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 79
Stran xi
... There are several ideas at once . You'll develop things that this book is not : your own style for dealing with them . This is not a teaching guide for The CME Project . That curriculum already contains extensive solutions and teaching ...
... There are several ideas at once . You'll develop things that this book is not : your own style for dealing with them . This is not a teaching guide for The CME Project . That curriculum already contains extensive solutions and teaching ...
Stran xiii
... there's a point to the end results . If you get tired , take a break or skip ahead . If you need something later , there will be pointers to the relevant problems . Acknowledgements The writing of this book was supported in part by NSF ...
... there's a point to the end results . If you get tired , take a break or skip ahead . If you need something later , there will be pointers to the relevant problems . Acknowledgements The writing of this book was supported in part by NSF ...
Stran xv
... difference column . Input Output Δ 42 43 0 0 1 1 1 → 2 3 1 I 2 4 3 -- 6 1 1 3 10 1 → 4 个 10 1 1 4 20 5 1 15 1 1 5 35 → 6 → 21 The third differences are constant , so there's a cubic. XV Annotated Table of Contents.
... difference column . Input Output Δ 42 43 0 0 1 1 1 → 2 3 1 I 2 4 3 -- 6 1 1 3 10 1 → 4 个 10 1 1 4 20 5 1 15 1 1 5 35 → 6 → 21 The third differences are constant , so there's a cubic. XV Annotated Table of Contents.
Stran xvi
... there's a cubic polynomial that will agree with this data . This fact , without proof , is about as far as any current high school curriculum takes the subject . In this chapter , we'll develop an extensive theory of finite differences ...
... there's a cubic polynomial that will agree with this data . This fact , without proof , is about as far as any current high school curriculum takes the subject . In this chapter , we'll develop an extensive theory of finite differences ...
Stran xvii
A Companion for Teachers and Others Al Cuoco. There's a great debate these days about the role of trigonometric identities in high school mathematics . Are “ identities ” a topic that can safely be dropped from the curriculum ? Is there ...
A Companion for Teachers and Others Al Cuoco. There's a great debate these days about the role of trigonometric identities in high school mathematics . Are “ identities ” a topic that can safely be dropped from the curriculum ? Is there ...
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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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agrees algebra am,k angle binomial buttons calculate called Chapter circle coefficients column combinations combinatorial complex numbers connected constant Corollary count course cubic defined definition derivative Describe develop difference difference table elements entries equal equation exactly example expanded expression f and g fact factor filled Julia set five formula give given graph high school ideas identity Input Output integer least length linear lock look mathematics means method multiply Notes for problem Notice obtained orbit origin Pascal's triangle pick picture plane points polynomial function polynomial of degree positive integer powers produce proof prove push quadratic replace result roots Show side Sm(x solve squares starting subsets Suppose teachers Theorem there's things true values we'll write zeros