Książki

This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler's formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us.

The exposition is engaging, precise and rigorous. The theorems are visually motivated with intuitive proofs appropriate for the intended audience. Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric.

Symmetry: A Mathematical Exploration

Preface.- Chapter 1 Introduction to Symmetry.- Chapter 2 The Algebra of Symmetry.- Chapter 3 Isomorphism.- Chapter 4 The Three Planar Classification Theorems.- Chapter 5 Subgroups and Product Groups.- Chapter 6 Permutations.- Chapter 7 Symmetries of Solid Objects.- Chapter 8 The Five Platonic Solids.- Chapter 9 What is a Number?.- Chapter 10 Cantor's Infinity.- Chapter 11 Euclidean Space.- Chapter 12 Symmetry and Matrices