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Matrix Groups for Undergraduates
Kristopher Tapp, Williams College, Williamstown, MA
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Student Mathematical Library
2005; 166 pp; softcover
Volume: 29
ISBN-10: 0-8218-3785-0
ISBN-13: 978-0-8218-3785-6
List Price: US$32
Member Price: US$25.60
Order Code: STML/29
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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.

Readership

Undergraduates and beginning graduate students interested in group theory.

Reviews

"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."

-- Mathematical Reviews

Table of 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
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