Matrix Groups for Undergraduates

Häftad, Engelska, 2016

Del i serien Student Mathematical Library

700 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-04-30
Mått:140 x 203 x undefined mm
Vikt:300 g
Format:Häftad
Språk:Engelska
Serie:Student Mathematical Library
Antal sidor:239
Upplaga:2
Förlag:American Mathematical Society
ISBN:9781470427221

Utforska kategorier

Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Mer om författaren

Kristopher Tapp, Saint Joseph's University, Philadelphia, PA, USA.

Recensioner i media

This book offers a very nice introduction to the theory of matrix groups and their Lie algebras. The background is kept to a minimum, only basics of calculus, linear algebra and group theory are assumed, while background on topology (of subsets of Euclidean space) is developed in the text. While the text gives complete and exact proofs, it is easy to read, appeals to intuition, and contains many pictures and helpful exercises." - A. Cap, Monatshefte für Mathematik"[T]he second edition is an expanded and improved version of the original. It can be strongly recommended for an undergraduate course in Lie groups, or as complementary reading for a course in group theory. Prerequisites are basic: knowledge of algebra, geometry, and analysis at an undergraduate level. Hence the book is suitable for a wide audience of readers who are meeting applications of group theory in other areas of mathematics and physics, or even further afield." - Alla S. Detinko, Mathematical Reviews"The author gives an inspiring presentation of the topics presented in this book." - Erich W. Ellers, Zentralblatt Math

Innehållsförteckning

Why study matrix groups?MatricesAll matrix groups are real matrix groupsThe orthogonal groupsThe topology of matrix groupsLie algebrasMatrix exponentiationMatrix groups are manifoldsThe Lie bracketMaximal toriHomogeneous manifoldsRootsBibliographyIndex