid
Kimberly Muller Ph.D., professor of mathematics and computer science, had her article "How Technology Can Promote the Learning of Proof," published in the February 2010 issue of "Mathematics Teacher" magazine, one of the most prestigious refereed journals of the mathematics field.
In her article, Muller describes how using the Geometer's Sketchpad can help students learn about geometric proof through exploration, discovery and conjecture.
Professor Muller's research has been published in the Proceedings of the American Mathematical Society, as well, most recently in Vol. 137, No. 7. Her article, "Vector Measures and the Strong Operator Topology," was co-written and researched with Paul Lewis Ph.D. of the University of North Texas and Andy Yingst Ph.D. of the University of North Carolina.
Optimization uses mathematical models to make the best possible decisions. Optimization models are widely used in design, manufacturing, and logistics. In this project, we investigate optimization modeling, the use of the modeling language AMPL, and the use of AMPL, together with Excel, to build, solve, visualize, and analyze large optimization models. |
Deep Dive into Mathematica's Numerics: Applications and Tips
Andrew Moylan
In this course from the Wolfram Mathematica Virtual Conference 2011, you'll learn how to best use Mathematica's numerics functions in advanced settings. Topics include techniques and best practices for using multiple numerics functions together, advanced numeric features, and understanding precision and accuracy.
Report Generation allows you to create documents quickly and easily using Wolfram Finance Platform documents. Get an overview of the features in this talk from the Wolfram Finance Platform Virtual Seminar.
Learn more about Wolfram's Programming for Kids programming curriculum. This Wolfram Technologies for STEM Education: Virtual Conference for Education talk shows how to get students started on programming in the Mathematica Language.
See the first public viewing of the revolutionary Wolfram Calculator. This Wolfram Technology for STEM Education: Virtual Conference for Education talk demonstrates the basic functionality as well as the predictive interface of the Wolfram Calculator.
Learn how to design interactive digital material for the classroom. This Wolfram Technology for STEM Education: Virtual Conference for Education talk highlights the Wolfram Demonstrations Project and how teachers can create their own Demonstrationscomputerbasedmath.org has been engaged in a fundamental rethink of math education. This Wolfram Technology for STEM Education: Virtual Conference for Education talk shares some of the thinking behind the new curriculum that computerbasedmath.org is developing and how Wolfram technologies can assistImmerse yourself in Wolfram Community—a networking portal of like-minded educators, students, researchers, and developers. This Wolfram Technologies for STEM Education: Virtual Conference for Education talk introduces the various uses and features of Wolfram Community.
Wolfram technologies are the tools for providing interactive and engaging materials for STEM education. In this video, Conrad Wolfram shares examples and explains why Wolfram is uniquely positioned to be a leader in STEM education. |
homework set 16
Course Number:
COMPUTER S Math 225,
Spring
2010
College/University: Bilkent University
Word Count: 433
Rating:
Document Preview
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS Homework set # 16 U.Muan g July 16, 2008
FUNDAMENTAL SET OF SOLUTIONS 1) a) b) c) Find the Wronskian of the following given pair of functions: e2x , e-3x/2 . x, xex . ex sin x, ex cos x.
2) Determine the largest interval in which the given I.V.P. is certain to have a unique twice differentiable solution. Do not find...
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Homework set # 19 U.Muan g July 16, 2008VARIATION OF PARAMETERS 1) Find a particular solution of the following D.E. by using the variation of parameters. T
ECE 2574 Introduction to Data Structures and Algorithms Programming Assignment 2: Part (a)Problem: Polynomial addition and multiplication Objective: The main goal of this assignment is to learn about linked lists and their implementation. Other goals are
Mitosis a. The slides: 1. Telophase - The two divided cells are being de-condensed and become grouped in new nuclei. 2. One is displaying anaphase, while the other is displaying metaphase. 3. Anaphase - The cells look like they are just starting to break
7. DNA Exercise 1: a. Sugar, Nitrogenous base, and Phosphates b. Adenine, Thymine, Cytosine, and Guanine Exercise 2: a. It would take 12 nucleotides to construct the coding standard of the globin molecule. b. It would take 24 nucleotides to model this par
8. Extraction of DNA a. Under my microscope, it seems like I can only see clumps of strings, but not the DNA itself. b. No, I expected to see a single identifiable strand of DNA. c. Although I did not expect to see the double helix formation, I did expect
Lab 12 / Michael Schonfeld Exercise 1 A. The sample I observed the most microbial growth was the kitchen sponge. However, to my surprise, the electric light switch had the least microbial growth. B. The differences seemed to have a correlation between the
Lab 6 - Part 2 / Michael Schonfeld A. When I blew air into the Bromothymol Blue solution, I added oxygen to it, and it changed color to yellow. This happened because the CO2 dissolved in the water, and was added to the solution. Bromothymol Blue turns yel
Lifting Scheme: Wavelets were defined as translates and dilates of one mother wavelet function and were used to analyze and represent a general function. Several techniques exist to construct wavelet bases and one of those techniques is lifting scheme. It
Meyer wavelet The first orthonormal wavelets were constructed by Meyer and they were bandlimited. Let (t ) be a real valued function with a Fourier transform ( ) that satisfies the following: 1. It is real and positive in the range 4 / 3 and is zero at fr
Bandlimited WaveletsThe orthonormal basis generating wavelets which are bandlimited are said to be bandlimited wavelets. It is possible to have orthonormal basis generating wavelets that are bandlimited; that is, their Fourier transforms are supported co |
In this book, you will learn about the concepts of algebra. You will learn to use mathematical skills and algebra skills. Why do you need these skills? Many jobs use mathematics and algebra. People who work in banking, food service, printing, electronics, construction, surveying, insurance, and retail all use these skills on the job. Algebra skills are also useful in your everyday life, at home and in school.
Geometry is the study of how points, lines, and planes can be used to picture to space around us. In this book, the main attention will be placed on plane geometry. Plane geometry studies geometric figures in a plane, like squares, triangles, and circles. Later, we will learn about solid figures like cubes, prisms, and spheres |
where can i brush up on my basic math online?
where can i brush up on my basic math online? basically i finally get to go back to school to get a BS in zoology and i need to pass the placement test from pre-algebra through geometry so i can "speed" my way to the harder classes such as calculus and statistics of science. i bought some demystified math books to help brush up but are there a few online sites that help? i really dont want to repeat classes i've taken in highschool. thx!
Suggestion by Kenneth L Try ( and it should be very helpful.
It doesn't include any advanced mathematical concepts like calculus of trigonometry,but it's good enough to get your through most of precalculus and college algebra.
Or, try answering some questions on Yahoo!Answers.
Buy some books also.
If you can really read (probably get 700+ on English SAT), go to (mathworld.wolfram)
That may not be the full name of the website, but it should lead you somewhere lol.
What do you think? Answer below!
How can I show "pictorial examples of integer problems"? I am in 8th grade, and I have a project due tomorrow for math class (pre – algebra). Can someone tell me how I'm supposed to show this? Here are the actual instructions: "Design a poster that shows pictorial examples of all of the different types of integer problems."
Thanks.
Suggestion by M R "pictorial" only means picture, or a graph.
and integer(a whole number) problems means negative,positive integers, a number line, dividing,multiplying,subtracting,adding integers, integer coordinates in a grid,etc
if you need additional help look online… |
Get your best grades with this Cambridge International AS and A Level Geography Revision Guide .: Manage your own revision with step-by-step support from experienced examiners Garrett Nagle and Paul Guinness.; Use specific case studies to improve your knowledge of geographical patterns, processes and changes.; Get the top marks by applying geographical... more...
Provide a true international perspective with relevant, up-to-date case studies and a free Student's CD in this new edition of the market leading text. The only title endorsed by Cambridge International Examinations for 2013!. It has been written for the revised Cambridge IGCSE (0450) and Cambridge O Level Business Studies (7115) syllabuses,... more...
Build confidence and understanding throughout the year with hundreds of additional practice questions. This Workbook supports our bestselling Checkpoint series, with exercises specifically matched to the Cambridge Progression tests and the Checkpoint tests.; Develops understanding and builds confidence ahead of assessment with exercises matched to... more...
The perfect book for mastering all the essentials of college algebra, with coverage of: the coordinate plane, circles, lines and intercepts, parabolas, nonlinear equations, functions, graphs of functions, exponents and logarithms, and more You'll be able to learn more in less time, evaluate your areas of strength and weakness and reinforce your... more...
Learn the basics of practical accounting easily and painlessly with Accounting For Dummies, 4th Edition , which features new information on accounting methods and standards to keep you up to date. With this guide, you can avoid accounting fraud, minimize confusion, maximize profits, and make sense of accounting basics with this plain-English guide... more...
This core text actively encourages students to ask questions and examine evidence. Emphasizing research and evaluation of research methods, it will foster open-minded critical thinkers who can apply knowledge practically. A chapter on exam preparation provides assessment strategies, and support for the IA and extended essay is also included |
Math Mammoth Geometry 3 can be used after the student has finished Math Mammoth Geometry 1, and is suitable for grades 5-7. This book does not require the students to calculate area or volume, and... More > that is why it is not necessary to study Math Mammoth Geometry 2 (which deals with those topics in depth) before this book.
We start out with basic angle relationships, such as adjacent angles (angles along a line), vertical angles, and corresponding angles (the last only briefly). The lesson Angles in Polygons is a sequel to studying angles in a triangle.
The next set of lessons deals with congruent and similar figures.
The last section of this book teaches some basic compass-and-ruler constructions.
Note: At this time (2014), this book is in "beta" stage. It will be revised with more lessons (such as about The Pythagorean Theorem) probably in early 2015.< Less
This book with charts will illustrate some hidden, never before revealed aspects of GPS coordinates as they directly relate to People, Places and Time. These involve number patterns based on GPS,... More > sacred geometry and ley-lines.
Chapter one will examine the Dallas city grid and ley-lines in relation to the Kennedy assassination on November 22, 1963.
Chapter two examines the Earth grid pattern of the Royals of London that might well be planned out to coordinate to certain astronomical or occultic alignments.
Chapter three will look and decipher an apparent hidden 'code of years' in Earth's longitude. These degrees of longitude pertain to the pyramid that is configured on the grounds of the Hampton Court Palace west of London.
These GPS coordinates will reveal that in fact, these specific longitude-to-year intervals have been marked out by design to formulate a direct association to key Persons, Places & Time
This is an atlas similar to Uranometria 2000.
Includes 107 charts to 11 magnitude, with 30º charts.
Spiral bound for easy use at the telescope A includes a selection of the best deep sky objects and it is very handy to plan quick deep sky sessions with 25 charts showing 9th magnitude stars 1 includes the first 300 charts and a visual index of all charts. Volume 2 contains the remaining charts 2 includes charts 301 to 571 and a visual index of all charts. Volume 1 contains the first 300 charts.< Less
Dr. Fair's wealth of experience as a police chaplain includes working with the witnesses and victims of several high profile "hot spots." His first such assignment was to coordinate the... More > Critical Incident Stress Debriefing for 90 employees of the Killeen (TX) Police Department after the lunchtime massacre that occurred there in 1991. More recently, he spent a week with with the Port Authority of New York and New Jersey during the rescue and recovery operations at Ground Zero in the aftermath of 9-11, and counseled on-site with NASA employees involved in the grid searches of the debris field left in the wake of the Columbia explosion. Learn how to master Chaplaincy based on published articles by Chaplain Fair.< Less |
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Algebra is an elementary algebra text from one of the leading mathematicians of the world -- a major contribution to the teaching of the very first high school level course in a centuries old topic -- refreshed by the author's inimitable pedagogical style and deep understanding of mathematics and how it is taught and learned.
This book is about algebra. The main part of the book is made up of problems. The best way to deal with them is : Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it ( it is not heavily used in the sequel) and return to it later.
"The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gelfand and Shen. There are specific 'practical' problems but there is much more development of the ideas...[The authors] have shown how to write a serious yet lively look at algebra." -- R. Askey, The American Mathematics Monthly
"Were Algebrato be used solely for supplementary reading, it could be wholeheartedly recommended to any high school student of any teacher... In fact, given the long tradition of mistreating algebra as a disjointed collection of techniques in the schools, there should be some urgency in making this book compulsory reading for anyone interested in learning mathematics." -- H. Wu, The Mathematical Intelligencer
Above are extracts from the book Algebra and from the publisher Birkhauser (with permission of the publishers).
There are no teacher's guide, workbook or answer key for this book. Solutions are provided for some of the problems.
Please note that this book is not published in Singapore.
Algebra by Gelfand and Shen
Introduction
Exchange of terms in addition
Exchange of terms in multiplication
Addition in the decimal number system
The multiplication table and the multiplication algorithm
The division algorithm
The binary system
The commutative law
The associative law
The use of parentheses
The distributive law
Letters in algebra
The addition of negative numbers
The multiplication of negative numbers
Dealing with fractions
Powers
Big numbers around us
Negative powers
Small numbers around us
How to multiply am by an, or why our definition is convenient
The rule of multiplication for powers
Formula for short multiplication: The square of a sum
How to explain the square of the sum formula to your younger brother or sister
The difference of squares
The cube of the sum formula
The formula for (a+b)4
Formulas for (a+b)5, (a+b)6,... and Pascal's triangle
Polynomials
A digression: When are polynomials equal?
How many monomials do we get?
Coefficients and values
Factoring
Rational expressions
Converting a rational expression into the quotient of two polynomials
Polynomials in one variable
Division of polynomials in one variable; the remainder
The remainder when dividing by x - a
Values of polynomials, and interpolation
Arithmetic progressions
The sum of an arithmetic progression
Geometric progressions
The sum of a geometric progression
Different problems about progressions
The well-tempered clavier
The sum of an infinite geometric progression
Equations
A short glossary
Quadratic equations
The case p = 0. Square roots
Rules for square roots
The equation x2+px+ q=0
Vieta's theorem
Factoring ax2+bx+c
A formula for ax2+bx+c=0(where a does not equal 0)
One more formula concerning quadratic equations
A quadratic equation becomes linear
The graph of the quadratic polynomial
Quadratic inequalities
Maximum and minimum values of a quadratic polynomial
Biquadratic equations
Symmetric equations
How to confuse students on an exam
Roots
Non-integer powers
Proving inequalities
Arithmetic and geometric means
The geometric mean does not exceed the arithmetic mean
Problems about maximum and minimum
Geometric illustrations
The arithmetic and geometric means of several numbers
The quadratic mean
The harmonic mean
Our recommendation:
This book is recommended for Mathematics teachers and "serious" Mathematics students.
It does not cover all topics in algebra 1 or 2, and concentrates on theory rather than application.
It would be ideal for math clubs or a supplement to other algebra. |
Hirsch, Devaney, and Smale's the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems.
Classic text by three of the world's most prominent mathematicians
Continues the tradition of expository excellence
Contains updated material and expanded applications for use in applied studiesThe 2nd edition of Global Politics: A New Introduction continues to provide a completely original way of teaching and learning about world politics. The book engages directly with the issues in global politics that students are most interested in, helping them to understand the key questions and theories and also to develop a critical and inquiring perspective. Completely revised and updated throughout, the 2nd edition also offers additional chapters on key issues such as environmental politics, nationalism, the internet, democratization, colonialism, the financial crisis, political violence and human rights.
Introduction to Languages and the Theory of Computation, 4th edition by John Martin
English | 2010 | ISBN: 0073191469 | 448 pages | PDF | 3.42 MB
Introduction to Languages and the Theory of Computation helps students make the connection between the practice of computing and an understanding of the profound ideas that defines it. The book's organization and the author's ability to explain complex topics clearly make this introduction to the theory of computation an excellent resource for a broad range of upper level students.
The author has learned through many years of teaching that the best way to present theoretical concepts is to take advantage of the precision and clarity of mathematical language. In a way that is accessible to students still learning this language, he presents the necessary mathematical tools gently and gradually which provides discussion and examples that make the language intelligible.
Computer-Aided Control Systems Design: Practical Applications Using MATLAB® and Simulink® supplies a solid foundation in applied control to help you bridge the gap between control theory and its real-world applications. Working from basic principles, the book delves into control systems design through the practical examples of the ALSTOM gasifier system in power stations and underwater robotic vehicles in the marine industry. It also shows how powerful software such as MATLAB® and Simulink® can aid in control systems design |
Linear Algebra Through Geometry - 2nd edition
Summary: Linear Algebra Through Geometryintroduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Top...show moreics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms. The final chapter treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only prerequisite for reading this book (with the exception of one section on systems of differential equations) are high school geometry, algebra, and introductory trigonometry50 +$3.99 s/h
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Just a thought: People write bad checks partially because they don't know how to balance their check book. Algebra might just be the ticket. Kids go to casinos and spend their collage fund or student loan that is supposed to be for school because they don't understand that the casino always wins. Calculus might prevent some of this. Wishful thinking? |
Find a Kearny, NJ Geometry
...The quadratic formula is presented, along with an introduction to complex numbers. The laws of exponents are extended to the cases of zero, negative and fractional exponents. The idea of a function and its inverse is introduced. |
The Calculus Tutor DVD Series will help students understand the fundamental elements of calculus- -how to take algebra and extends it to include rates of change between quantities. Concepts are introduced in an easy to understand way and step-by-step example problems help students understand each part of the process.
This lesson introduces students to the technique of integration known as integration by parts; students are taught how to recognize when a problem could be solved using this technique of integration. Grades 9-12. 29 minutes on DVD.
