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Mathematical Connections: A Companion for Teachers and Others has been published by the Mathematical Association of America. Click here to visit the MAA Bookstore online for more information about the book (search for "Cuoco").
The book is rooted in familiar high school mathematics — finding patterns, polynomial functions, trigonometric identities, the complex numbers, and counting problems — but delves much deeper to reveal many of the connections that make these topics all part of the same fabric. Special topics include solving difference equations, the Mahler polynomials, algebraic differentiation, the Chebyshev polynomials, Cardano's formula for the roots of a cubic polynomial, symmetric functions, complex dynamics, the golden ratio and Fibonacci numbers, Bernoulli polynomials, Stirling numbers of the first and second kind and much more.
Mathematical Connections focuses on a closely-knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. 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 its 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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