Matrix Groups for Undergraduates
About this Title
Kristopher Tapp, Williams College, Williamstown, MA
Publication: The Student Mathematical Library
Publication Year 2005: Volume 29
ISBNs: 978-0-8218-3785-6 (print); 978-1-4704-2140-3 (online)
MathSciNet review: MR2141985
MSC: Primary 20-01; Secondary 15-01, 15A30, 17-01, 20G15, 22-01
Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups.
Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.
Undergraduates and beginning graduate students interested in group theory.
Table of Contents
- Why study matrix groups?
- Chapter 1. Matrices
- Chapter 2. All matrix groups are real matrix groups
- Chapter 3. The orthogonal groups
- Chapter 4. The topology of matrix groups
- Chapter 5. Lie algebras
- Chapter 6. Matrix exponentiation
- Chapter 7. Matrix groups are manifolds
- Chapter 8. The Lie bracket
- Chapter 9. Maximal tori