 | GetTextbooks.com Compare Prices & Save up to 90% | | |
|
| Login | Sign up | Settings | New! iPhone App | My Wish List | My iBundle |
 | | Naive Lie Theory (Undergraduate Texts in Mathematics) by John Stillwell ISBN-10: 9780387782140 ISBN-10: 0-387-78214-1 ISBN-13: 9780387782140 ISBN-13: 978-0-387-78214-0 Hardcover 2008-07-24 Springer Find Lowest Price |
Editorials | ||
Product Description 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). | ||
Reviews | ||
a modern introduction to quantum field theory A very good text for graduate students with a little or no knowledge of Quantum Field Theory. | ||
Excellent read An excellent read. In just 200 pages the author explains what Lie groups and algebras actually are. Most books on Lie theory are aimed at professional mathematicians, so begin with lots of topological and algebraic preliminaries and finally define a Lie group as a group that is also a manifold, or something similar. Stillwell begins with an example of the simplest Lie group, SO(2), as a group of rotations in the circle, then proceeds methodically to the next example SU(2), the first non-commutative Lie group. In short order all the other classical groups are discussed and, in chapter 5, the concepts of tangent space and Lie algebra are made clear through more examples. An undergraduate who has taken the calculus series, had a course in linear algebra that discusses matrices, has some knowledge of complex variables and some understanding of group theory should easily follow the material to this point. Topology, usually a graduate topic, is introduced later while showing which Lie groups are simply-connected, and how this is used to distinguish between similar Lie groups. The material was clearly discussed and I found only a couple of typos. But I also found the use of the word vector and matrix for the same object in the same paragraph somewhat dis-quieting. Lastly, I would have liked to have seen some mention of Lie theory connections with modern physics. | ||
An excellent introduction to Lie Theory I'm no expert in Lie groups or Lie algebras, I didn't read any of that stuff in my M. Sc. Eng. Phys. so i decided to try Professor Stilwells book as an introduction to the subject. I am very glad that I bought this book. What Prof. Stilwell promises in the foreword is true - you can read and understand this book with a background of only calculus and linear algebra. The book introduces a lot of advanced concepts, but in a very clear and logic way - there is no problem for an undergraduate to comprehend the material. I guess the book is meant to be a school text book - it was a little hard for me to try to self-study some of the excercises, because there are no solutions provided. I like that every chapter starts with a preview to give an orientation of what will be presented in the chapter. Every chapter also ends with a discussion, which gives historical aspects of the presented theory, and some suggestions for further litterature on the various subjects. This is nice - it gives a wider perspective to the subject. I think this book is a very good stepping-stone on the reader's way from undergrad math to graduate topics, and I hope there will be more books of this kind. | ||