This book is about some of the topics that form the foundations for high school mathematics. Most of the ideas are classical: fitting polynomial functions to data, summing powers of integers, visualizing the iterates of a function defined on the complex plane, or 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 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.
Table of Contents
Annotated Table of Contents
1. Difference Tables and Polynomial Fits
2. Form and Function: The Algebra of Polynomials
3. Complex Numbers, Complex Maps, and Trigonometry
4. Combinations and Locks
5. Sums of Powers
About the Author
About the Author
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 Woburn, Massachusetts public schools from 1969 until 1993. At EDC, he has worked in curriculum development, professional development, and education policy. A student of Ralph Greenberg, he received a PhD from Brandeis in 1980, with a thesis and research in algebraic number theory. His favorite publication (except for this book) is his 1991 article in The American Mathematical Monthly, described by his wife as “an attempt to explain a number system no one understands with a picture no one can see.”
This is a very valuable and well written book that goes into depth about certain high school mathematics topics, connects them, and in the process illustrates how to think like a mathematician. Its primary audience is strong high school teachers, especially in workshops and study groups, and professors who teach current or future teachers. However, most professional mathematicians would enjoy the book too and find things they didn't know. Continued...