Matrix Groups for Undergraduates: Second Edition
About this Title
Kristopher Tapp, Saint Joseph’s University, Philadelphia, PA
Publication: The Student Mathematical Library
Publication Year: 2016; Volume 79
ISBNs: 978-1-4704-2722-1 (print); 978-1-4704-2938-6 (online)
MathSciNet review: MR3468869
MSC: Primary 22E15; Secondary 15-01, 17B20, 20G15, 20H20, 22E46
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 the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots.
This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.
From reviews of the First Edition:
This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. … The book combines an intuitive style of writing with rigorous definitions and proofs, giving examples from fields of mathematics, physics, and other sciences where matrices are successfully applied. The book will surely be interesting and helpful for students in algebra and their teachers.
—European Mathematical Society Newsletters
This is an excellent, well-written textbook which is strongly recommended to a wide audience of readers interested in mathematics and its applications. The book is suitable for a one semester undergraduate lecture course in matrix groups, and would also be useful supplementary reading for more general group theory courses.
—MathSciNet (or Mathematical Reviews)
Undergraduate and graduate students and research mathematicians interested in teaching and learning Lie groups, in particular, classical Lie groups.
Table of Contents
- Chapter 1. Why study matrix groups?
- Chapter 2. Matrices
- Chapter 3. All matrix groups are real matrix groups
- Chapter 4. The orthogonal groups
- Chapter 5. The topology of matrix groups
- Chapter 6. Lie algebras
- Chapter 7. Matrix exponentiation
- Chapter 8. Matrix groups are manifolds
- Chapter 9. The Lie bracket
- Chapter 10. Maximal tori
- Chapter 11. Homogeneous manifolds
- Chapter 12. Roots