Mathematical Connections: A Companion for Teachers and Others

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Cambridge University Press, Aug 11, 2005 - Mathematics - 239 pages
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This book 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. Most importantly, the book is about some mathematical ways of thinking the author found extremely useful, both in his roles as a mathematician and as a mentor of young people learning to do mathematics.
  

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Contents

Difference Tables and Polynomial Fits
1
The Algebra of Polynomials
53
Complex Numbers Complex Maps and Trigonometry
101
Combinations and Locks
161
Sums of Powers
199
Bibliography
235
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About the author (2005)

Al Cuoco is Senior Scientist and Director of the Center for Mathematics Education at Education Development Center. He taught high school mathematics to a wide range of students in the Woburn, Massachusetts public schools from 1969 until 1993, and received his Ph.D. from Brandeis University in 1980.

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