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Roots to Research: A Vertical Development of Mathematical Problems
 
Judith D. Sally Northwestern University, Evanston, IL
Paul J. Sally, Jr. University of Chicago, Chicago, IL
Roots to Research
Roots to Research
Hardcover ISBN:  978-0-8218-4403-8
Product Code:  MBK/48
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-1-4704-1198-5
Product Code:  MBK/48.E
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
Hardcover ISBN:  978-0-8218-4403-8
eBook: ISBN:  978-1-4704-1198-5
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
Roots to Research
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Roots to Research
Roots to Research: A Vertical Development of Mathematical Problems
Judith D. Sally Northwestern University, Evanston, IL
Paul J. Sally, Jr. University of Chicago, Chicago, IL
Hardcover ISBN:  978-0-8218-4403-8
Product Code:  MBK/48
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-1-4704-1198-5
Product Code:  MBK/48.E
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
Hardcover ISBN:  978-0-8218-4403-8
eBook ISBN:  978-1-4704-1198-5
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 Details
     
     
    2007; 338 pp
    MSC: 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 extra-curricular projects.

    Readership

    High 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
  • 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 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2007; 338 pp
MSC: 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 extra-curricular projects.

Readership

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 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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