Mathematical Connections: A Companion for Teachers and OthersAmerican Mathematical Soc., 31. dec. 2005 - 239 strani Mathematical Connections is about some of the topics that form the foundations for high school mathematics. It focuses on a closely knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. Most of the ideas are classical: methods for fitting polynomial functions to data, for summing powers of integers, for visualizing the iterates of a function defined on the complex plane, or for obtaining identities among entries in Pascal's triangle. Some of these ideas, previously considered quite advanced, have become tractable because of advances in computational technology. Others are just beautiful classical mathematics--topics that have fallen out of fashion and that deserve to be resurrected. While the book will appeal to many audiences, one of the primary audiences is high school teachers, both practicing and prospective. It can be used as a text for undergraduate or professional courses, and the design lends itself to self study. Of course, good mathematics for teaching is also good for many other uses, so readers of all persuasions can enjoy exploring some of the beautiful ideas presented in the pages of this book. |
Iz vsebine knjige
Zadetki 1–5 od 90
Stran xvi
... we'll develop an extensive theory of finite differences : • We'll look at why a constant third difference implies a cubic fit . And more generally . we'll see why a constant nth difference means an nth degree polynomial will work . • We ...
... we'll develop an extensive theory of finite differences : • We'll look at why a constant third difference implies a cubic fit . And more generally . we'll see why a constant nth difference means an nth degree polynomial will work . • We ...
Stran xvii
... We'll look at this small important collection and find similar formulas for The polynomials are called sin nx and cos nx for any positive integer n . This will involve creating a seChebyshev polynomials . Using a CAS , we'll be able to ...
... We'll look at this small important collection and find similar formulas for The polynomials are called sin nx and cos nx for any positive integer n . This will involve creating a seChebyshev polynomials . Using a CAS , we'll be able to ...
Stran xviii
... they must be equal . In this chapter , you'll practice using combinatorial proofs in algebra ( the binomial theorem ) , geometry ( counting paths ) , and , of course , combinatorics . This is a wonderful skill to develop . We'll also ...
... they must be equal . In this chapter , you'll practice using combinatorial proofs in algebra ( the binomial theorem ) , geometry ( counting paths ) , and , of course , combinatorics . This is a wonderful skill to develop . We'll also ...
Stran xix
... we'll occasionally need to multiply matrices , and , although we assume no specific prerequisites , some of the ideas will be connected to basic ideas in linear algebra . • Chapter 5 requires the ideas from Chapters 1 , 2 , and 4 , and ...
... we'll occasionally need to multiply matrices , and , although we assume no specific prerequisites , some of the ideas will be connected to basic ideas in linear algebra . • Chapter 5 requires the ideas from Chapters 1 , 2 , and 4 , and ...
Stran 1
... We'll see why in the next section . Sometimes , the differences between successive outputs are not constant , but ... we want to investigate in this chapter . More precisely : Let's hope they are asked to find a formula rather than the ...
... We'll see why in the next section . Sometimes , the differences between successive outputs are not constant , but ... we want to investigate in this chapter . More precisely : Let's hope they are asked to find a formula rather than the ...
Vsebina
1 | |
The Algebra of Polynomials | 53 |
Chapter 3 Complex Numbers Complex Maps and Trigonometry | 101 |
Chapter 4 Combinations and Locks | 161 |
Chapter 5 Sums of Powers | 199 |
Bibliography | 235 |
Index | 237 |
About the Author | 239 |
Back cover | 241 |
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