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 54
Stran xi
... fact can be deduced nections among the topics . This is more about how mathematics is conceived from previous ones . This is an than how it is presented . More about this approach in a minute . extremely efficient , and often elegant ...
... fact can be deduced nections among the topics . This is more about how mathematics is conceived from previous ones . This is an than how it is presented . More about this approach in a minute . extremely efficient , and often elegant ...
Stran xii
... fact that there's a distinct bias towards algebra and algebraic thinking in most of the chapters . I've found it productive to focus on one thing at a time , and the particular approaches used in this book — things like abstracting ...
... fact that there's a distinct bias towards algebra and algebraic thinking in most of the chapters . I've found it productive to focus on one thing at a time , and the particular approaches used in this book — things like abstracting ...
Stran xvi
... 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 : • We'll look at why a constant third difference implies a cubic ...
... 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 : • We'll look at why a constant third difference implies a cubic ...
Stran xvii
... come up just two of the many books with the fact that the sum of the entries in any row of Pascal's triangle is a power devoted to this approach . ubiquitous among middle and high school students , turns out Annotated Table of Contents ...
... come up just two of the many books with the fact that the sum of the entries in any row of Pascal's triangle is a power devoted to this approach . ubiquitous among middle and high school students , turns out Annotated Table of Contents ...
Stran 5
... fact , it's on - 3 : Δ2 – ΔΔ 0 -3 6 3 1 One strategy in this game is to keep taking differences until you either run out of outputs or get a constant difference . Notice that the next difference column ( the A3 column ) will be constant ...
... fact , it's on - 3 : Δ2 – ΔΔ 0 -3 6 3 1 One strategy in this game is to keep taking differences until you either run out of outputs or get a constant difference . Notice that the next difference column ( the A3 column ) will be constant ...
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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