Customer Reviews for Calculus Tutor: Integration By Parts DVD
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Introduction to Topology
Book Description: This text is intended for a one-semester undergraduate course in topology. The fundamental concepts of general topology are covered rigorously but at a gentle pace and an elementary level. It is accessible to students with only an elementary calculus background. In particular, abstract algebra is not a prerequisite. The first chapter develops the elementary concepts of sets and functions, and in Chapter 2 the general topological space is introduced. Subspaces, continuity, and homeomorphisms are covered in Chapter 3. The remaining chapters cover product spaces, connected spaces, separation properties, and metric spaces |
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Inverse Trig Functions
At TMC13, I was in a group of people talking about precalculus. One of the exercises we did was make a list of some of the topics we found challenging to teach as teachers — and we broke out in groups to try to come up with ways to tackle those topics.
Our initial task was to find the deep mathematical idea behind the topic… why we teach it, what we think we can get out of it conceptually… and what we sort-of converged on is that the topic really illuminates the idea of inverses and restricted domains. And that's about it. And when push came to shove, we decided we didn't find that restricted domain is something we really care about. We decided we didn't really care about the inverse trig graphs, and the work we put into that side of things wasn't really worth what we little we were able to squeeze out of it. It's not that it is horrible, but we just didn't couldn't justify it.
So, honestly, we decided to just focus on inverses, and the idea of them as "backwards problems."
Thus, we came up with two things:
1. A packet that has students secretly engage with inverse problem work before they even know what they're doing. So the first packet is meant to be used before any unit circle trig is introduced. (A few of us, especially April, did something similar in her classes, and randomly, Greg Taylor did a my favorites on the same essential idea!)
In fact, if I were to use this in the classroom, I would not even mention the words "trigonometry." I would focus on the idea of coordinate planes and circles, and simply leave it there.
2. A packet that students work on after they learn unit circle trig — and that more formally introduced the idea of the inverse trig functions. It tries to draw connections between the unit circle, the sine/cosine graphs, and their calculators.
There are concept-y questions for both packets. I'm including both packets below in one document. I'm posting one with a few teacher notes, and one with the teacher notes hidden. (The .docx is here if you want to edit!)
We did all this planning in pretty much an hour and a bit — from start to finish. And then I pulled together the ideas to make this document. I'm not sure I was able to capture everything we talked about, but I think I got most of the big things. Apologies to my collaborators if I totally botched the translation of our vision to reality!
Of course, this makes me wonder about motivating the topic in a more general way: why are inverse functions important (if they are)? Is it worth starting (or finishing) with some conversation about that broader question?
I have long thought that the whole inverse idea is the 'dirty little secret' of Algebra I and Algebra II and that we do not give it sufficient time in the daylight. I'll joke with my kids that every time I teach them anything in these courses, they can expect to be taught how to undo what we've just done. Adding/subtracting, multiplying/dividing, distribution/factoring, exponents/radicals, variable exponents/logarithms.
The graphs of the inverse trig functions bother me even more than it sounds like they bothered you guys. I have seen texts with different conclusions about the graphs of inverse secant or inverse cosecant. I try to avoid them almost completely other than a quick peek at GeoGebra (or maybe Desmos if I can fall in love with that sufficiently)
There's something really neat about inverses being a core idea of high school math. I don't normally see that listed when ppl think about what's truly important — it is usually just something people do abstractly and then forget until it reappears (when I say "people", I mean "me").
But I wonder…if I were to think of it as a core idea in high school math, I would feel more of a push to talk about restricted domains when talking about inverses — because talking about the inverse of squaring would necessitate talking about restricted domains…
You're totally right about the lack of consistency when it comes to various textbooks and the inverse trig. Yeesh.
Yeah, I'd have to say that I disagreed with the original post when you dismissed domain restrictions. I think that this sort of backward thinking required when engaging with inverse functions is much more rich when we consider domains/ranges and where the answers for these functions are even meaningful. Trying to squeeze some context in always helps as far as I can tell.
Your example of the inverse of squaring is spot on – that is where we can first meaningfully discuss restrictions. When I introduce the idea of inverse trig functions I play a mean game where I say 'I'm thinking of an angle whose cosine is 1/2. What is the angle?' And, of course, I can always tell the student that they are wrong no matter what answer they give me. This leads to a nice conversation about domain restrictions and the power of functions being creatures where there is one answer to one question.
I keep flipping back and forth in my opinion on them. Not whether they are a useful thing to teach per se — because I've realized I'm Mr. Conceptual Teacher and there are some deep conceptual things from this domain restriction stuffs — but given all that we have to cover, if something needs to go, it feels like given a choice between for example:
1) doing fun explorations with matrices and their applications
or
2) talking about domain restrictions in a deep way (with the graphs)
I wrote an introductory trig unit for Geometry in which students make their own "mini" trig tables using this: Students are then asked to use their table of trig ratios to answer questions "forwards and backwards." The emphasis is on the ratios and their relationship with the angles. This may be a good starter in precal, too. Here are the lessons: and
Sam, while stealing things off the TMC13 site, I noticed that you had collected Precalc resources on SugarSync. Are those only available to TMC participants? I would love to copy them and see how I can use them. Thanks for this great lesson on inverse trig functions. |
The WordCalc app is a mathematical expression solver within Microsoft Word 2013. To solve a mathematical expression select the expression or type the expression in textbox provided and press enter. The resulting value of the expression will be shown at the top of the result box. The app also features a history of previously solved expressions and results for the current session. Students can solve math problems within Word 2013 without opening another program. It supports the following operators and functions: Operators: +, -, *, /, and ^. Functions: sin, cos, tan, asin, acos, atan, sqrt, abs, floor, ceil, log, min, max, and avg. |
Digitalize your math equations to land on the right answer with the Texas InstrumentsTI30XA Scientific Calculator. This 10-digit scientific calculator is ideal for general math, pre-algebra, algebra 1 and 2, trigonometry and biology.
It performs trigonometric functions, logarithms, roots, powers, reciprocals, and factorials. One-variable statistics include results for mean and standard deviation. This calculator also adds, subtracts, multiplies, and divides fractions entered in traditional numerator/denominator format. Help make your student a math wiz with the TI30XA Scientific Calculator.
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In the previous sections, you observed students using the Reasoning and Proof Standard. You explored your own relation to these concept in the Part B Interactive Activity on triangular and square numbers. In Part C, we developed working definitions of some of the related concepts and explored their value. Now that you are familiar with the Standard and some of its aspects, it's time to apply it in an actual classroom setting.
Harriette Davis is working with her eleventh-grade pre-calculus course to find functions that provide "boundaries" for trigonometric functions. In the class these are termed "enveloping" functions. They will use this information as they reason about and build understanding of symmetries, asymptotes, and, limits.
Before we view the students' work, please use this activity to review the underlying mathematics.
The interactive feature on this page requires the FLASH 5 player/plugin. |
Overview - WRITE MATH ANSWERS - STUDENT BOOK LV H
Teach students how to provide constructed answers to algebra problems with this practical series. The four-page lessons encourage students to show their work, explain how they found each answer, and write explanations.
Student Book Each 80-page Student Book contains 19 lessons with 2 pages devoted to practice 3-4 problems. Practice pages have enough space for students to show their work. Questions model those found on standardized tests. |
Equation Illustrator V has been designed to ease the difficult task of combining picture, vector graphics and complicated formatted text such as math equations in electronic and printed documents. A WYSIWYG interface keeps automation to a minimum and allows you to put what you want where you want it. Equation Illustrator V is the most popular chemistry download. Chemical Reagent Calculator is the second most popular chemistry download.
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Product description
Advanced Mathematics fully integrates topics from algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis. Word problems are developed throughout the problem sets and become progressively more elaborate. With this practice, high-school level students will be able to solve challenging problems such as rate problems and work problems involving abstract quantities. Conceptually oriented problems that help prepare students for college entrance exams are included in the problem sets.
Type: Boxed Set ()Category: > Home SchoolingISBN / UPC: 9781565771277/1565771273Publish Date: 6/1/2000Item No: 106942Vendor: Saxon Publishers |
Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics. less |
ceived by the author as an introduction to "why the calculus works" (otherwise known as "analysis"), this volume represents a critical reexamination of the infinite processes encountered in elementary mathematics. Part I presents a broad description of the coming parts, and Part II offers a detailed examination of the infinite processes arising in the realm of number--rational and irrational numbers and their representation as infinite decimals. Most of the text is devoted to analysis of specific examples. Part III explores the extent to which the familiar geometric notions of length, area, and volume depend on infinite processes. Part IV defines the evolution of the concept of functions by examining the most familiar examples--polynomial, rational, exponential, and trigonometric functions. Exercises form an integral part of the text, and the author has provided numerous opportunities for students to reinforce their newly acquired skills. Unabridged republication of Infinite Processes as published by Springer-Verlag, New York, 1982. Preface. Advice to the Reader. Index. |
MATLAB Student Version
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Students in engineering, math or science have a new technical computing resource designed for their needs. The MathWorks' MATLAB Student Version includes full-featured versions of MATLAB and Simulink, the software products used by engineers, scientists and mathematicians at leading universities, research labs, technology companies and government labs. MATLAB integrates computation, data analysis, visualization and programming in one environment. Simulink is one of the leading interactive environments for modeling, simulating and analyzing dynamic systems. In addition, there is no difference between the student and professional versions of the program, which, according to the company, is important because students are learning skills with the same tools they may use in a professional arena. The program also comes with MATLAB and Simulink books to help students get started. This product has a special student price of $99. The MathWorks, (508) 647-7000, |
Yoshiwara and Yoshiwara's MODELING, FUNCTIONS, AND GRAPHS: ALGEBRA FOR COLLEGE STUDENTS includes content found in a typical algebra course, along with introductions to curve-fitting and display of data. Yoshiwara and Yoshiwara focus on three core themes throughout their textbook: Modeling, Functions, and Graphs. In their work of modeling and functions, the authors utilize the Rule of Four, which is that all problems should be considered using algebraic, numerical, graphical, and verbal methods. The authors motivate students to acquire the skills and techniques of algebra by placing them in the context of simple applications that use real-life data. |
If you feel that your ACC Assessment Test score does not really reflect your
current skill level or that the advice we are giving is not appropriate for
you, please feel free to talk with an advisor, either in the Advising Center
or in the mathematics department. On the Web, you can look at a
discussion of what the advisor will explore with you.
Your score indicates that indicates that you are able to demonstrate some basic
algebraic skills. You have a choice of two courses at this point.
Before you choose a course at this level is the time to think about what you
might major in and check on what math courses are required for that
major. Be sure that you are preparing for the correct sequence.
The course that most students take is Elementary Algebra, MATD 0370.
It is a part of the standard mathematics sequence and a dedicated teacher will
work with you to develop a solid foundation in algebra for later courses and
in applications in many areas. When you finish this course, you should be able
to prepare for and pass the THEA test, which would allow you to enroll in MATH
1332, 1333, or 1342. Another semester of Developmental Math (Intermediate Algebra,
MATD 0390) will be necessary to prepare for Math for Business and Economics,
College Algebra, or higher mathematics courses.
(Due to declining enrollments, MATD 0360 is no longer
offered.)Your other choice is Topics in Developmental
Math, MATD 0360. This course covers the same
algebraic topics as MATD 0370, but not in as much depth (fewer and less complex
problems). You will work with a dedicated teacher to make sure that you have
a solid understanding of all the algebraic concepts and a number of other mathematical
topics, which are covered in more depth than in our algebra courses. These topics
that are most relevant for succeeding in several of ACC's college-level mathematics
courses: MATH 1332, College Mathematics, MATH 1342, Elementary Statistics, and
MATH 1333, Mathematics for Measurement. The TASP test also covers these topics.
When you finish this course, you should be able to pass the THEA test, which
would allow you to enroll in MATH 1332, 1333, or 1342. If you need to take
other college-level mathematics courses, such as College Algebra, MATH 1314,
or Math for Business and Economics, MATH 1324, you should NOT take this route.
You should take MATD 0370, as described in the previous paragraph.
You have demonstrated that you recall enough algebraic skills and other mathematical
skills to be able to do many of the real-life applications of mathematics and
to begin some of the college-credit mathematics courses. Which course is appropriate
for you depends first on what is required for your educational
goal.
If you do not need to take higher-level math courses, and if your educational
plan requires one of these college math courses (MATH 1332, College Mathematics;
MATH 1333, Mathematics for Measurement; or MATH 1342, Elementary Statistics.),
then you are ready to begin these. These are fine college-level, transferable
courses, but they do not prepare you to take higher-level math courses.
If you will need to take more mathematics or if you plan to fulfill your
math requirement by taking Math for Business and Economics, MATH 1324, or
College Algebra, MATH 1314, then you will need to take the current ACC Assessment
Test in order to measure your current algebra skill. The main question here
is whether you have adequate algebra skills to go directly into these "algebra-intensive"
courses or whether you will need to take Intermediate Algebra, MATD 0390,
to improve your algebra skills first. |
These standards-based activities are designed to use gamma-ray bursts -- unimaginably huge explosions which signal the births...
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These standards-based activities are designed to use gamma-ray bursts -- unimaginably huge explosions which signal the births of a black holes -- to engage your students and teach them science and math concepts.
In the author's words, his site "collects various areas in which ideas from discrete and computational geometry ... meet some...
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In the author's words, his site "collects various areas in which ideas from discrete and computational geometry ... meet some real world applications." Areas in which the geometry is applied include design and manufacturing, graphics and visualization, information systems, medicine and biology, physical sciences, etc. The content on this site differs from that on the author's other site, "The Geometry Junkyard," in that the latter deals more with pure mathematics.
Quoted from the site: "IDEA is an interdisciplinary effort to provide students and teachers around the world with...
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Quoted from the site: "IDEA is an interdisciplinary effort to provide students and teachers around the world with computer based activities for differential equations in a wide variety of disciplines." Currently, IDEA contains nearly twenty activities. These are applications of differential equations to areas as diverse as bungee jumping and salmon migration. Some of these applications are presented as text with illustrations, but others include interactive graphics.
JEP is a Java package for parsing and evaluating mathematical expressions. It supports user defined variables, constants, and...
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JEP is a Java package for parsing and evaluating mathematical expressions. It supports user defined variables, constants, and functions. A number of common mathematical functions and constants are included.
This is a collection of 339 videos that work out typical exercises that first, second and third semester calculus students...
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This is a collection of 339 videos that work out typical exercises that first, second and third semester calculus students are asked to solve. The lengths of the videos range from a couple of minutes to up to seven minute depending on the complexity of the exercise. They are all closed captioned, and graphs and other diagrams accompany the words and equations when applicable. |
The family in this book is moving to a new neighborhood. They have a lot of work to do! They need to unload the moving truck, unpack boxes, and put everything away. The kids make new friends and discover all the fun they can have with the empty boxes. While building forts from the empty packing boxes, the kids discover many new shapes and their dimensions.... more...
egghead's Guide to Geometry will help students improve their understanding of the fundamental concepts of geometry. With the help of Peterson's new character, egghead, students can strengthen their math skills with narrative cartoons and graphics. Along the way there are plenty of study tips and exercises, making this the perfect guide for students... more...
The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies... more...
This book mainly deals with the Bochner–Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner–Riesz means and important achievements attained in the last 50 years. For the Bochner–Riesz means of multiple Fourier integral, it... more...
You, Too, Can Understand Geometry - Just Ask Dr. Math ! Have you started studying geometry in math class? Do you get totally lost trying to find the perimeter of a rectangle or the circumference of a circle? Don't worry. Grasping the basics of geometry doesn't have to be as scary as it sounds. Dr. Math-the popular online math resource-is here to help!... more...
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The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the... more...
Maximize student use of the TI-Nspire while processing and learning algebraic concepts with this resource. Lessons provided delve into the five environments of the TI-Nspire including calculator, graphs and geometry, lists and spreadsheets, notes, and data analysis. more... |
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approaches to other students in the class.
Filled with dozens of quick and fun algebra activities that can be used inside and outside the classroom
Designed to help students practice problem-solving and algebra skills
The activities address a wide range of topics, skills, and ability levels, so teachers can choose whichever best suit the students' needs.
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Meet the Author
Frances McBroom Thompson, Ph.D., has taught mathematics at the junior and senior high school levels and was a professor of mathematics education at Texas Woman's University. She has served as a K-12 mathematics specialist, a curriculum developer, and a teacher trainer; and she is also the author of numerous articles and books on math education, including Hands-On Algebra and the Math Essentials series from Jossey-Bass |
ial/Salzman's Essential Mathematics, 2e, gives students the necessary tools to succeed in developmental math courses and prepares them for future math courses and the rest of their lives. The Lial developmental team creates a pattern for success by emphasizing problem-solving skills, vocabulary comprehension, real-world applications, and strong exercise sets. In keeping with its proven track record, this revision includes an effective new design, many new exercises and applications, and increased Summary Exercises to enhance comprehension and challenge students' knowledge of the subject matter. |
Elementary Algebra - 8th edition
Algebra is accessible and engaging with this popular text from Charles ?Pat? McKeague! ELEMENTARY ALGEBRA is infused with McKeague?s passion for teaching mathematics. With years of classroom experience, he knows how to write in a way that you will understand and appreciate. McKeague?s attention to detail and exceptionally clear writing style help yo...show moreu to move through each new concept with ease. Real-world applications in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book?s multimedia learning resources, including ThomsonNOW for ELEMENTARY ALGEBRA, a personalized online learning companion00 +$3.99 s/h
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The book "Vedic Mathematics" essentially deals with arithmetic of the middle and high-school level. Its claims that "there is no part of mathematics, pure or applied, which is ... 'Vedicmaths ' will condemn ...
