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Roots to Research: A Vertical Development of Mathematical Problems
Judith D. Sally, Northwestern University, Evanston, IL, and Paul J. Sally, Jr., University of Chicago, IL

2007; 338 pp; hardcover
ISBN-10: 0-8218-4403-2
ISBN-13: 978-0-8218-4403-8
List Price: US$50
Member Price: US$40
Order Code: MBK/48
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See also:

Mathematical Connections: A Capstone Course - John B Conway

Geometry: A Guide for Teachers - Judith D Sally and Paul J Sally, Jr

Certain contemporary mathematical problems are of particular interest to teachers and students because their origin lies in mathematics covered in the elementary school curriculum and their development can be traced through high school, college, and university level mathematics. This book is intended to provide a source for the mathematics (from beginning to advanced) needed to understand the emergence and evolution of five of these problems: The Four Numbers Problem, Rational Right Triangles, Lattice Point Geometry, Rational Approximation, and Dissection.

Each chapter begins with the elementary geometry and number theory at the source of the problem, and proceeds (with the exception of the first problem) to a discussion of important results in current research. The introduction to each chapter summarizes the contents of its various sections, as well as the background required.

The book is intended for students and teachers of mathematics from high school through graduate school. It should also be of interest to working mathematicians who are curious about mathematical results in fields other than their own. It can be used by teachers at all of the above mentioned levels for the enhancement of standard curriculum materials or extra-curricular projects.

Request an examination or desk copy.


High school students, undergraduate and graduate students, and teachers of all levels interested in mathematics.


"I am a huge fan of this book! ... "Roots to Research" is very accessible, supported throughout with insightful examples and exercises that motivate both the ideas and the formal notation. I recommend this book to future and current math teachers, math majors, and working mathematicians who are interested in reading about cool math. ... the Sallys have done the mathematical community a service by writing a book that illustrates an approach that more of us should take when teaching upper-level undergraduate and graduate math courses."

-- MAA Monthly

"Many references are given but the book is largely self-contained. The authors have done a remarkable job of giving a seamless presentation of material at very different levels of difficulty. Teachers and students will appreciate this book both for the information it contains and as a model of expository writing."

-- Mathematical Reviews

"The book gives a very good introduction in how to solve mathematical problems and it is well suited as a basis for a beginner's seminar at universities."

-- Zentralblatt MATH

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