ABSTRACT

Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors' successful work with undergraduate students at the University of Chicago, seventh

chapter 0|10 pages

Warm- up: The Triangle Game

chapter 1|34 pages

The Beginnings of Number Theory

chapter 2|22 pages

Axioms in Number Theory

chapter 3|20 pages

Divisibility and Primes

chapter 4|20 pages

The Division and Euclidean Algorithms

chapter 5|22 pages

Variations on a Theme

chapter 6|26 pages

Congruences and Groups

chapter 7|16 pages

Applications of Congruences

chapter 8|16 pages

Rational Numbers and Real Numbers

chapter 9|8 pages

Introduction to Geometry and Symmetry

chapter 10|16 pages

Polygons and Their Construction

chapter 11|24 pages

Symmetry Groups

chapter 12|16 pages

Permutations

chapter 13|46 pages

Polyhedra

chapter 14|32 pages

Graph Theory

chapter 15|44 pages

Tessellations

chapter 16|20 pages

Connections