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The Vedic Mathematics Sutras This list of sutras is taken from the bookVedic Mathematics, which includes a full list of the sixteen Sutras in Sanskrit, but in some cases a translation of the Sanskrit is not
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The present system of VedicMaths is based on sixteen basic sutras formulated by Swami Bharati Krisna Tirthaji Maharaj in his book 'Vedic Mathematics'. He claims to have culled these formulae from the Atharvaveda; however, nowhere in the Atharvaveda
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Design of High Speed Vedic Square by using Vedic Multiplication Techniques G.Ganesh Kumar*, ... It is part of Sthapatya- Veda (book on civil engineering and architecture), which is an upa-veda (supplement) of Atharva Veda. ... Vedicmaths deals with several basic as well as complex mathematical ...
This e-book is free! This publication is protected by international copyright laws. You have the ... our VedicMaths ebook at Now multiply the 7 by the 2 of twelve giving 14. Add this to 70 giving 84.
book titled 'Vedic Mathematics' written by Swami Bharati Krishna Tirtha. The serious shortcomings of the book and thelack ofhonestyreflected inthetitle andin several ofthe author's claims have been pointed out by Dani (ibid.).
operations andthesecond onebelongs toourancient mathsi e. ., Vedicmaths. In this book I have laid emphasis on my own approach of multiplication, because years of research in numeric maths I have found that I myself and mystudents find it comfortable as
Application of VedicMaths in Competition Exams Test papers Answers Testimonials WONDER SERIES oLrqfu"B xf.kr 18 fnuksa esa pEkRdkj lHkh izfr; ... book and with this end in view all types of solved questions with a huge collection of practisable
Vedicmaths is helpful to software developers as it is more scientific than the normal system ... Vedic mathematics is part of four Vedas (books of wisdom). It is part of Sthapatya-Veda (book on civil engineering and architecture), which is an upa-veda (supplement) ...
I was instantly amazed by this book. It actually changed my life in ways I could have never predicted. As I read the book, ... The Vedic system is becoming more popular today. But at the same time, the educational establishment isn't quick to
(Goddess of vedic, music and book knowledge. She thus helps Lord Brahma in creation. Vedas are to be ... *VedicMaths India *CSS2 *The Primal Revelation at the Heart of Civilization *Krishna Worship: One of Humanity's Most Ancient Traditions
wisdom). It is part of Sthapatya- Veda (book on civil engineer--veda (supplement) of Atharva Veda. It gives explanation of several mathematical ... Vedicmaths has already crossed the boundaries of India and has become an interesting topic of research abroad.
Simulation of Vedic Multiplier in DCT Applications Vaijyanath Kunchigi JNTU Hyderabad A.P, ... seminal bookVedic Mathematics, wrote about this special use of sutras[7]. ... VedicMaths': facts and myths, One India One People, Vol 4/6, January 2001, pp. 20-21; (available on
converted to subtraction and addition operations using VedicMaths. Square of both Average and Deviation is read out simultaneously by using a two port memory to reduce memory ... (book on civil engineering and architecture), which is an upa-veda (supplement) of Atharva
Here all the problems are worked out by different method from text book methods. All ... ICSE VEDICMATHS, NEPAL COUNTRY TEXT BOOKS. I hope this may be helpful to the student very much. Here more explanations are given for easy understanding and these explanations need not be
tions of solving multiplication with VedicMaths techmques and its applications in computing with the help ... He wrote a book called Vedic Mathematics, which is considered to be the startmg point of all research on Vedic Mathematics.
Vedic Mathematics for the New Millennium: DVD (Pub:2002) $ 45 100 gm Dolphin Human Connections: Jain shows VedicMaths ... The Book of Phi, Vol 1 (The Living Maths of Nature. Pub:2002, 172pp) $ 50 550 gm In The Next Dimension (The Book of Phi, Vol 2.
de Santillana and Hertha von Dechend (1969) in their famous book Hamlet's Mill which appeared more than twenty ve years ago. By uncovering the astronomical frames of myths from various ancient cultures, ... This brings us to the Vedic times of India. Veda means knowledge in Sanskrit. |
hematics: Its Power and Utility
Explores the power and historic impact of mathematics and helps students harness that power by developing an effective approach to problem solving. ...Show synopsisExplores the power and historic impact of mathematics and helps students harness that power by developing an effective approach to problem solving. This title also explores the utility and application of math concepts to a wide variety of real-life situations: money management; handling of credit cards; inflation; and, many other topics.Hide synopsis
Description:Very good. Hardcover. Instructor Edition: Same as student...Very good. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Has minor wear and/or markings. SKU: 9781111581527-3Fine. Hardcover. Instructor Edition: Same as student edition...Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9781111581527-2New. 1111577420 #Instructor's Edition. Identical to student...New. 1111577420 #Instructor's Edition. Identical to student edition except has publisher notations on cover and extra information for professors. Great way to save on this book. WE SHIP DAILY! !
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Reviews of Mathematics: Its Power and Utility
Excellent material for pre-high school studants, or for people who want to advance their understanding of math. Includes Alegebraic problem solving, Geometry,Statistics, Logic and Sets.
Well written, lots of illustrations |
The content of Algebra 1 is organized around families of functions, with special emphasis on linear and quadratic
The content of Algebra 1 is organized around families of functions, with special emphasis on linear and quadratic functions. In addition to its algebra content, Algebra 1 includes lessons on probability and data analysis as well as numerous examples and exercises involving geometry. 1 In addition to its algebra content, Algebra 2 includes lessons on probability and data analysis as well as numerous examples and exercises involving geometry and trigonometry. These math topics often appear on standardized tests, so maintaining your familiarity with them is important. To help you prepare for standardized tests, Algebra 2 In addition to its algebra content, Algebra 2 includes lessons on probability and data analysis as well as numerous examples and exercises involving geometry and trigonometry.
This market-leading text continues to provide students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a two-term course, the new Seventh Edition retains the features that have made Algebra and Trigonometry a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises.
As part of the market-leading Graphing Approach series by Larson, Hostetler, and Edwards, Algebra and Trigonometry: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality and quantity of the exercises, combined with interesting applications, cutting-edge design, and innovative resources, make teaching easier and help students succeed in mathematics. This edition, intended for algebra and trigonometry courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra |
Quantitative Aptitude is a book that's popular among every student who's registered for competitive exams or job interviews. It remains a bestseller till date, mainly because of its comprehensive nature.
Often considered as the absolute bible for every aspirant, Quantitative Aptitude by R. S. Aggarwal helps students prepare for competitive exams and job interviews. The book covers an array of topics and its content is split across two sections: Arithmetic Ability and Data Interpretation.
The book features extensive examples and exercises that cover topics like HCF/LCM, Decimal Fractions, Profit and Loss, Time and Distance, Chain Rule, Surds and Indices, Age Problems, Simple and Compound Interest, Probability, Heights and Distances, Volume and Surface Areas and Permutations and Combinations under the broad umbrella of Arithmetic Ability.
This is the perfect handbook for every student as the examples are easy to comprehend.
About The Author R.S. Aggarwal was born in the city of Delhi. A graduate from Kirorimal College in Delhi, he then took on a position in N.A.S. College as a teacher following his post graduation in Mathematics in the year 1969.
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Twelfth graders define limits and use the delta epsilon definition to solve limits. In this calculus lesson plan, 12th graders investigate the x and y axis using delta epsilon limits. They learn a song to help them remember the definition.
In this limiting reactants worksheet, students answer questions about basic everyday items such as sandwiches and cars to demonstrate the components used to make these items limit how many products can be made.
Students explore the concept of recursive sequences. In this recursive sequences lesson, students discuss the recursive routines involved in the intake/elimination of fluids in the body. Students collect data on the amount of medicine in the body over time.
Students create a Hexaflexagon using a formula. For this calculus lesson, students apply the definition of delta epsilon as it relates to limit to create a shape using creases. They relate the same rule to triangles and investigate angles.
Students investigate how even low concentrations of alcohol affect a person's functioning. They examine alcohol-related risks affect both the individual and the public. They create a policy for alcohol use and defend its use.
Students explore the local linearity of several functions at different points. They investigate the local linearity given a function and a point and then connect that notion with the function's differentiability at that point.
In this understanding limits, students determine the convergence of given sequences. They use properties of limits to evaluate functions. This two-page worksheet contains examples and explanations, as well as eleven problems.
Students study the limited government within the Declaration of Independence. They discuss the characteristics of a limited government in contrast to a despotic government. They identify principles of the limited government within the Declaration of Independence. They summarize the principles and prepare a paper or electronic display.
In this limits worksheet, students apply L'Hopital's rule to solve four limits problems. They solve a total of eleven short answer problems. The final seven problems ask students to find the asymptotes of functionsIn this college level calculus worksheet, students evaluate limit and indicate any limit rules they apply. If the limit does not exist they explain why. The two page worksheet contains seven problems. Answers are not provided.
Students view examples of art work that illustrate limits in calculus. Students will lecture on limits and then complete practice drill. This lesson does not include a defined procedure or practice problems. All the art links work but none of the other ones available do.
Students compare and contrast the characteristics of a limited and unlimited government. In groups, they use this information to create a chart and write a description of how leaders are chosen in each. They share their information with the class to end the lesson plan.
Students are introduced to the concept of population fluctuation. In groups, they participate in a penguin activity in which they discover how populations are affected by various factors. They relate what these new terms mean for a population as a whole.
Students debate imposing tariffs on imported shoes. In this tariffs lesson, the class is divided into two groups: those that oppose a tariff on imported shoes, and those that support it. Groups read about each position, write position statements, and take turns presenting their perspectives until one side convinces the other or time runs out. |
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Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources |
guide updated and expanded for today's mathphobes Written by two pioneers of the concept of math anxiety and how to overcome it, Arithmetic and Algebra Again has helped tens of thousands of people conquer their irrational fear of math. This revised and expanded second edition of the perennial bestseller: Features the latest techniques for breaking through common anxieties about numbers Takes a real-world approach that lets mathphobes learn the math they need as they need it Covers all key math areas--from whole numbers and fractions to basic algebra Features a section on practical math for banking, mortgages, interest, and statistics and probability Includes a new section on the graphing calculator, a chapter on the metric system, a section on word problems, and all updated exercises |
Alpine, NJ AlgebraVarious parts of discrete math were used in all the other math courses I took as well. I used elements of discrete math and graph theory to invent a new online authentication method. The company I worked for (RSA security) has filed for a patent and listed me as the primary inventor. |
Select Contents 1. Ancient and non-Western traditions 2. The Western Middle Ages and the Renaissance 3. Calculus and mathematical analysis 4. Functions, series and methods in analysis 5. Logic, set theories, and the foundations of mathematics 6. Algebras and number theory 7. Geometries and topology 8. Mechanics and mechanical engineering 9. Physics and mathematical physics, and electrical engineering 10. Probability and statistics, and the social sciences 11. Higher education and institutions 12. Mathematics and culture.
(source: Nielsen Book Data)
Publisher's Summary:
This Companion Encyclopedia examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century. In 176 articles contributed by authors of 18 nationalities, the work describes and analyses the variety of theories, proofs, and techniques, as well as practical applications, of pure, applied and statistical mathematics. It demonstrates the importance of the subject today, treating its historical interactions with the related disciplines of physics, astronomy, engineering, philosophy and the social sciences. It also covers the history of higher education in mathematics and the growth of institutions and organizations connected with the development of the subject. Special Features * 176 articles contributed by authors of eighteen nationalities * Annotated bibliographies of both classic and contemporary sources * Unique coverage of Ancient and non-Western traditions of mathematics * illustrated with line figures, 47 half-tones and 3 tables * Chronological table of main events in the development of mathematics * Fully integrated index of people, events and topics. (source: Nielsen Book Data) |
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The purpose of this collection of applets and activities is to make students familiar with the basic principles of complex numbers. Combining explanatory text, exercises and interactive GeoGebra applets, this resource is suitable for both classroom lectures and distance learning.
Geometry Playground (v1.3) is a free Java application for doing "ruler and compass" constructions in both Euclidean, Spherical, Projective, Hyperbolic, Toroidal, Manhattan and Conical geometries. Its purpose is to help users develop a familiarity with various conceptualizations of these geometries. |
All professional education content courses leading to certification shall include teaching and assessment ofthe Wisconsin Content Standards in the content area.
In this column, list the Wisconsin Content Standards that are included in this course. The Standards for each content area are found in the Wisconsin Content Standards document.
In this column, indicate the nature of the performance assessments used in this course to evaluate student proficiency in each standard.
The structures within the discipline, the historical roots and evolving nature of mathematics, and the interaction between technology and the discipline.
Both computers and calculators are used to develop mathematical ideas, solve problems, and to study the structure of mathematics.
Facilitating the building of student conceptual and procedural understanding.
Homework, tests, and labs using both computers, models, and manipulatives focus on conceptual understanding and how / why procedures/ algorithms work. Students are assessed on their understanding and ability to model the use of manipulatives both in lab/homework and on tests. Manipulatives such as base blocks, Cuisenaire rods, pattern blocks, and polydrons, are used to model mathematical concepts and principles.
Helping all students build understanding of the discipline including:
. Confidence in their abilities to utilize mathematical knowledge.
. Awareness of the usefulness of mathematics.
. The economic implications of fine mathematical preparation.
The focus of the course is building understanding of mathematics and is demonstrated through labs in class in the computer lab, homework, tests, and projects. Applications, especially through projects and labs build confidence and awareness of the usefulness of mathematics.
Exploring, conjecturing, examining and testing all aspects of problem solving.
Through labs, homework, and tests, students demonstrate their knowledge of strategies. Labs provide an environment for exploring, conjecturing, and solving problems. This is an area of focus in the course and is utilized throughout the semester.
As pre-service teachers, students create mathematical tasks/problems for future students to solve both in lab and on written assessments (homework, tests) Students also share their problems and solutions in class and compare strategies.
Proofs without words, using models and diagrams in labs, homework, and tests. Inductive and deductive arguments are developed when focusing on patterns (specific to general) shared in small group discussion, homework and tests.
Expressing ideas orally, in writing, and visually-, using mathematical language, notation, and symbolism; translating mathematical ideas between and among contexts.
Connecting the concepts and procedures of mathematics, drawing connections between mathematical strands, between mathematics and other disciplines, and with daily life.
Students ability to solve practical problems using technology and paper and pencil methods on labs, homework, and tests. Completion (and demonstration) of a technology integrated project connecting mathematics and other disciplines and daily life.
Selecting appropriate representations to facilitate mathematical problem solving and translating between and among representations to explicate problem-solving situations.
Students share their representation methods used in solving problems and discuss these in a lab setting. Discussing advantages and disadvantages of these approaches.
Mathematical processes including:
. Problem solving.
. Communication.
. Reasoning and formal and informal argument.
. Mathematical connections.
. Representations.
. Technology.
As a standards based math curriculum, students exhibit their abilities related to problem solving, communication, reasoning, representations, connections, and use of technology through discussion, labs, projects, homework, and tests (applied to the current math content topic).
Number operations and relationships from both abstract and concrete perspectives identifying real world applications, and representing and connecting mathematical concepts and procedures including:
. Number sense.
. Set theory.
. Number and operation.
. Composition and decomposition of numbers, including place value, primes, factors, multiples, inverses, and the extension of these concepts throughout mathematics.
. Number systems through the real numbers, their properties and relations.
. Computational procedures.
. Proportional reasoning.
. Number theory.
Number sense, number and operations, number systems, and computational procedures as related to rational numbers and integers are a focus of this course. Students demonstrate their knowledge in class discussion, through homework, labs, projects, and tests.
Set theory, in particular set operations as used to solve probability problems, are assessed through labs, homework, and exams.
Number systems through the real numbers, their properties and relations, and proportional reasoning are assessed through homework, labs, and tests.
Number theory focusing on divisibility and the fundamental theorem of arithmetic is assessed through homework, labs, and exams.
Mathematical concepts and procedures, and the connections among them for teaching upper level number operations and relationships including:
. Advanced counting procedures, including union and intersection of sets, and parenthetical operations.
. Algebraic and transcendental numbers.
. The complex number system, including polar coordinates.
. Approximation techniques as a basis for numerical integration, fractals, and numerical-based proofs.
. Situations in which numerical arguments presented in a variety of classroom and real-world situations (e.g., political, economic, scientific, social) can be created and critically evaluated.
. Opportunities in which acceptable limits of error can be assessed (e.g., evaluating strategies, testing the reasonableness of results, and using technology to carry out computations).
Counting procedures, set operations (including union, intersection, and complement) and parenthetical operations are demonstrated through lab work, homework, and quizzes.
Estimation and approximation techniques are used to check the reasonableness of results, especially in problem solving situations in the homework and in the lab.
Calculators and computers are used to carry out complicated computations.
Geometry and measurement from both abstract and concrete perspectives and to identify real world applications, and mathematical concepts, procedures and connections among them including:
. Formal and informal argument.
. Names, properties, and relationships of two- and three-dimensional shapes.
. Spatial sense.
. Spatial reasoning and the use of geometric models to represent, visualize, and solve problems.
