Hardcover ISBN:  9780821844038 
Product Code:  MBK/48 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470411985 
Product Code:  MBK/48.E 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
Hardcover ISBN:  9780821844038 
eBook: ISBN:  9781470411985 
Product Code:  MBK/48.B 
List Price:  $124.00 $94.50 
MAA Member Price:  $111.60 $85.05 
AMS Member Price:  $99.20 $75.60 
Hardcover ISBN:  9780821844038 
Product Code:  MBK/48 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470411985 
Product Code:  MBK/48.E 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
Hardcover ISBN:  9780821844038 
eBook ISBN:  9781470411985 
Product Code:  MBK/48.B 
List Price:  $124.00 $94.50 
MAA Member Price:  $111.60 $85.05 
AMS Member Price:  $99.20 $75.60 

Book Details2007; 338 ppMSC: Primary 00; 11; 52;
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 extracurricular projects.
ReadershipHigh school students, undergraduate and graduate students, and teachers of all levels interested in mathematics.

Table of Contents

Chapters

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


Additional Material

Reviews

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 upperlevel undergraduate and graduate math courses.
MAA Monthly 
Many references are given but the book is largely selfcontained. 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


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
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 extracurricular projects.
High school students, undergraduate and graduate students, and teachers of all levels interested in mathematics.

Chapters

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

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 upperlevel undergraduate and graduate math courses.
MAA Monthly 
Many references are given but the book is largely selfcontained. 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