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. |
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Zadetki 1–5 od 28
Stran ix
... Combinatorial Polynomials 1.4 Making It Formal : The A Operator 1.5 Going the Other Way : Polynomials to Tables 1.6 Conversions 1.7 From Newton to Lagrange 1.8 Agreeing to Disagree 3 10 17 .22 .30 . 35 .38 .42 . 53 2 Form and Function ...
... Combinatorial Polynomials 1.4 Making It Formal : The A Operator 1.5 Going the Other Way : Polynomials to Tables 1.6 Conversions 1.7 From Newton to Lagrange 1.8 Agreeing to Disagree 3 10 17 .22 .30 . 35 .38 .42 . 53 2 Form and Function ...
Stran x
... Combinatorial Proofs and Identities 4.2 The Simplex Lock 4.3 Some Approaches to the Simplex Lock Problem 4.4 Connections to the Mahler Basis . . 161 . 165 173 174 185 5 Sums of Powers 5.1 Summatory Polynomials 5.2 Bernoulli's Method 199 ...
... Combinatorial Proofs and Identities 4.2 The Simplex Lock 4.3 Some Approaches to the Simplex Lock Problem 4.4 Connections to the Mahler Basis . . 161 . 165 173 174 185 5 Sums of Powers 5.1 Summatory Polynomials 5.2 Bernoulli's Method 199 ...
Stran xii
... combinatorial proofs or difference calculus helps me design rich problem sets , field questions in class , connect ideas from one course to another , and know when a student's idea is likely to grow into something that will be valuable ...
... combinatorial proofs or difference calculus helps me design rich problem sets , field questions in class , connect ideas from one course to another , and know when a student's idea is likely to grow into something that will be valuable ...
Stran xvii
... Combinatorial proofs go by many names : " combinatorial Chapter 4. Combinations and Locks arguments , ” “ story proofs , " " counting without counting , " There's one aspect of combinatorics that has been extremely useful in my teachand ...
... Combinatorial proofs go by many names : " combinatorial Chapter 4. Combinations and Locks arguments , ” “ story proofs , " " counting without counting , " There's one aspect of combinatorics that has been extremely useful in my teachand ...
Stran xviii
... combinatorial proofs in algebra ( the binomial theorem ) , geometry ( counting paths ) , and , of course , combinatorics . This is a wonderful skill to develop . We'll also look at a combinatorial problem that I've been using with high ...
... combinatorial proofs in algebra ( the binomial theorem ) , geometry ( counting paths ) , and , of course , combinatorics . This is a wonderful skill to develop . We'll also look at a combinatorial problem that I've been using with high ...
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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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