. Transformations and the ways in which rotation, reflection, and translation of shapes can illustrate concepts, properties, and relationships.
. Coordinate geometry systems including relations between coordinate and synthetic geometry, and generalizing geometric principles from a two-dimensional system to a three-dimensional system.
. Concepts of measurement, including measurable attributes, standard and non-standard units, precision and accuracy, and use of appropriate tools.
. The structure of systems of measurement, including the development and use of measurement systems and the relationships among different systems. Measurement including length, area, volume, size of angles, weight and mass, time, temperature, and money.
. Measuring, estimating, and using measurement to describe and compare geometric phenomena.
. Indirect measurement and its uses, including developing formulas and procedures for determining measure to solve problems.
Informal argument, proofs without words, through models and diagrams are used by the student in lab, homework, and tests.
Names, properties, relationships of three-dimensional objects, spatial sense, spatial reasoning and the use of geometric models are used to represent, visualize, and solve problems, and are assessed through labs using models such as polydrons and 3-d solids, homework, and tests.
Concepts of measurement and estimation, including measuring attributes, standard and non-standard units, precision, accuracy, and use of non-standard units to measure surface area and volume are assessed through discussion in class lab, use of computer software, homework, and tests.
Indirect measurements using similarity are assessed using labs, homework, and exams.
The structure of systems of measurement, including the development and use of measurement systems and the relationships among different systems, are assessed through discussion in class lab, use of computer software, and through homework and exams.
Mathematical concepts, procedures, and the connections among them for teaching upper level geometry and measurement including:
. Transformations, coordinates, and vectors and their use in problem solving. Three-dimensional geometry and its generalization to other dimensions. Topology, including topological properties and transformations.
. Opportunities to present convincing arguments by means of demonstration, informal proof, counter-examples, or other logical means to show the truth of statements and/or generalizations.
Opportunities to present convincing arguments by means of demonstration, informal proof, counter-examples, or other logical means to show the truth of statements and/or generalizations are given in class, lab, through the use of computer software and in tests.
Statistics and probability from both abstract and concrete perspectives and to identify real world applications, and the mathematical concepts, procedures and the connections between them including:
. Use of data to explore real-world issues.
. The process of investigation including formulation of a problem, designing a data collection plan, and collecting, recording, and organizing data.
. Probability as a way to describe chances or risk in simple and compound events.
. Outcome prediction based on experimentation or theoretical probabilities.
Use of data to explore real-world issues is assessed through in class labs and homework.
The process of investigation including formulation of a problem, collecting, recording, and organizing data is assessed through labs, homework, and tests.
Data representation through graphs, tables, and summary statistics to describe data distributions, central tendency, and spread are assessed through labs, homework, and exams.
Randomness, probability as a way to describe chances or risk in simple and compound events, and outcome analysis and prediction based on experimentation or theoretical probabilities are assessed through labs, through the use of software, and homework, projects, and tests.
Data collection for experiments using real game implements both from our present culture and implements from previous cultures and cultures outside the United States used by students in labs, homework, projects, and exams.
Mathematical concepts, procedures, and the connections among them for teaching upper level statistics and probability including:
. Use of the random variable in the generation and interpretation of probability distributions.
. Descriptive and inferential statistics, measures of disbursement, including validity and reliability, and correlation.
. Probability theory and its link to inferential statistics.
. Discrete and continuous probability distributions as bases for inference.
. Situations in which students can analyze, evaluate, and critique the methods and conclusions of statistical experiments reported in journals, magazines, news media, advertising, etc.
Descriptive statistics and situations where students analyze, evaluate, and critique methods and conclusions based on probability experiments are used in labs, homework, and projects.
Functions, algebra, and basic concepts underlying calculus from both abstract and concrete perspectives and to identify real world applications, and the mathematical concepts, procedures and the connections among them including:
. Patterns.
. Functions as used to describe relations and to model real world situations.
. Representations of situations that involve variable quantities with expressions, equations and inequalities and that include algebraic and geometric relationships.
. Multiple representations of relations, the strengths and limitations of each representation, and conversion from one representation to another.
Concrete models are used to solve problems, demonstrate mathematical concepts and procedures. These models are demonstrated and discussed by students in lab using manipulatives and computer software, as well as being assessed in homework, and tests.
Discrete processes from both abstract and concrete perspectives and to identify real world applications, and the mathematical concepts, procedures and the connections among them including: |
O Level Mathematics (syllabus D) (4024)O Level Mathematics (syllabus D) (4024) 1/1 O Level Mathematics (syllabus D) (4024) Will students be given a formula sheet to help them in the exam or do they need to |
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Game Theory and Strategy by Philip Straffin
Game Theory and Strategy is an elegant, crystal clear expository work. Key concepts are emphasized and clearly explained. --Nature
The range of problems discussed is truly extraordinary...The only mathematical background necessary is that found in the college track high school curriculum...Well worth the (small) effort it takes to read, this book will hopefully lead to an expansion of game theory into many areas where it is currently underutilized. --Mathematics and Computer Education
This important addition to the New Mathematical Library series pays careful attention to applications of game theory in a wide variety of disciplines. The applications are treated in considerable depth. The book assumes only high school algebra, yet gently builds to mathematical thinking of some sophistication. Game Theory and Strategy might serve as an introduction to both axiomatic mathematical thinking and the fundamental process of mathematical modelling. It gives insight into both the nature of pure mathematics, and the way in which mathematics can be applied to real problems. |
This book introduces MDS as a psychological model and as a data analysis technique for the applied researcher. It also discusses, in detail, how to use two MDS programs, Proxscal (a module of SPSS) and Smacof (an R-package). Thebook is unique in its orientation on the applied researcher, whose primary interest is in using MDS as a tool to build substantive theories. This is done by emphasizing practical issues (such as evaluating model fit), by presenting ways to enforce theoretical expectations on the MDS solution, and by discussing typical mistakes that MDS users tend to make. The primary audience of this book are psychologists, social scientists, and market researchers. No particular background knowledge is required, beyond a basic knowledge of statistics.
The Practical Zone System: for Film and Digital Photography 4th edition is an updated version of what has become the classic book on thetechnique developed by Ansel Adams in the 1940's. The zone system was designed to provide photographers with a precise and intuitive way to control the dynamic range of their negatives to produce printable results regardless of the contrast of the subjects they are shooting.
Practice makes perfect-and helps deepen your understanding of algebra 1 You start with some basic operations, move on to algebraic properties, polynomials, and quadratic equations, and finish up with graphing. |
More than 140 schools are currently teaching with Eric Schulz's interactive digital textbook.
WALLA WALLA - In his State of the Union address last week, President Obama discussed how students will be able to "take classes with a digital textbook" as part of the digital age.
Walla Walla Community College mathematics professor Eric Schulz has authored an interactive digital math textbook that allows students to do just that.
Schulz co-wrote a new calculus book released this year by Pearson, the world's largest textbook company. Schulz was responsible for the interactive e-book, which includes more than 650 interactive aspects.
The e-book covers four college courses of calculus and costs $75, as compared to $180 for a traditional book in print form.
The e-book includes the same information as the print book, but all of the illustrations are interactive. The illustrations allow students to rotate three-dimensional graphs and see the graphs move as the variables change. Rather than looking at a static image on a page, the students can better visualize the image in multiple dimensions. The electronic format brings the concepts alive.
"It is the only completely interactive e-book I know of," Schulz said. "The main goal I had was to bring the book alive."
Schulz said he is a visual learner who grasps concepts better through images than through text. He wanted to make it easier for visual learners to understand mathematical concepts.
"In the world of mathematicians, some of us are really heavy in terms of visual thinkers," Schulz said. "I was in that group of visual learners."
One benefit of having the interactive aspect is that the illustrations better reinforce the concepts than a traditional textbook.
"By putting the figures right in the midst of the words, you create what we call a 'dance.' The reader is going back and forth between the two. The pictures reinforce the words, and the words explain the pictures," Schulz said.
Schulz used his extensive background in teaching calculus to design the interactive illustrations so students can easily understand them.
"Every one of those figures benefits from 25 years of teaching in calculus and understanding what it is a student needs to see, and what it is that I want them to pull out of that visualization," Schulz said.
Schulz hopes that eventually all textbooks will have e-book components. And he hopes that rather than using static pdf versions that do not offer interactive elements, that the e-books will all be interactive.
This interactive e-book is incredibly useful not only for students, but for professors as well, he said. Schulz noted not all colleges have the resources to visually represent all of the concepts. With the e-book, professors can use the interactive illustrations in their lectures, and then the students will have the same illustrations in their e-books for when they are studying later.
"It becomes an innovative way of using a resource to teach in the class that connects to the students studying later on," Schulz said.
More than 140 schools are currently teaching with this textbook in either digital or print form. These schools include Walla Walla Community College, Yale University, Vanderbilt University, Oregon State University and the University of Virginia, among others.
The book was just released this fall, but is already the most successful first-edition calculus book published in the past five years, Schulz said. Pearson honored the textbook with awards for the product of the year in college-level arts and sciences, and well as for the product of the year at any academic level. |
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Beginning Algebra:The Lial series has helped thousands of students succeed in developmental mathematics through its friendly writing style, numerous realistic examples, extensive problem sets, and complete supplements package. In keeping with its proven track record, this revision includes a new open design, more exercises and applications, and additional features to help both students and instructors succeed.
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Rent Beginning Algebra 9th edition today, or search our site for Margaret L. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. |
A unit designed to improve students' understanding and appreciation of basic geometric shapes used in architecture. It describes various plane geometric figures and discusses in detail the properties of several of these...
A searchable index of the CAD Centre, a postgraduate teaching and research unit in design manufacture and engineering management, with research focused on design methods and computer support of the design process for...
This site has information regarding the U.S. Army?s requirements for the construction and performance of aircraft power plants, brought to you by GlobalSecurity.org. The basic requirements, including reliability, d...
A community dedicated to high-quality mathematics instruction at the adult level. ANN conducts pre-conferences at the annual NCTM national meetings; publishes the Math Practitioner Newsletter; sponsors the Numeracy List... |
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Building on principles learned in algebra and geometry, calculus deals with limits. Two sub-categories of calculus are differential calculus and integral calculus. Integral calculus deals with the idea of accumulation, while differential calculus deals with the rate of change. These calculus courses and lectures give you insight into this branch of mathematics and help you understand the concepts involved. |
Should College Classes Ditch the Calculator?
Should College Classes Ditch the Calculator?
According to Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research and Development Center, using calculators in college math classes may be doing more harm than good. In a limited study conducted with undergraduate engineering students and published in the British Journal of Educational Technology, King has determined that our use of calculators may be serving as an alternative to an actual, deep understanding of mathematical material.
"We really can't assume that calculators are helping students," says King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
King, along with co-author and director of the Mathematics Education Centre at Loughborough University, Carol Robinson, conducted the study by interviewing 10 second-year undergraduate students who were enrolled in a competitive engineering program. The students were given a number of mathematical questions dealing with sine waves, which are mathematical curves that describe a smooth repetitive oscillation. To help solve the problems, the students were given the option of using a calculator instead of completing the work entirely by hand. Over half of the students questioned opted to utilize their calculators in order to solve the problems and plot the sine waves.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," says King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the work, King and Robinson interviewed the students about how they approached the material. One student who used the calculator stated that she had trouble remembering the rules for how sine waves operate, and found it generally easier to use a calculator instead. In contrast, however, a student who opted to complete the work without a calculator stated that they couldn't see why anyone would have trouble completing the question, but did admit that it would likely be easier with a calculator. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
Given the small sample size used in the study, it is entirely possible that King's findings are largely anecdotal in how our usage of calculators and understanding of mathematical concepts may positively or negatively correlate. However, King does stress that while all the evidence may not be in, his study does raise important questions regarding how, when and why students choose to use calculators, and in doing so, we may develop a more holistic approach to math instruction |
31
SUBJECTS OF INSTRUCTION
MATHEMATICS.
Dr. Dalley.
Mr. Robb.
Mr. Woodbury
Algebra a. This course affords a thorough. and complete treatment of addition and subtraction, parentheses, multiplication, division, simple equations, factoring, highest common factor, lowest common multiple, fractions, simultaneous equations, inequalities, involution, theory of exponents, radicals, quadratic equations, and equations solved like quadratics.
Wells's The Essentials of Algebra is the text book in use.
Five hours per week throughout the year.
Algebra b. This course treats simultaneous quadratic equations, theory of quadratic equations, ratio, proportion, and variation, arithmetical, geometrical, and harmonica) progressions, imaginary numbers, and logarithms.
Two hours per week throughout the year.
Plane Geometry. This course covers the five books in plane geometry It aims to familiarize the students with the forms of rigid deductive reasoning, and to develop accuracy of statement and the power of logical proof. Considerable time is devoted to the demonstra- |
Click on a spirolateral in one of these galleries to display a full-size version; see a self-running demonstration of a variety of spirolaterals, or generate one of your own and see all the reversals. "The Art of...
Utilizing dynamic models to explain different aspects of geometry can be a powerful pedagogical tool. This is exactly what inspired Eduardo Veloso and Rita Bastos to write this classroom exercise for the Mathematical...
Rewritten and updated excerpts from the 30th Edition of the CRC Standard Mathematical Tables and Formulas. Covers all of geometry, minus differential geometry. Very complete collection of definitions, formulas, tables...
A 3rd grade lesson plan on "Seeing Near and Far": students learn how overlapping and size differences show perspective, and that on a level surface, the lowest part of a near subject is lower in a picture than the...
This course, designed for Miami Dade Community College, integrates arithmetic and beginning algebra for the undergraduate student. By applying math to real-life situations most students experience during college, the... |
Video Summary: This learning video presents an introduction to graph theory through two fun, puzzle-like problems: "The Seven Bridges of Königsberg" and "The Chinese Postman Problem". Any high school student in a college-preparatory math class should be able to participate in this lesson. Materials needed include: pen and paper for the students; if possible, printed-out copies of the graphs and image that are used in the module; and a blackboard or equivalent. During this video lesson, students will learn graph theory by finding a route through a city/town/village without crossing the same path twice. They will also learn to determine the length of the shortest route that covers all the roads in a city/town/village. To achieve these two learning objectives, they will use nodes and arcs to create a graph and represent a real problem. This video lesson cannot be completed in one usual class period of approximately 55 minutes. It is suggested that the lesson be presented over two class sessions |
It's very good at calculus and analysis and pretty good at most areas of math. The recent versions include lots of data sets from fields outside of math in an (apparent) attempt to broaden its appeal; it seems to work pretty poorly outside of pure math. Within math the only program that comes close to its scope is Maple, though within particular fields there are programs that improve on it. For example, in number theory PARI/GP is usually better; in algebra GAP is usually more appropriate; in statistics R is more powerful; for linear algebra Matlab is hard to beat.
If you have the money and you don't see yourself working in one of those narrower fields Mathematica is a good choice. Even if you do it's worth using if your university has a licensing program that lets you use a copy for cheap or free.
As a Example in Wolfram Alpha we input the radius (r) of a circle = 1, Answer is Pi=22/7=3.14
plotting the Circle figure with radius =1.
Now the User entering the text in English (for English version), if the user is entering the french version, the end user of the application will type in french characters and the answer will be in french content. |
Lesson study is a professional development process that teachers engage in to systematically examine their practice, with the goal of becoming more effective. Originating in Japan, lesson study has gained significant momentum in the mathematics education community in recent years. As a process for professional development, lesson study became highly... more...
Build student success in math with the only comprehensive guide for developing math talent among advanced learners. The authors, nationally recognized math education experts, offer a focused look at educating gifted and talented students for success in math. More than just a guidebook for educators, this book offers a comprehensive approach to mathematics... more...
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing... more...
This Ebook is designed for science and engineering students taking a course in numerical methods of differential equations. Most of the material in this Ebook has its origin based on lecture courses given to advanced and early postgraduate students. This Ebook covers linear difference equations, linear multistep methods, Runge Kutta methods and finite... more...
This book covers the discourse and equity in mathematics education research. Given the inherent connection between discourse and equity, this book focuses on two approaches to the connection. Contributors consider the ways in which the social, mathematical, cultural, and political aspects of classroom interactions impact students' opportunities... more...
