Roots to Research: A Vertical Development of Mathematical Problems
About this Title
Judith D. Sally, Northwestern University, Evanston, IL and Paul J. Sally Jr., University of Chicago, Chicago, IL
Publication: Miscellaneous Books
Publication Year 2007: Volume 48
ISBNs: 978-0-8218-4403-8 (print); 978-1-4704-1198-5 (online)
MathSciNet review: MR2359908
MSC: Primary 00-01; Secondary 00-02, 11-01, 52-01
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.
High school students, undergraduate and graduate students, and teachers of all levels interested in mathematics.
Table of Contents
- Chapter 1. The four numbers problem
- Chapter 2. Rational right triangles and the congruent number problem
- Chapter 3. Lattice point geometry
- Chapter 4. Rational approximation
- Chapter 5. Dissection
- Appendix A. Volume
- Appendix B. Convexity