Overview

"In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called ""classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994)."

Full Product Details

Author:   John Stillwell
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2008 ed.
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   1.120kg
ISBN:  

9780387782140

ISBN 10:   0387782141
Pages:   217
Publication Date:   24 July 2008
Audience:   College/higher education ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Geometry of complex numbers and quaternions.- Groups.- Generalized rotation groups.- The exponential map.- The tangent space.- Structure of Lie algebras.- The matrix logarithm.- Topology.- Simply connected Lie groups.

Reviews

From the reviews: <p> This is a beautifully clear exposition of the main points of Lie theory, aimed at undergraduates who have a ] calculus and linear algebra. a ] The book is well equipped with examples a ] . The book has a very strong geometric flavor, both in the use of rotation groups and in the connection between Lie algebras and Lie groups. (Allen Stenger, The Mathematical Association of America, October, 2008)

From the reviews: This is a beautifully clear exposition of the main points of Lie theory, aimed at undergraduates who have ! calculus and linear algebra. ! The book is well equipped with examples ! . The book has a very strong geometric flavor, both in the use of rotation groups and in the connection between Lie algebras and Lie groups. (Allen Stenger, The Mathematical Association of America, October, 2008) Lie theory, basically the study of continuous symmetry, certainly occupies a central position in modern mathematics ! . In Naive Lie Theory, Stillwell (Univ. of San Franciso) concentrates on the simplest examples and stops short of representation theory ! . Summing Up: Recommended. Upper-division undergraduates and graduate students. (D. V. Feldman, Choice, Vol. 46 (9), May, 2009) This book provides an introduction to Lie groups and Lie algebras suitable for undergraduates having no more background than calculus and linear algebra. ! Each chapter concludes with a lively and informative account of the history behind the mathematics in it. The author writes in a clear and engaging style ! . The book is a welcome addition to the literature in representation theory. (William M. McGovern, Mathematical Reviews, Issue 2009 g)

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