This book considers the views of participants in the process of becoming a mathematician, that is, the students and the graduates. This book investigates the people who carry out mathematics rather than the topics of mathematics. Learning is about change in a person, the development of an identity and ways of interacting with the world. It investigates... more... |
3.2 Keeping a record: a learning file This unit explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognise mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the Calculator Book, Tapping into Mathematics With the TI-83 Graphics Calculator. The unit ends by asking you to reflect on the process of studying mathematics. In order to complete this unit you will need to have obtained a Texas I Symmetry in three dimensions We all encounter symmetry in our everyday lives, in both natural and man-made structures. The mathematical concepts surrounding symmetry can be a bit more difficult to grasp. This unit explains such concepts as direct and indirect symmetries, Cayley tables and groups through exercises, audio and videoEgyptian mathematics The Egyptians are known for being ahead of their time in comparison to some civilisations that came after them. This unit looks at how the Egyptians solved mathematical problems in everyday life and the technology they used. An understanding of this area has only been possible following the translation of the Rosetta StoneGlobal Eradication of Infectious Diseases: Can 'Not Very Much' undermine the goal of 'None at All'? Despite the well-publicised success of global smallpox eradication, 'zero' remains an elusive goal for the majority of vaccine-preventable diseases, making reduced pathogen circulation, or direct protection of the vulnerable more achievable strategies. We will consider potential deleterious consequences of reduced infection transmission, in the context of diseases such as influenza and pertussis, where immunity following natural exposure may be superior to that following immunisation. Implicati Author(s): Jodie McVernon
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Stability and Complexity in Model Banking Systems The recent banking crises have made it clear that increasingly complex strategies for managing risk in individual banks and investment funds (pension funds, etc) has not been matched by corresponding attention to overall systemic risks. Simple mathematical caricatures of 'banking ecosystems', which capture some of the essential dynamics and which have some parallels (along with significant differences) with earlier work on stability and complexity in ecological food webs, have interesting implic Author(s): Robert May
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Learning to Think Mathematically Concerned that most students leave college thinking of mathematics as a fixed body of knowledge to be memorized, Cooperstein designed a new course to help students learn to think mathematically for themselves. This website serves as a course portfolio that documents the new class, Introduction to Mathematical Problem Solving. The principal activity in the class involved students working on and discussing novel problems which required them to formulate experiments, work out cases, look for patter Author(s): No creator set
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DNA Microarrays: Background, Interactive Databases, and Hands-on Data Analysis DNA microarrays are influencing many areas of biology. DNA microarrays allow investigators to measure simultaneously the activity of every gene in a genome. This paper provides the reader with background information, a set of interactive questions, and most importantly, free software (MAGIC Tool) for use in the undergraduate curriculum. MAGIC Tool ( resources allow the user to understand how DNA microarray data are analyzed by providing raw data, instructions, mathemat Author(s): No creator set
Classroom Innovations through Lesson Study Classroom Innovations through Lesson Study is an APEC EDNET Project that aims to improve the quality of education in the area of Mathematics. This project is sponsored by APEC Members Japan and Thailand. The APEC-Tsukuba International Conference III was broadcast live from Tokyo, December 9-10, 2007. The project has produced useful papers describing mathematical thinking, lesson videos of classroom instruction.
This project focuses on Lesson Study with the goal of improving the quality of educatPrivate Universe Project in Mathematics: Workshop 2. Are You Convinced? Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proof—proof by cases and proof by induction—naturally grow out of the need to justify and convince others.,Englewood, New Jersey—Teachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part to give Author(s): Harvard-Smithsonian Center for Astrophysics
The Great Magnet, the Earth This site provides a non-mathematical introduction to the magnetism of the Earth, the Sun, the planets and their environments, following a historical thread. In 1600, four hundred years ago William Gilbert, later physician to Queen Elizabeth I of England, published his great study of magnetism, "De Magnete"--"On the Magnet". It gave the first rational explanation to the mysterious ability of the compass needle to point north-south: the Earth itself was magnetic. "De Magnete" opened the era of mo Author(s): No creator set
I am finding my students are increasingly using spreadsheets to solve mathematical problems in class and represent their data and findings in meaningful ways. Th
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Rights not set14.12 Economic Applications of Game Theory (MIT) Game Theory is a misnomer for Multiperson Decision Theory, the analysis of situations in which payoffs to agents depend on the behavior of other agents. It involves the analysis of conflict, cooperation, and (tacit) communication. Game theory has applications in several fields, such as economics, politics, law, biology, and computer science. In this course, I will introduce the basic tools of game theoretic analysis. In the process, I will outline some of the many applications of game theory, pr Author(s): Yildiz, MuhametWorkshop 2: Intellectual Development Explore the power of the mind and consider the notion that every child can learn everything. Harvard Professor Eleanor Duckworth discusses the importance of teaching for a deep and lasting understanding and explains why it is important to give students time to work through their own ideas and experience confusion in order to achieve such understanding. Author(s): No creator set |
I recently declared a philosophy major to go along with my secondary education/social studies B.S.. I am having second thoughts about the secondary ed major however. My university offers quite a variety of Mathematics majors. I've never been that great at math (I failed algebra in high school), but I going to dedicate a lot of time over the summer towards refreshing and learning new concepts. The farthest I went was algebra II, and I'm in a 091 course right now (passing with a 125/130) that covers intermediate algebra. I plan on going as far as I can independently; ideally, up to pre-calc. I am not at the point where I am seriously considering a math major, but if I get to the point where I genuinely enjoy it, I'll go in that direction. Maths also compliment Philosophy extremely well considering a huge chunk of modern analytic philosophy revolves around symbolic logic (which I love).
Are there any Math majors here, and is there anyone who has been in or is currently doing a MA or PhD?
If there are, I'd love some recommendations as far as books, sites, or general resources when it comes to independent mathematical studies go. Please don't recommend my mom or something like that. =)
Not a math major but my field uses quite a lot of math (mostly applied though) and I really good resource I've been using is this siteL
very helpful and "reader-friendly" and has lots of examples/pictures when necessary.
from the theory that we've done so far, I can definitely say that high school math is not a good indicator of what math is really about - the focus in high school is primarily computation and memorizing certain algorithms but there is a lot more to math. take a look at the link I posted, and read through a few proofs (maybe this one? and you'll see that there is a world of difference between the math presented there and the one you see in high school.
@silentstar Thanks for the link. I was looking for something almost identical to this.
@strangerthanfiction Math is actually one of the best fields to go into as far as well paying and intellectually rewarding jobs are concerned. Obviously, it helps to study something like economics or business where the math is integrated into a different area-of-emphasis. The same can't be said for philosophy, but I think its a shame. Philosophy revolves around critical thinking and effective reasoning. It's certainly the most rigorous subject within the humanities, and is the most diverse. There is no such thing as a philosophy class aside from the standard introductory classes. I plan on becoming a professor though.
If you want to major in math you should mix it with something useful. I love statistics, it is honestly one of my favorite subjects but the classes are so much work, and you would have to minor in math not statistics which sucks. Btw I'm in business majoring in marketing. I mean if you like math and like to think why not do like engineering or sociology at least math will be more applicable if you were to do it.
Hey I'm an engineering student and have been studying applied math and I would really recommend going through khan academy for your basic math like algebra refreshers and trig stuff. Then Once you think you are ready for calculus (single and multivariate) take the mit open courseware math courses. That will get you through calculus, linear algebra, and differential equations. At that point you should be pretty good at math and able to learn by just reading textbooks. I recommend going on to numerical analysis and possibly even abstract algebra at that point. You can find sample curriculum at a lot of schools websites. For calculus I strongly recommend the Stewart calculus books. I used the second edition and found it to be fantastic. It isn't too complex but it is brief and gives great examples. As far as getting better at basic math, honestly it's best to start at the very beginning. You would not believe how frequently I see new students fail math courses because they don't have the basics down. That being said,taking calc 1 and learning the pieces you don't know along the way is how I started.
@Funeralopolis I am practically cemented on doing a Philosophy major, but I plan on going all of the way to the PhD level. I am not sure which area though. I'm considering going into logistics and the philosophy of language, but my philosophy adviser often tells me that ethicists are very employable in the medial and corporate fields. I'd much rather seek the classic route and become a professor. Grad School programs within the humanities also provide decent stipends at the PhD level. It just seems natural to me to seek mathematics whether it be on my own, or in an academic environment. Analytic philosophy (the predominant school in the English-speaking world) is very mathematical as it deals with formal and symbolic logic, and often goes hand-in-hand with the natural sciences. In other words, a hell of a lot of Boolean Algebra and set-theory.
@Mchailas I'll have to check that out. I used Khan Academy ages ago when I was still in high school. I wasn't very serious about academics back then, I just used it for last-minute cramming. I'll probably have to start from factoring polynomials and quadratic equations. I'm very solid on pre-algebra, but I'm still shit at algebra II concepts. That, and I'm sure I've forgotten most of the Geometry and the Trig that I studied.
I considered majoring in math before deciding to switch to digital forensics and cybersecurity and getting my masters.
I then wanted to minor in english, but decided to minor in Arabic since it's relative to my ideal field. I can't tell you how often I've looked at another route and switched majors, but such is life. Whatever it is you do, be passionate about it. People say there is no money in philosophy, but you know, who would have thought there would be money in posting YouTube videos of yourself playing Xbox.
@Calc I could go the Dennett, Dawkins, and Hitchens route I suppose but, I honestly don't give a damn about religion or lack of religion for that matter. Philosophy doesn't have much of anything to do with religion anymore, unless one were to make preconceived strides towards making it about religion.
@SitarHero Cool. Was it just at an undergraduate level?
@puddlespuddles Right. I'd much rather follow my passions as opposed to doing something for the sole sake of making money. I plan on staying single as well. Obviously things don't always go as planned and in many cases, go contra to the desired outcomes, but there's no harm in forging and making honest efforts towards sticking to those plans. Being open to and considering change is important though. I think it's normal for people to switch careers numerous times in a given lifetime.
It's easy to get a job with any college degree. People are just freaking out about 'not getting a job after college' because they have 0 knowledge of history and have no idea that available jobs will be numerous in the next decade as the baby boomer generation dies.
The real threat is keeping technology safe and preventing any government or power structure from becoming too powerful. This will be hard living among a bunch of rats in a race trying to make as much money for themselves as possible because they have focused so hard on 'getting a job after college' they lose site of everything else in life but money.
Math drop-out here, thinking about going back to finish my last 2-3 semesters. The vague uselessness of the degree starting to gnaw at me so I dropped out and attempted some sort of "soul searching" or whatever and I'm right back where I started. Everything is useless anyway right? YOLO RIGHT
it absolutely puzzles me how stupid some students are.. you study what you like, and you will get good grades, a good job and happiness. you study something you hate, not only are you wasting 3 years, but ur gna get depressed, bored and your not going to get a job.
You can just tell by the wise tone in this guy Beefshoes' statements that he is going to be multiple
times more successful in essentially every criteria than the bitter people making jokes about him not getting a job. Karma at its finest.
@Sleaper Yeah, I love math. I used to find it agonizing, but that was during a time when I found everything except music frustrating: high school. I couldn't agree more. If baffles me at how many of my friends are seeking engineering and especially education degrees; yet not a single one of them has a passion for math, science, or other academic subjects. No matter where you are, your career or job is a major aspect of your life. I understand the drive towards earning as much money as possible, but I think it's just such a waste seeking something for the sake of money. I suppose money can buy a certain degree of happiness, but if you're earning that money through something that you enjoy, it has to be a fantastic feeling in comparison to the contrary. Of course, I've not been in either position so I don't know, and I am positive that it differs for everyone.
I don't understand the criticism and social stigma behind going into a field that isn't known for paying well. Some people genuinely look offended when I tell them that I'm majoring in philosophy. lol
People have no clue what philosophy even is. They just think 'bad degree', because they were told so by their television and are incapable of making decisions or forming opinions on their own due to their ignorance that makes toddlers of the 20th century seem informed.
Yeah. You can't do much of anything with it unless you get a PhD, but it depends on the area of emphasis. If you get an MA in logic, you could probably get your feet wet in software design and programming fairly easily, especially if you're good at maths.
Most philosophy undergrads take the LSAT and go to law school. I have no interest in that, or going $100,000 in debt.
Philosophy PhD programs often provide stipends if you take on a TA or a research position, so it's completely possible to go without going a single dollar in debt.
yeah can't stand when people talk about "networking" at university. but I guess it shouldn't be a surprise under an economic system like this when even human relationships are viewed only in economic terms
not sure what jobs you're referring to, especially when that statement means literally nothing without specifying the type of jobs + wages associated
counting aside specialists (mba, med school, law), your degree plays a huge role in your employment, particularly in sciences. I'm not well versed with the arts side but I can guarantee you an arts student would never be found in scientific research, programming, engineering, finance etc
It all depends on your effort. Philosophy degrees are relatively easy to obtain, yet that has nothing to do with the philosophy majors who obsess over their studies and actually learn something extremely valuable.
Yes it is about networking. The entire government is run by cronyism and despotism, there is no doubt that networking is the single most influential aspect of getting a job.
pure math is theoretical, engineering is applied. while we do enough derivations/proofs to get a decent sense of where everything comes from, getting a pure math degree will focus a lot more on such topics.
also, pure math => academia, while engineering => academia + industry
it really depends on your interests and where you see yourself: as far as I know, the two fields are not comparable enough to be called similar
Not that I know, but I would imagine it is not as hard as you imagine to get an engineering degree, judging by the people I know who have them. Yes they are good at math but they aren't genius' by any means.
@satellite what i meant by a "good job" is one where people pay you disgusting amounts for pitiful work - those are the jobs that require networking. Of course you will find a higher paying job with a different degree than a philosophy major, but what is debatable is whether you are actually happier with that job/money than a philosophy major - and not to be a dick, but judging by your tone vs Beefshoes - I highly doubt that is the case. I could be wrong though, best wishes
My aunt who is a psychology PHD once mentioned this study that showed people's happiness doesn't depend on money once they reach the point of not living in poverty and having enough to survive. I think the number was 45k a year, once you make that and aren't worried about being on the streets, the extra income, on average, doesn't result in greater happiness.
So if you ask me it's all about doing something you like with your 60 or so years left on earth rather than slaving a way for a piece of paper that people overrate in terms of the happiness it will bring you.
Also there are many ways to become rich without using your degree. Some of the best professional sports betters and poker players have philosophy degrees - it teaches logical thinking and there are numerous ways you can outwit people (for a monetary gain if you like) with that knowledge.
i don't work at a place to be happy and--not to be a dick--anyone who does is a fucking retard. i work there so can pay rent and have enough money left over to support my main ambitions and party and go on vacation and shit. in turn, i am very happy.
alsowhat did i say that was "versus beefshoes"? i was merely making fun of the sort of bullshit execuspeak that i hear the dullest of my dumb coworkers prattle on about every day.
Consider Physics/Astrophysics, it's a lot more interesting than at school (quantum mechanics, nuclear physics, cosmology etc) and also goes well with philosophy (goes better with it really than maths). The maths can get pretty heavy but it won't be as abstract as a pure maths degree.
Idk to me people insulting people on the internet, for no reason, implies a certain degree of unhappiness that Beefshoes is not displaying and you are. Like I said maybe I was wrong and you are just joking.
But what are your 'main ambitions'? And how do you think using up over half of your waking moments of life doing something you don't like will achieve them?
I mean there is a balance, you can be a teacher and love what you do and still have money and time for vacation and partying, making the most money possible and being happy aren't mutually exclusive but hearing people talk about 'philosophy is worthless' you would think they are.
I mean some people's main ambitions in life are to learn as much about the world around them before
they die for eternity. It sounds kind of shallow when you tell those people they are fucking retards
because they aren't slaving away half their lives to save up for a trip to Cancun where they can buy
hookers and drugs. It would be one thing if you couldn't afford rent etc. with a philosophy degree,
but that is clearly not the case; this is about adequate money vs lots of money and whether the effort
justifies the latter.
I'm planing on taking physics next year, but my school doesn't offer it as a major (sadly). My school is big on geology and biology. It probably has something to do with living in West Virginia. The coal mining industry is a huge industry here.
you're really going fully strawman on me here bro. when did i say philosophy is worthless? when did i even say anything directed to beefshoes? i hit ctrl+f and everything but couldn't find those comments :/
my main ambition is stand-up comedy, which i perform anywhere from 2-4 times a week. i get paid MAYBE in the mid double digits for this if i'm lucky, so until that changes i'm content working a dull office job where i can get high in my car and look at weird shit on the internet all day.
Nope. There's a history of religions course in the philosophy course outline, but I'll probably skip it and take something more useful and interesting like biomedical ethics. I can't speak for other states, but the public schools in West Virginia have an optional bible class up though the 8th grade. |
About This Book:
Mathematical Introduction to Fluid Mechanics presents some selected highlights of currently interesting topics in fluid mechanics in a compact form, as well as providing a concise and appealing exposition of the basic theory of fluid mechanics. The first chapter contains an elementary derivation of the equations, and the concept of vorticity is introduced. The second chapter contains a discussion of potential flow, vortex motion, and boundary layers. A construction of boundary layers using vortex sheets and random walks is presented. Chapter 3 contains an analysis of one-dimensional gas flow from a mildly modern point of view. Weak solution, Riemann problems, Glimm's scheme, and combustion waves are covered |
PreAlgebra ActivityCreates instant, customized worksheets for over 2 dozen pre-algebra topics, including solving equations, simplifying functions, graphing lines, graphing points, statistics, function tables, slope and intercepts, reading graphed points, and much more. Varying levels of difficulty and specific math skills can be selected for each generated worksheet. The program can print custom graph papers as well as quadrant-graph worksheets. Create multiple choice, fill-in, or matching quizzes. Fun worksheets such as graphing secret pictures and equation riddle sheets can be created instantly. Answer sheets are generated for every activity.
Very easy to print worksheets for all sorts of things my daughter needs. Everything is laid out well and intuitive. I was making practice sheets in minutes. Website says the program was written by a teacher--- and it shows.
Cons
The interface is a bit clunky-looking, but it's easy to use and the printed sheets are nice.
Summary
Highly recommended. It made equation practice sheets (with answer keys! That's important!) that my daughter could begin working with right away. The price is also dirt cheap, so no complaints all-around |
Using spreadsheets to foster algebraic reasoning in the middle school mathematics classroom
Author:
Chávez-López, Óscar, 1963-
Date:
2003-04-11
Abstract:
What is Algebra? For most people, algebra means using and manipulating (algebraic)
symbols, and solving equations. The Algebra Standard, as it is stated in the Principles and Standards for School Mathematics, expects more than that from students and teachers. In this workshop we will address some of the ways in which spreadsheets can help to promote algebraic thinking in the middle school mathematics classroom.
