Matrix Groups for Undergraduates

Erscheinungsjahr 2005
ISBN: 978-0-8218-3785-6
Verlag: American Mathematical Society

Buch, Englisch, 166 Seiten, Gewicht: 223 g

Reihe: Student Mathematical Library

Matrix groups are a beautiful subject and are central to many fields in mathematics and physics. They touch upon an enormous spectrum within the mathematical arena. This textbook brings them into the undergraduate curriculum. It is excellent for a 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. The volume is suitable for graduate students and researchers interested in group theory.

Contents

- Why study matrix groups?

- Matrices

- All matrix groups are real matrix groups

- The orthogonal groups

- The topology of matrix groups

- Lie algebras

- Matrix exponentiation

- Matrix groups are manifolds

- The Lie bracket

- Maximal tori

- Bibliography

- Index

Zielgruppe

Graduate students and researchers interested in group theory.

Autoren/Hrsg.

Tapp, Kristopher

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Über Autor(innen)

Kristopher Tapp, Williams College, Williamstown, MA