URI:
Items in MOspace are protected by copyright, with all rights reserved, unless otherwise indicated. |
The CSM Course covers the most important academic skills for educational and professional success:
Math and literacy skills for academic success.
Math and Literacy Skills for Academic Success
The CSM curriculum comprises the most important skills that are used across many
occupations and industries, as well as in college. The goal is to give students
the skills that they will need as they progress in their career path, as well as
the skills that they will rely on to succeed through college.
CSM aims for skills to be transferable by students into their classes, work and lives.
Towards that goal, CSM emphasizes the following:
Depth of Understanding. CSM teaches skills in ways that emphasize conceptual
understanding. For example, most curricula treat the concept of percents as simply
a set of procedures, like "What is 20% of 240?". In contrast, take a look at the
CSM percent problem below:
This problem requires students to have an deep and intuitive sense of percents, to
understand scale and magnitude, and to have facility with mental math -- it can't
be done procedurally.
Integrated Math and Literacy. Math and literacy are almost always taught
in isolation from each other, but most issues that come up in the workplace require
both math and literacy to solve. CSM problems integrate math and literacy, which also allows
CSM to tackle some integrated problems that slip between the silos of conventional
math and literacy instruction.
Workforce Contextualized. All problems on CSM are workforce contextualized,
so students understand the importance and applications of the skills they are learning.
The CSM curriculum teaches the skills that are used every day in academic programs, and further support
decision-making in the workplace. CSM emphasizes depth of understanding and fluency of these skills.
Problem-solving and thinking skills.
Problem-Solving and Thinking Skills
CSM has an explicit problem-solving and thinking skills curriculum that extends across
the CSM Course and into the Challenge Problems.
CSM Course
In the CSM Course, problem-solving focuses on planning. Students often don't realize
that there are two steps to a solving a problem -- planning and execution (as their
coursework usually focuses almost exclusively on the execution of isolated procedures). CSM
emphasizes the planning step by giving students problems where they are just asked to
plan the solution (but not carry out their plan), and simultaneously teaches problem-solving
strategies like chunking, sequencing, working backwards, and more.
Challenge Problems
In the Challenge Problems (optionally taken after completion of the CSM Course, and also
free), students are faced with increasingly difficult problems that
climb Bloom's Taxonomy. They learn how to
attack problems that they've never seen before, which might include
problems with contexts in which the student is unfamiliar, or problems with
solutions that requires methodologies that the student hasn't been taught. The Challenge
Problems contain hints rather than direct instruction to encourage students to figure out the
solution on their own and earn an "aha" moment.
CSM equips students with specific problem-solving strategies and the problem-solving
mindset to help them tackle real-world challenges.
Active learning.
Active Learning
A major focus of CSM is teaching students how to learn skills on their own. It's
good if a student knows a skill, but it's GREAT if the student learned the skill
independently.
Why is this important? Independent
learning is the hallmark of a college student who is ready to succeed, and an employee who
can adapt to changing work and technology.
CSM transforms student learning in many ways, including:
Thinking about thinking and learning. Metacognition is a critical skill for
independent learning -- a good learner will consistently be reflecting on their own
learning, what they know and don't know, and what they could do to learn something better.
CSM consistently challenges students to think about their own learning through
"reflection questions" that ask them how they are feeling about the skill, and
whether they need more help.
Multiple learning styles and lesson types. CSM knows that different students
learn in different ways. CSM provides conceptual
(cognitivist) and procedural (behaviorist) lessons for every skill, with other
lessons such as contextual (constructivist) examples, multiple solutions (so that
the student can find their own best solution), tips, advice on checking the answers,
etc. CSM provides students with feedback on what they're reading and whether or not
it is helping them learn. It also suggests specific lessons that might be particularly
useful for the student.
Teacher focus on teaching learning. In most computer-based learning, the purpose of
the teacher is the instructor of last resort. In CSM, the role of the teacher is
to teach learning, not skills. Thus, students must learn on their own in order to
progress through the curriculum.
Learning through reading. Most student learning in school is through passively
listening to a teacher lecture. Instead, CSM focuses on learning through reading,
because it is the most powerful form of learning in college and in the workplace.
To help the student learn independent learning through reading, CSM measures and responds to many aspects of
student reading (what types of lessons they read, when they read the lessons, and how they read the lessons).
It synthesizes these measurements into
learning decisions and reading effectiveness.
Independent learning is a key skill for success in both college and in today's rapidly
changing work environments. CSM is designed to break the cycle of passive learning
and empower students to solve problems and learn new material on their own.
Being a successful student requires good academic habits of mind like persistence,
carefulness, confidence, self-reliance and self-efficacy. CSM is unique among adaptive
learning systems in measuring and responding to these important affective aspects
of self-regulated learning.
Persistence and grit
Most learning systems respond to a student who is stuck on a skill by alerting the teacher
that the student needs a personal lesson on that skill -- the role of the teacher is the instructor of
"last resort". This strategy, however, saps student persistence and self-reliance as they
that they don't need to try very hard on their own -- the easiest way to move forward is to have
the teacher help them. This makes the student more dependent on the instructor for learning.
CSM, on the other hand, wants students to learn how to keep trying until they experience success.
To do this, CSM doesn't call over a teacher when a student gets stuck, but simply gives the student a break
by moving them to another skill for a while. As they are returned to the difficult skill, they learn
that it's up to them to learn the skill, and generally put in more effort. When the student
finally masters the skill, they have also learned deeper persistence and self-reliance as well.
Confidence and overcoming learned helplessness.
Many students respond to questions that seem hard by just giving up. They might say to
themselves "I can't do the problem because I'm
not smart enough or I've forgotten how to do it, and why bother? If I spend 5 minutes
on the problem, I still won't be able to do it, and then I'll feel even worse.
So I won't even try."
CSM addresses these patterns of learned helplessness in many ways. For example,
after learning a skill, students are informed of what fraction of all adults and
4-year college graduates could do the problem.
After the student
has seen this type of information a number of times, they gain confidence in their own
abilities and their internal narrative changes to: "I can't do the problem, but it's
not because I'm dumb -- it's because these are difficult problems. I've learned that I
can do tricky problems if I try, and it will feel really good because I'll
be able to do things that even many college graduates can't do. Let's get started!"
Attention to detail and A-level work
Attention to detail and carefulness are traits that are highly prized by employers, but
they are generally undermined in most educational technology and the many classes that rely
on multiple choice tests with a low passing grade. CSM requires extraordinary levels of
accuracy and attention to detail to complete.
All work done on CSM must be "A-level" work in order for a student to
make progress. CSM's high mastery level helps to teach students what A-level work demands, that they are
capable of A-level work, and how good A-level performance feels - so that they are
more likely to demonstrate such performance in other classes and as they transition to
the workforce.
CSM is a new generation of educational technology that devotes as much attention to
a student's habits of mind as to the skills being taught.
Who is the CSM Course designed for?
Everyone can benefit from CSM, from 8th graders through adult learners. CSM's adaptive learning
system adjusts to the needs of widely diverse students -- all students learn all of the Core Skills, and are
guided to as many Supporting Skills as they need. CSM will fill in
gaps down to 3rd grade math and 6th grade literacy, but is also appropriate for
college-level students. CSM has many
applications
in secondary schools, adult and workforce education, and postsecondary education.
How is the CSM Course structured?
The CSM Course covers core math and literacy skills and key problem-solving
strategies, and takes about 10 to 80 hours to complete, depending on student preparation.
Students who finish the CSM Course are eligible for the CSM Certificate.
Students who complete the CSM Course have access to the Challenge Problems,
which focus on advanced problem solving and critical thinking with an emphasis on
teaching how to attack novel problems in unfamiliar situations. The Challenge Problems can take dozens of hours.
There are two ways to incorporate CSM into an educational program -- competency-based or seat-time.
In a competency-based class, students will work on CSM for as long as it takes them
to reach their goal, which is usually completion of the CSM Course (but programs can opt to include some of
the Challenge Problems as well). In
a seat-time class, students will get as far as they can on CSM in the time alotted -- some will spend most
or all of their time in the CSM Course, while others will progress quickly through the Course and get deep into
the Challenge Problems. If you use CSM in a seat-time class, we recommend approximately a semester-long class, or about
60 hours, which will allow most students to complete the CSM Course.
How does CSM teach?
To achieve the highest learning efficiency, CSM is an adaptive learning system that
personalizes instruction by guiding each student on a unique path through the
lessons according to his or her individual needs.
Students move through "trees" of skills, earning yellow, red and black belts
Zone of proximal development. CSM maintains students at their "edge of knowledge"
where lessons are neither too
easy and boring, nor too hard and frustrating. At this edge of knowledge, learning
is both fastest and most rewarding.
No traditional tests. In most computer-based instruction, students spend a lot of their time in tests
at the beginning and end of each lesson, rather than in instruction.
In contrast, in CSM, testing and training are
woven together seamlessly. CSM formatively analyzes each
student interaction in terms of skills acquisition, independent learning, and
habits of mind to guide them on their
optimal path through the curriculum.
Feedback tailored to specific errors. CSM analyzes every incorrect answer
to determine the specific error made by the student, and in most cases, CSM identifies
the problem and immediately provides the student with their thinking
error to help them correct their mistake.
Durability of mastery. CSM uses a karate belt metaphor to bring students to
back to skills over weeks as they move from yellow to red belt, and finally to a
black belt. Instead of just giving students a check-mark and moving on, CSM
determines that the student can reproduce the skill over an extended period, demonstrating
that the skills acquisition is deep, secure and durable.
Guided metacognition. CSM guides students through the process of metacognition, by
asking them to consider their learning and needs every time they miss a question. CSM also helps
students learn how they learn best by providing many lesson types that are geared towards various learning
styles, as well as feedback to students on which lessons they are reading and which lessons are most
successful in helping them learn.
Measurment of and response to effort and learning. Most adaptive learning systems focus exclusively
on the cognitive aspects of a student's performance. CSM addresses the whole student by also
measuring and responding to effort and learning.
A new and higher standard for college and work readiness
CSM's goal isn't college and workforce readiness, it's providing students with the skills they need for college
completion and career success.
College
Many college readiness programs are simply test-prep for college placement tests. However,
studies show that performance on these tests correlates poorly with college completion,
leading to low graduation rates at many colleges -- only 20% of community college students
graduate within 6 years, and the percentage goes below 10% for those who
require any developmental education.
In contrast, CSM teaches the skills needed for college completion -- that is, the
math, literacy, problem-solving, independent learning, and
academic traits and habits of mind that students can use every day as they
progress towards graduation.
Work
When many employers hear the term "workforce ready", they think of low-skill, entry-level
work. In contrast, CSM is oriented towards the problem-solving and decision-making skills
that are crucial in supervisory and managerial positions of strategic value to employers.
Is it really free?
Yes, the CSM Course really is completely free for everyone, and professional development
for teachers is free, as well. The CSM Course is maintained as free through revenues from
the CSM Certificate and other CSM services. Our company's goal is to educate people
and raise the skills of the world population, so keeping the CSM Course free is the best way to
have an impact on as many people as possible. |
More About
This Textbook
Overview
For close to two decades, Math into LaTeX has been the standard introduction and complete reference for writing articles and books containing mathematical formulas. In this fourth edition, the reader is provided with important updates on articles and books. An important new topic is discussed: transparencies (computer projections). Key features of More Math into LaTeX, 4th edition: Installation instructions for PC and Mac users An example-based, visual approach and a gentle introduction with the Short Course A detailed exposition of multiline math formulas with a Visual Guide A unified approach to TeX, LaTeX, and the AMS enhancements A quick introduction to creating presentations with computer projections
Editorial Reviews
From the Publisher
"There are several Latex guides, but this one wins hands down for the elegance of its approach and breadth of coverage."
—Amazon.com, Best of 2000, Editor's Choice
"A very helpful and useful tool for all scientists and engineers."
—Review of Astronomical Tools
"A novice reader will be able to learn the most essential features of Latex sufficient to begin typesetting papers within a few hours of time . . . An experienced Tex user, on the other hand, will find a systematic and detailed discussion of all Latex features, supporting software, and many other advanced technical issues."
Related Subjects
Meet the Author
George Grätzer is a Doctor of Science at the University of Manitoba. He authored three other books on LaTex: First Steps in LaTeX and Math into LateX, which is now in its third edition and has sold more than 6000 copies. Math into LaTeX was chosen by the Mathematics Editor of Amazon.com as one of the ten best books of 2000. He has also written many articles and a few books on the subject of lattices and universal algebra. In addition, Grätzer is the founder of the international mathematical journal, Algebra Universal |
Professors of the University of Washington, Bothell Campus, have designed this course that aims to apply scientific and mathematical discovery to social science questions. Students are trained ?to conduct surveys, e...
This course seeks to explain how the exercise of government affects daily lives using statistical analysis and mathematical concepts. In particular, the website provides polling projects wherein students take polls and...
Seattle Central Community College offers this course on the biodiversity of the Pacific Northwest. The course aims to help students understand how environmental justice affects their lives, cultural communities, and...
This course, created by Kathleen Perillo and Bill Monroe of Clark College, combines environmental science and math in a project-based, group-oriented class. Interpretation and analysis of graphs and models are...
The American Mathematical Association of Two-Year Colleges (AMATYC) has compiled a collection of mathematics resources related to various subjects and disciplines. ?Math Across the Community College Curriculum? is the... |
...
More About
This Book
specific theorems than are found in most contemporary treatments of the subject.
The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups.
Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints.
In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number |
Quick Review Math Handbook hot words hot topics
9780078601262
ISBN:
0078601266
Pub Date: 2004 Publisher: McGraw-Hill Higher Education
Summary: "Quick Review Math Handbook: Hot Words, Hot Topics" (available in English and Spanish) provides students and parents with a comprehensive reference of important mathematical terms and concepts to help them build their mathematics literacy. This handbook also includes short-instruction and practice of key standards for Middle School and High School success.
Glencoe McGraw-Hill Staff is the author of Quick Rev...iew Math Handbook hot words hot topics, published 2004 under ISBN 9780078601262 and 0078601266. Four hundred thirty Quick Review Math Handbook hot words hot topics textbooks are available for sale on ValoreBooks.com, three hundred twenty eight used from the cheapest price of $0.01, or buy new starting at $10.00 |
Date: Dec 1, 2012 10:59 PM
Author: Robert Hansen
Subject: Treatment of Negative Numbers
The following are the chapters on negative numbers from 3 different textbooks dating from 1952 through 1973. The first book is the predecessor to the Dolciani series. Two of its 3 authors (Freilich & Berman) are two of the three authors of the first batch of Dolciani S&M books in the 1960's. The other author or the S&M books is of course Dolciani.
Interestingly, the formula for the Dolciani books, with the oral and written exercises, followed by word problems, along with the extra for experts sections, was already established in the much earlier Freilich books. In fact, several of the "History of Mathematics" inserts in the later Dolciani books are from the Freilich books. All of the books were published by Houghton Mifflin. These are all Algebra 1 books. The Algebra 2 books had only a review section on real numbers (including signed numbers).
In my most modern Algebra 1 book, a 2012 Holt version on the iPad, negative numbers are not covered much at all. They are listed in the introduction to Algebra section along with their arithmetic rules, that's it. Likewise with the Discovering Nothing book. In fact the Discovering Nothing book makes more of a deal about the difference between the "minus" key and the "sign" key on the calculator than it does about negative numbers.
I don't have any pre-algebra texts, and even though I know that negative numbers are introduced quite early (by 3rd grade) in order to close subtraction, you can't really treat them properly till algebra. So add another deficiency to the list of deficiencies in modern curriculums. Also, I note that Joe mentioned the case of Not Not, which is a good point. Unfortunately, truth tables are a scarcity in modern curriculums as well.
Back to the classics...
All three of the texts spend 30 to 40 pages on the subject. The two earlier books (1952, 1963) deal with negative numbers separately while the later book (1973) deals with real numbers altogether. I think the later approach is better.
The later (1973) book is great on the axioms but short on providing exemplary applications of negative numbers in the text. The 1963 and 1952 books spend a lot more time with examples of applying negative numbers. The Freilich (1952) book doesn't use the axioms like the Dolciani (1965) book does. The influence of SMSG and New Math no doubt.
As a mix of "key points" (for Joe's satisfaction) I like the 1965 book the best, but I would would rework it (hindsight is 20/20, right?). The following elements would still be my focus...
1. The Number Line
2. Adding and Subtracting Signed Numbers
I would use many examples of this, math examples and application examples. The students need to learn how to state something negatively. The first two books did a good job of challenging the students to keep up with the signage.
3. Ample Use of Parenthesis
This drives home the fact that the "minus sign" is part of the number, not a subtraction operation. Also, it helps the student traverse situations like (-2) - (-3).
4. The Axioms
By this time the student has a solid feeling for most of the axioms, and they are not only equally valid here but helpful as well. And this is the perfect time to state them more formally, although I would drop the "For every x in ...".
5. Exemplary Applications Throughout
Money, Temperature, etc. (see item 8)
6. Multiplication as Repeated Addition (Repeated Subtraction in the Case of Negative Numbers).
If (-2) * (7) = (-14) then (-14) / (-2) must equal (7) <- This derivation dates back to 3rd and 4th grade.
8. Word Problems and Examples
Write an expression for the fuel left in a tank that is leaking 100 gallons an hour. If the tank has 1000 gallons now, how much did it have 3 hours ago.? I saw problems like this in the Freilich book. The student must learn how to think negatively in either direction and to keep that all straight in the algebra.
9. Close it all up with a review of the math and application of negative numbers and leave the students realizing that all we did was expand the set of numbers, not create two different sets.
And this all should come earlier than later. The Freilich book is odd in that it hits formulas, exponents and graphs all in the first two chapters. I would talk about numbers before that. |
The perfect book for mastering all the essentials of college algebra, with coverage of: the coordinate plane, circles, lines and intercepts, parabolas, nonlinear equations, functions, graphs of functions, exponents and logarithms, and more You'll be able to learn more in less time, evaluate your areas of strength and weakness and reinforce your...A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for... more... |
Summary: Here's the perfect self-teaching guide to help anyone master differential equations--a common stumbling block for students looking to progress to advanced topics in both science and math. Covers First Order Equations, Second Order Equations and Higher, Properties, Solutions, Series Solutions, Fourier Series and Orthogonal Systems, Partial Differential Equations and Boundary Value Problems, Numerical Techniques, and more.
A. Vector Fields B. Flows and Trajectories C. Poincare-Bendixon Theory V. Power Series Solutions A. Review of Key Properties of Power Series B. Series Solutions for First Order Equations C. Second Order Linear: Ordinary Points D. Regular Singular Points1440259 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). |
108517 / ISBN-13: 9780023108518
Introductory Algebra for College Students
The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum appeal. Blitzer's ...Show synopsis Introductory Algebra for College Students
tHIS IS NOT THE COVER Of the book. Its orange and has a bottle cap on the cover. BUUT this book is great. It clearly lists the steps and reasons for the math eq. and such. Although I DESPISE the ANSWER KEY in the back because it only lists the answers for ODD NUMBERS. Other than that, the condition ...
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Unfortunately, this text was required for my class. I got to use the Lial series for PreAlgebra, and I will get to for Intermediate as well. They are much better for those who need more examples, description, worked problems, etc. This one assumes you know a lot |
Introduction to Group Theory
Book Description: Group theory is an important subject that has come a long way in recent years. Introduction to Group Theory presents the fundamentals of both finite and infinite group theory, with a focus on finite groups. It provides students with the ability to prove the Thomas normal p-complement theorem and to classify simple finite groups. A large portion of the text is devoted to general linear groups. Additional topics covered include the construction of BN pairs, Coexeter groups, Hall–Higham theory, and Bender results. The text also offers an in-depth exploration of the complex relationship between groups, coding, and cryptography |
Free Maths courses online for Leaving Cert students
Griffith College now offer a new comprehensive online resource for Leaving Certificate mathematics (ordinary level) students.
This resource supplements the successful revision classes delivered by Griffith College in Dublin, Cork and Limerick in April. Over 700 students attended these revision sessions.
The days were split into 90 minute sessions. Each session covered a specific topic in its entirety, including all examination questions on that topic since 2000. The sessions were recorded on video and are now available to all students at The site contains a complete set of revision notes, summaries and videos for each question topic on the Leaving Certificate Ordinary Level Mathematics. While the site has only been live for a few days, many students throughout the country have individually spent over 10 hours using and re-using the resource.
In providing the online resource in bite-sized chunks, much like a dictionary, Griffith College hopes it will help students to fill in any particular gap they may have in their understanding, while recognising the extensive knowledge and skills they have already mastered. By providing the resource free, it balances the opportunity for all students, regardless of their financial means.
Admit It When You Don't Know Something
No one knows everything, so remember that its okay when you don't know something. Ask. Find out. Then move on. Don't try to hide it. Otherwise, it will come back to haunt you |
GED Mathematics review Product Description
This overview of high school mathematics--including arithmetic, charts and graphs, probability, statistics, algebra, geometry, number operations, data analysis, and coordinate geometry--is designed to aid viewers in passing the GED test. GED Mathematics movie Practice problems, test-taking strategies, and time saving tips are also featured as viewers are guided by a friendly math professor at the chalkboard, offering step-by-step solutions and clear explanations along the way. ...See Full Description |
Get the Math is funded by Next Generation Learning Challenges and the Moody's Foundation.
Get the Math is a multimedia project about algebra in the real world. See how professionals working in fashion, videogame design, and music production use algebraic thinking. Then take on interactive challenges related to those careers.
Using segments and web interactives from Get the Math, this self-paced lesson helps students see how Algebra I can be applied in basketball, challenging them to use algebraic concepts and reasoning to calculate the perfect free throw shot.
Using segments and web interactives from Get the Math, this lesson helps students see how Algebra I can be applied to the world of fashion, challenging them to use algebraic concepts and reasoning to modify garments and meet target price points.
Using segments and web interactives from Get the Math, this lesson helps students see how Algebra I can be applied in the music world, challenging them to use algebraic concepts and reasoning to calculate the tempos of different music samples.
Using segments and web interactives from Get the Math, this self-paced lesson helps students see how Algebra I can be applied in special effects, challenging them to use algebraic reasoning to calculate lighting high-speed effects like explosions.
Using video segments and web interactives from Get the Math, this lesson helps students see how Algebra I can be applied in the world of videogame design and challenges them to use algebraic reasoning to plot the linear paths of items in a videogame. |
Students can put fractions into a real-life context by using pizza. Developmental math instructors can use these examples to explain more complex mathematical concepts, or create new activities and homework assignments...
Giorgio Ingargiola, Associate Profession of Computer and Information Science at Temple University, has created the Wumpus World as an example of knowledge representation, reasoning, and planning to "introduce the...
This page, presented by the College Board, describes the course and exams for high school Advanced Placement Calculus AB focusing on differential and integral calculus. The three broad topics here are: Functions,...
This page, presented by the College Board, describes the course and exams for high school Advanced Placement Calculus BC focusing on differential and integral calculus (covered in Calculus AB) as well as additional... |
Mathematics for Teachers: Interactive Approach for Grade K-8
9780495561668
ISBN:
0495561665
Edition: 4 Pub Date: 2009 Publisher: Brooks/Cole
Summary: Sonnabend, Thomas is the author of Mathematics for Teachers: Interactive Approach for Grade K-8, published 2009 under ISBN 9780495561668 and 0495561665. Six hundred twenty Mathematics for Teachers: Interactive Approach for Grade K-8 textbooks are available for sale on ValoreBooks.com, one hundred twenty six used from the cheapest price of $72.77, or buy new starting at $199 [more55617125561712-2-0-12 Orders ship the same or next business day. Expedited shi [more]
ALTERNATE EDITION: Instructor Edition: Same as student edition but has free copy markings. Almost new condition. SKU:9780495561712-2-0-12 Orders ship the same or next business day. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less] |
Topics such as negatives, exponents, radicals and linear equations are presented in a clear, logical manner for all students to grasp
Includes a valuable CD-ROM full of printable worksheets and interactive whiteboard resources
Meets NCTM correlated standards
Product Information
Subject :
Algebra
Age(s) :
Ages 9-14
Grade Level(s) :
Grade 4-12
ISBN :
ISBN 0044222201579
Usage Ideas :
Topics such as negatives, exponents, radicals, and linear equations are presented in a clear, logical manner for all students to grasp. Includes a valuable CD-ROM full of printable worksheets and interactive whiteboard resources. |
Commerce, CA Algebra 2 emphasizes equation problem solving and graphing. The student's knowledge and confidence of equation work will expand as they learn topics such as: rational expressions, factoring, polynomials, radical expressions, and quadratics. The pace of the material covered will depend on the students' comfort level and understanding |
integralCALCCourse Description
Need some tips for Calculus 1A? Or maybe you're madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
Lessons in this Course
1.
Functions vs. Equations
5:22
2.
How to Use the Vertical Line Test
2:58
3.
Limits and Continuity
6:26
4.
Prove the Limit Doesn't Exist | Example
5:37
5.
Precise Definition of a Limit | Example
9:19
6.
Derivatives
6:53
7.
Definition of the Derivative | Example
3:43
8.
Equation of the Tangent Line | Example
16:49
9.
Implicit Differentiation | Example
9:35
10.
Optimization
8:55
11.
Related Rates
8:16
What is included in the course?
All of the video-based lessons listed on the Course Description tab, including interactive exercises and attached
files you can use along with the lesson. You also can ask the teacher (and other students) questions, and submit a
video or photo of your work to get direct feedback from the teacher.
What is Curious.com?
Curious.com is a site that enables teachers like integralCALC to make money by
teaching online to students around the world.
Where does my money go?
Most of the money goes directly to the teacher. The rest goes to Curious for the hardware and software and human
support required to make the delivery of this awesome course possible.
How do I access the course when I want to learn?
You can access the course, and any other Curious lessons you have enrolled in, by logging into on
your computer or tablet. You will be prompted to create an account when you purchase the course if you don't have one
already.
How long do I have access to the course?
For life. Really.
What if I don't learn, or don't like it?
We are confident you will love this course--like literally thousands of others before you--but if you don't for any
reason we will be happy to refund your money and disable your access to it.
vanessa v comment: whats the easiest way to learn calculus when you're 10 years old?
Krista K comment: make sure first that you're really good with algebra. from there, google "calculus and limits".... and let me know if you have trouble! :)
Allan P comment: Thanks for the refresher. I think this course will be very useful. One Love!
joni d comment: It's been 40 years since I took calculus. This is on my bucket list!
bailey m comment: when I was in the sixth grade i didn't turn my homework in so they stuck me ion regular math for another year so in the eighth grade i took pre-algebra now I'm getting ready to go into the ninth grade and i really want to get a good grade in algebra. How would I go about doing that? do you have any suggestions?
Shane B comment: Found it a bit complicated. haven't done calculas since high school in the 70s'.
Christopher T comment:
"jacinta k commented:
If i invest K50 a year for 40 years toward my POSF savings, and earn 8% a year on my investments, how much will i have when i retire?"
Answer: 1,086,226.075
Students in this lesson (567)
About the TeacherTable of Contents
1.
Lesson Intro
0:23
2.
Functions vs. Equations
0:23
3.
What are Functions?
1:06
4.
Domain and Range
1:32
5.
What Functions are Not
1:02
6.
Combinations and Compositions
0:54
Lesson Description |
More About
This Textbook
Overview
A carefully revised edition of the well-respected ODE text, whose unique treatment provides a smooth transition to critical understanding of proofs of basic theorems. First chapters present a rigorous treatment of background material; middle chapters deal in detail with systems of nonlinear differential equations; final chapters are devoted to the study of second-order linear differential equations. The power of the theory of ODE is illustrated throughout by deriving the properties of important special functions, such as Bessel functions, hypergeometric functions, and the more common orthogonal polynomials, from their defining differential equations and boundary conditions. Contains several hundred exercises. Prerequisite is a first course in ODE |
...
Show More users' perception of math by exposing them to real-life situations through graphs and applications; and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book includes key topics in algebra such as linear equations and inequalities with one and two variables, systems of equations, polynomial functions and equations, quadratic functions and equations, exponential functions and equations, logarithmic functions an equations, rational and radical expressions, and conic sections. For professionals who wish to brush up on their algebra skills |
Definitions are central to mathematics. Even at the upper division undergraduate and begining graduate levels, the majority of the proofs that the student is asked to invent amount to little more than verification of definitions. It is essential that advanced students see the role that definition plays in mathematics.
But as a general rule, I don't believe that we should introduce definitions unless we plan to use them in arguments and, moreover, plan to require that students be able to recite both the definition and the arguments. (As every playwright knows: You don't drag a cannon onto the stage unless you're going to fire it.) I think that one of the reasons juniors and seniors have difficulty coming to see the importance of definition lies in our failure to observe this principle in our calculus sequences. When we introduce definitions that we do not ask them to recite or use, we teach them that definitions in mathematics are like those in Webster; determined by the context of a language and to be looked up when we don't know what somebody's talking about--if then.
Moreover, in choosing the definitions we deal with, I believe we should make use of students' serviceable intuitions. Owing, at least in part to the effective demise of proof in high school geometry courses, today's beginning calculus students have very little of proof in their personal histories. I think we need to accomodate them to proof and its necessity before we start discussing counter-intuitive things, trample on the correct intuitions that do have, or undertake to prove what they consider obvious.
Students do have serviceable intuition for continuity, for area, and for exponential behavior--among other things. It is, of course, incomplete. They can complete it at much the same time that they complete the reals--as juniors or seniors in a strong introductory analysis course--which we should require of all majors. But we should not think of beginning calculus as an introduction to analysis.
As I have suggested earlier, I ask them to deal with questions of approximation: How close must x be to 2 in order that we can be sure that x^2 - 6 x + 11 is within 1/250 of 3? To how many digits must we know \sqrt{2} if we want to be sure of the first 7 digits to the right of the decimal in \sqrt{\sqrt{2}}? I ask for correct and complete reasoning from them in their dealings with these questions. The student who has dealt carefully with questions like these will be ready for epsilons and deltas later on.
I prefer to take area as a primitive concept, and introduce Riemann sums after discussion of the Left-hand Rule, the Right-hand Rule, the Mid-point Rule, the Trapezoid Rule, and Simpson's Rule, as a very general way of approximating definite integrals. (But I do Riemann-Stieltjes integrals in my Advanced Calculus course. See, e.g., Widder's _Advanced Calculus_, republished a few years ago by Dover.) I pay careful attention to the error estimates for the standard definite-integral-approximation routines just mentioned. I do so not because those routines are particularly useful in practice, but because they are tied up with the notion of using a parameter to control closeness of approximation: That's the whole issue that underlies limits and continuity. Moreover, this discussion gives me good opportunities to ask them to show me that they know how to establishs bounds for functions, and this is a fundamental idea I think we've paid too little attention to in our moe traditional calculus sequences.
I think that giving the definition of the natural logarithm by means of a definite integral is one of the biggest mistakes we ever made in the traditional calculus sequence. That definition belongs in the strong introductory analysis course they will take later--if they major in mathematics. To begin with, that definition flies in the face of what we told them logarithms are just one course ago in their pre-calculus courses. To make matters worse, they have a very hazy idea of what a definite integral is (especially if one has taken the definite integral to be the limit of the Riemann sums as the mesh goes to zero) at the time that integral definition appears, and so it is, in effect, meaningless to them. (Ask them, in an informal situation--say, at a departmental picnic, what a definite integral is. Most of them will give you an operational definition: It's what you get by finding an antiderivative and then evaluating it at the limits and doing a subtraction. But their "definition" won't be nearly as succinct or to the point as the language I've just used. If you summarize their remarks in the language I just used, they'll say "Yeah--that's it.")
I'm quite happy with an intuitive extension of the exponential function from the rationals to the reals by continuity followed by definition of the logarithm as its inverse. The number e appears quite naturally as the value of a for which the function x -> a^x has derivative x -> a^x (or as the base for which the derivative of the function x -> log_a x becomes x -> 1/x). |
Mathematics
Program Purpose:Students who successfully complete Mathematics courses will be able to solve mathematical problems, demonstrate mathematical reasoning skills, analyze theoretical concepts, and transition between the abstract and the concrete in mathematical analysis.
PROGRAM MAPPING:
I: This program-level student learning outcome is INTRODUCED is this course. P: This program-level student learning outcome is PRACTICED in this course. M: This program-level student learning outcome is MASTERED in this course. Leave blank if program-level student learning outcome is not addressed. |
(3 cr.) This course examines the relationship between
geometry and algebra; the geometry of the number
line and of the Cartesian plane; logic and sets;
solving equations as an exercise in logic and set
theory. The relationship between mathematics and
language also is considered, as well as
probability and statistics. The class examines
the reasons why certain mathematical topics are
taught in the standard public school curricula
while others are avoided or delayed.
As Needed, All |
Practice Makes Perfect Precalculus - 12 edition
Summary: Don't be perplexed by precalculus. Master this math with practice, practice, practice! Practice Makes Perfect: Precalculus is a comprehensive guide and workbook that covers all the basics of precalculus that you need to understand this subject. Each chapter focuses on one major topic, with thorough explanations and many illustrative examples, so you can learn at your own pace and really absorb the information. You get to apply your knowledge and practice what you've learned through...show more a variety of exercises, with an answer key for instant feedback. Offering a winning solution for getting a handle on math right away, Practice Makes Perfect: Precalculus is your ultimate resource for building a solid understanding of precalculus fundamentals. ...show less
Textbook may contain underlining, highlighting or writing. Infotrac or untested CD may not be included. |
Idledale PrecalculusAlthough I dream of achieving lofty goals, I find comfort being grounded in a simple life. My family and I have lived in one modest house for over twenty-five years; we drive older cars, still use a land-line phone and a broadcast TV, and avoid expensive or unhealthy habits. Mostly like my wif...
...During my education, Matlab was the program for choice for signal processing, feedback problems, and filtering problems. Since graduating, I have used Matlab extensively for data analysis. This has allowed me to build on the fundamentals of Matlab, such as working with variables, defining array |
Chapter 3: Geometry TE - Enrichment
The goal of an enrichment section is just what is implied in the title, "to enrich." By enrichment, we mean something that breathes a new or different life into something else- to make it better to enliven it. This is the goal of this branch of the teacher's edition. This is an opportunity for you and your students to locate and explore the wonderful world of geometry in other subjects such as architecture or music or art. It is a chance for students to see how the world of mathematics can connect to other subjects that they are passionate about.
Our goal is that using this Enrichment Flexbook will help you to expand your own personal creativity as well as the creativity of your students. The projects/topics in this flexbook can be used in several different ways. They can be used as a discussion point, an example to highlight during a lesson, a project to expand on whether students complete the project in class or at home or as a way to broaden student thinking by using a web search once per week as an example. It is not the intention that every single lesson be used in this flexbook. Take what inspires you and use it to inspire your students. Isn't that what the world of mathematics is all about! |
...
Show More with: Exercises in: Hilbert space theory, Lie groups, Matrix-valued differential forms, Bose-Fermi operators and string theory. All other chapters have been updated with new problems and materials. Most chapters contain an introduction to the subject discussed in the text. Complex Numbers and Functions Sums and Products Discrete Fourier Transform Algebraic and Transcendental Equations Vector and Matrix Calculations Matrices and Groups Matrices and Eigenvalue Problems Functions of Matrices Transformations L'Hospital's Rule Lagrange Multiplier Method Linear Difference Equations Linear Differential Equations Integration Continuous Fourier Transform Complex Analysis Special Functions Inequalities Functional Analysis Combinatorics Convex Sets and Functions Optimization |
...Algebra 2 covers factoring, rational exponents, quadratic equations, functions, imaginary and complex numbers, and exponential and logarithmic functions and equations. We would always endeavor to tie into the world around us, the subject matter in Algebra 2. The student and I would work through |
ISBN13:978-0618247509 ISBN10: 0618247505 This edition has also been released as: ISBN13: 978-0030256714 ISBN10: 0030256712
Summary: Ostebee and Zorn provide concrete strategies that help students understand and master concepts in calculus. This user-friendly text continues to help students interact with the main calculus objects (functions, derivatives, integrals, etc.) not only symbolically but also, where appropriate, graphically and numerically. Ostebee/Zorn strikes an appropriate balance among these points of view, without overemphasizing any of them. New exercises, examples, and much more ha...show moreve added tremendously to this great book.
NAVIGATING CALCULUS, a new CD-ROM, is being released along with the second edition. The CD contains a variety of useful tools, and resources, including a powerful graphing calculator utility, a glossary with examples, and many live activities that deepen students' encounters with calculus ideas. The CD is keyed closely to the book's table of contents.
Any treatment of calculus involves many choices among competing alternatives: how and when to treat limits, which applications to include, what to prove, etc. To explain the authors' views on such matters, they've established an FAQ site at: ...show less
Functions, Calculus Style Graphs A Field Guide to Elementary Functions Amount Functions and Rate Functions: The Idea of the Derivative Estimating Derivatives: A Closer Look The Geometry of Derivatives The Geometry of Higher-Order Derivatives Chapter Summary Interlude: Zooming in on Differences
Areas and Integrals The Area Function The Fundamental Theorem of Calculus Finding Antiderivatives by Substitution Finding Antiderivatives Using Tables and Computers Approximating Sums: The Integral as a Limit Working with Approximating Sums Chapter Summary Interlude: Mean Value Theorems and Integrals
All text is legible, may contain markings, cover wear, loose/torn pages or staining and much writing. SKU:9780618247509-5-0
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smeikalbooks UK Hemel Hempstead,
1900 |
book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. |
Product Description
Learn how to see and teach math from a biblical worldview with this easy-to-read guidebook!
A great, general-purpose introduction for a typical parent. - James D. Nickel, author of Mathematics: Is God Silent?
This small gem discusses the general topic of thinking biblically as it applies to math. It gives examples from history, is illustrated with thought-provoking cartoons, and provides samples of practical application of thinking biblically as you teach math.
- Joyce Herzog, Choosing & Using Curriculum
Features:
Concise enough to read in one sitting.
You won't have to spend hours reading!
Written by a homeschool graduate with the homeschool parent in mind.
Written in every-day language.
This is one math book you don't have to fear! In fact, you may find that it takes the fear out of math.
Integratable with the curriculum of your choice
This book walks you through how to both select and modify a curriculum for your child. Includes reviews of a few common curriculums, and guidelines for finding a good math curriculum.
This Book Will Help You :
Get invigorated about math as you see how math's very existence reminds us of God's faithfulness.
Teach your child to view the world through a Christian perspective. You just may find that he is better able to understand and apply math. Things make so much more sense when we approach them correctly!
As I made my way through the pages I was captivated by the fresh perspective brought to the entire world of mathematics. Every homeschooling parent ought to read this book.
- Sandra A. Lovelace, homeschool pioneer, speaker, author, education consultant, and Lifework Forum director
So, if you are like me and avoid math, read this book to bring a glimmer of hope and purpose. If you delight in numbers, this book will bring a new depth to that delight. If you are teaching anyone math or thinking math is neutral, you have to read this book to protect the hearts and minds of yourself and those you love. – Carolyn (View entire review.)
New edition! The 2011 edition has a new cover, an expanded curriculum section, and miscellaneous updates throughout. |
First you read the assigned portion of the text until you understand every sentence. Keep your pen or pencil handy, because you are going to need it while you are reading. Unlike calculus books, upper-level books will have gaps that the author deliberately leaves for you to fill-in. Write out the missing steps, draw diagrams. This is an extremely important part of the learning process. Much of your personal growth and depth of understanding will come from filling-in these gaps. Don't let the author sneak anything past you! Occasionally there will be mistakes. Find them and correct them. If you get stuck trying to understand something on your first reading, you may want to leave it temporarily. After your first reading go back and work on the difficult parts. It may take two or three attempts before you conquer a sticky point.
After you can follow all the logic in a proof, go back and analyze. This is where the understanding comes. What are the hypotheses? Where were they used in the proof? Are they all necessary? Or can one or more of them be relaxed? What is the conclusion? What do you have to establish to justify the conclusion? Did the author accomplish this? What makes the proof work? Usually there are one or two main ideas on which the proof hinges. Maybe it is a fact from number theory or an application of an inequality. Remember this main idea as the key to the theorem. If you can recall the main idea, constructing a proof of the theorem should be a matter of filling in the details. This is how you learn a proof. You don't learn a proof by memorizing words. To "know" a theorem means you can state its hypotheses, you can state its conclusion, and you can write out its proof. When you come to class you should be able to write out the proofs of the theorems covered in the previous class without using your book or notebook.
Definitions. You cannot follow the logic in a proof unless you have a clear understanding of the definitions of terms used in the proof. Master all definitions. When you come to class you should be able to recite all previously covered definitions.
It may well take two to three hours to do all this! Now you are ready to do your homework exercises.
Why all this? Why can't you just learn the definitions and statements of the theorems? Because learning mathematics entails both content and process. The statements of definitions and theorems are the content. The process includes the activity described above as well as the working of homework exercises, the writing of hand-in assignments, classroom interaction, and discussions with the professor and other students. Years from now you may have forgotten the theorems, but the effects of the process will still be with you. It is through the process that you grow as a power thinker. Seize the opportunity to participate fully in this process and it will energize and transform your thinking capabilities. Besides you won't get an A otherwise.
"But my friends in other majors don't have to work this hard!" Maybe so, but if they don't, neither will they have your analytical abilities or starting salary. |
in a classroom setting rather than in the Math Lab. Only open to those needing 4 or 5 credits of Arithmetic Review. Credits in this course do not apply toward graduation requirements.
Explores sets; solving equations and inequalities; factoring; fractional, and rational expressions; graphing; and word problems. Credits in this course do not apply toward graduation requirements. (Offered only in the Math Lab.)
Prerequisite: Intermediate Algebra or its equivalent and passing score on Mathematics Proficiency Exam. Explores algebraic, circular and trigonometric equations and identities; and inequalities. Credit cannot be received for this course if MAT 1112 or MAT 1114 has been taken.
Prerequisite: Intermediate Algebra or its equivalent and passing score on Mathematics Proficiency Exam. Explores inequalities and algebraic functions: linear, quadratic, polynomial and rational. This is a portion of MAT 1110; credit cannot be received for taking both courses. (Offered only in the Math Lab.)
Studies the development of circular and trigonometric functions; right-triangle applications; trigonometric equations; and identities. This is a portion of MAT 1110; credit cannot be received for taking both courses. (Offered only in the Math Lab.)
Prerequisite: Intermediate Algebra or its equivalent and passing score on Mathematics Proficiency exam. An applications-oriented course with an intuitive approach, including introduction to both differential and integral calculus. Examples drawn from business, economics, biology, and the social and behavioral sciences. This course is not the prerequisite for 1226, nor can credit be received if 1225 or its equivalent has been taken.
Prerequisite: MAT 1110 or its equivalent and passing score on Mathematics Proficiency exam. Explores differential and integral calculus of functions of one or more variables. Sequence begins both Autumn and Winter Quarters.
Prerequisite: Intermediate Algebra or its equivalent and passing score on Mathematics Proficiency exam. Explores topics that illustrate how mathematical methods and models permeate our economic, political, and personal lives. By investigation of diverse applications, a variety of problem-solving techniques will be introduced, including using the computer as a tool.
Prerequisite: Passing score on Mathematics Proficiency exam or completion of Arithmetic review. Includes the study of sets, numeration systems, arithmetic, algebra, number theory and statistics, and relates topics to the elementary school mathematics curriculum. Available for general education credit only to students in elementary education.
Prerequisite: MAT 2530 completed with a grade of C- or better. Includes topics from probability, geometry, and measurement, and relates topics to the elementary school mathematics curriculum. Available for general education credit only to students in elementary education.
Prerequisite: MAT 1228 and 2401. Uses the axiomatic method to prove basic results from set theory and real analysis. Topics include functions, set cardinality, the real number system, and the topology of the real line.
Prerequisites: MAT 1228, 2228, 2375, and facility with mathematically oriented software. Focuses on construction and analysis of mathematical models for problems in the real world. The problems will be chosen from a variety of fields, including the biological and social sciences. Offered alternate years.
Prerequisite: 9 credits of upper-division mathematics or instructor permission. This senior capstone course will explore the culture of mathematics through readings and classroom discussions during the Autumn Quarter. Students will synthesize mathematical ideas within the context of a Christian worldview. The student will write a significant paper and make an oral presentation within the following two quarters. |
This broad, enjoyable introduction to university-level mathematics assumes some prior knowledge, as described on our MathsChoices website. The module shows how mathematics can be applied to answer some key questions from science, technology, and everyday life. You will study a range of fundamental techniques, including calculus, recurrence relations, matrices and vectors and statistics, and use integrated specialist mathematical software to solve problems. The skills of communicating results and defining problems are also developed. This is not a module for beginners – at the MathsChoices website (mathschoices.open.ac.uk) there are quizzes, sample material and advice to help you determine if this module is right for you.
Register for the course
What you will study
A few weeks before the module begins you'll receive a Revision Pack, including two assignments (see Preparatory Work below) – to help you revise the mathematical skills you need before you start the module – so you are advised to register early.
The module begins with Starting points, which features a first exploration of the main software package applied to some basic mathematical material. The rest of the module is in four sections.
Mathematics and modelling starts from situations in the world that can be modelled by mathematical techniques. The models use such mathematics as the properties and representations of arithmetic and geometric sequences, lines and circles, and functions such as x2, sin x, cos x and ex.
Discrete modelling deals with population models and their long-term behaviour, and introduces the arithmetic of matrices and vectors in order to examine the interdependence of different subpopulations. Vectors are also used to model problems involving various physical quantities, such as forces.
Continuous models covers calculus and introduces the process of differentiation. Derivatives are obtained for many functions, and these are used to model motion and to solve optimisation problems. Next we look at integration, first as the reverse of differentiation and then as the limit of an infinite sum. A list of standard integrals is obtained, and these are applied to solve simple differential equations, to find areas, and in other modelling contexts.
Modelling uncertainty is about probability and statistics. A chapter on chance invokes intuitive ideas of randomness and adds to your experience of thinking about probability through the use of purpose-designed software. This is followed by computer-aided exploration of sampling and sampling distributions and by an examination of regression.
The module also develops skills beyond mathematical technique, such as identifying and defining problems and communicating the results of your mathematical work – these are required for the effective application of mathematics to solve problems.
There are samples of the study material, including example assessment questions, available at the Maths Choices website.
The module introduces the use of computer software to help your mathematics. This is an integral part of its approach, so you will need regular and convenient access to a suitable personal computer.
You will learn
Successful study of this module should begin to develop your skills in:
expressing problems in mathematical language
finding solutions to problems
communicating mathematical ideas clearly and succinctly.
Entry
This is a key introductory Level 1 module. Level 1 modules provide core subject knowledge and study skills needed for both higher education and distance learning, to help you progress to modules at Level 2.
The module assumes that you already have a good knowledge and understanding of:
algebraic manipulation, such as multiplying out brackets, factorisation of simple expressions, interpreting inequalities and solving linear and quadratic equations;
properties of triangles, rectangles and circles;
the trigonometric ratios sine, cosine and tangent;
equations of straight lines;
quadratic, exponential, logarithmic and trigonometric functions, and their graphs.
A mathematical A-level, or a good pass in the highest-level GCSE mathematics (or the equivalent), would normally provide this. If all you need is a reminder of some of these topics, you can use the MST121 Revision Pack to revise them. However, if much of the list is unfamiliar, you should consider taking MST121 after completing our Level 1 module Discovering mathematics (MU123). MST121 relies on a very good understanding of most of MU123, or equivalent from previous study.
MST121 is the second module in the mathematics entry suite, following on from Discovering mathematics (MU123) and leading to Exploring mathematics (MS221). Your choice of which to take depends on how much mathematical knowledge you already have and on the degree you have in mind. It is not advisable to take either MST121 or MS221 in the same year as MU123, and you should not take MS221 before MST121.
If you start in October, it is possible – for some qualifications where regulations allow – to study MST121 and MS221 together in a single year as if they are a 60-credit module, as the material in the two modules is linked.
The Maths Choices website contains a self-assessment quiz to help you decide if MST121 is the right module for you.
Preparatory work
A few weeks before the module begins you will be sent a Revision Pack (which covers similar topics to those found in Discovering mathematics (MU123)) and a self-assessment quiz to help you judge what preparation you need to do.
You will also be sent two assignments which assess the mathematics covered in the Revision Pack. It is not compulsory to submit these assignments, and the scores that you obtain will not count in any way towards your final module result, but you are advised to submit them because they give you an opportunity to receive feedback on your mathematical skills and on the way you present your work. One of the assignments is marked by computer and you are advised to submit it during the four weeks before the start of the module. The other assignment is marked by your tutor, and you are advised to submit it during the two weeks before the start of the module.
If you want to do some study before you receive the revision material, we suggest Countdown to Mathematics: Volume 1 by Lynne Graham and David Sargent (1981, Addison-Wesley). Modules 2 and 3, in particular, provide practice in algebra. To gain even greater fluency with algebra and in trigonometry, you could use the companion book Countdown to Mathematics: Volume 2 (authors, date and publisher as above). It is worth trying some examples from each module of Volume 2, but there is a lot of material, so don't expect to work through every exercise in every section.
Regulations
As a student of The Open University, you should be aware of the content of the Module Regulations and the Student Regulations which are
available on our Essential documents website.
If you have a disability
We are trying to make the study materials accessible to as many people as possible. The module makes considerable use of audio and video material and transcripts for these are available. All the printed study material is available in comb-bound format. Adobe Portable Document Format (PDF) versions of printed material are also available. However some Adobe PDF components may not be available or fully accessible using a screen reader and formula, diagrams and certain mathematical elements may be particularly difficult to read in this way. The study materials are available on audio in DAISY Digital Talking Book format. Other formats may be available in the future. Our Services for disabled students website has the latest information about availability.
It is important to note that use of the module software, which includes on-screen graphs and mathematical notation, will be an integral part of your study website books, audio CD, DVD (for video material), CD-ROM and website.
You will need
You require access to the internet at least once a week during the module to download module resources and assignments, submit assignments and to keep up to date with module news. If your tutor offers online tutorials, we also recommend a headset with a microphone and earphones to talk to your tutor and other students We may also be able to offer group tutorials or day schools that you are encouraged, but not obliged, to attend. Where your tutorials are held will depend on the distribution of students taking the module.
Assessment
The assessment details for this module can be found in the facts box above.
Please note that TMAs for all undergraduate mathematics and statistics modules must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system.
The assessment during the module consists of four tutor-marked assignments (TMAs) (all approximately six weeks apart). (There is also a TMA and a CMA, associated with the revision material, but your scores for these do not count towards your module result.) All TMAs are to be submitted on paper, and the CMA must be submitted online using our eCMA system.
Assessment is an essential part of the teaching, so you are expected to complete it all. But if you unavoidably miss or do badly in an assignment in MST121 you are allowed a 'substitution score' for one of the TMAs only. You will be given more detailed information when you begin the module.
The examination consists of two parts, both covering the whole of the module. The first section contains multiple choice questions, the second short answer questions.
Professional recognition
Using mathematics is sometimes accepted as an acceptable equivalent qualification to GCSE grade C in mathematics by teacher training institutions, but always at the discretion of each institution. So, if you hope to use this module for this purpose, you are advised to check as early as possible with your chosen teacher training institution(s).
Future availability
The details given here are for the module that starts in January and October 2013 when it will be available for the last time. A replacement module, Essential mathematics 1 (MST124), is planned for February 2014This was a challenging course for someone who hadn't studied in 25 years and I enjoyed it enormously.
The TMAs ..."
Read more
"MST121 was an extraordinary mathematical journey. It started off with a very rapid review or core maths skills and very |
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