 | GetTextbooks.com Compare Prices & Save up to 90% | | |
|
| Login | Sign up | Settings | New! iPhone App | My Wish List | My iBundle |
 | | Emergence of the Theory of Lie Groups by Thomas Hawkins ISBN-10: 9780387989631 ISBN-10: 0-387-98963-3 ISBN-13: 9780387989631 ISBN-13: 978-0-387-98963-1 Hardcover 2000-07-19 Springer Find Lowest Price |
Editorials | ||
Product Description Written by the recipient of the 1997 MAA Chauvenet Prize for mathematical exposition, this book tells how the theory of Lie groups emerged from a fascinating cross fertilization of many strains of 19th and early 20th century geometry, analysis, mathematical physics, algebra and topology. The reader will meet a host of mathematicians from the period and become acquainted with the major mathematical schools. The first part describes the geometrical and analytical considerations that initiated the theory at the hands of the Norwegian mathematician, Sophus Lie. The main figure in the second part is Weierstrass' student Wilhelm Killing, whose interest in the foundations of non-Euclidean geometry led to his discovery of almost all the central concepts and theorems on the structure and classification of semisimple Lie algebras. The scene then shifts to the Paris mathematical community and Elie Cartan's work on the representation of Lie algebras. The final part describes the influential, unifying contributions of Hermann Weyl and their context: Hilbert's Goettingen, general relativity and the Frobenius-Schur theory of characters. The book is written with the conviction that mathematical understanding is deepened by familiarity with underlying motivations and the less formal, more intuitive manner of original conception. The human side of the story is evoked through extensive use of correspondence between mathematicians. The book should prove enlightening to a broad range of readers, including prospective students of Lie theory, mathematicians, physicists and historians and philosophers of science. | ||
Reviews | ||
I'm in heaven I can't remember the last time I purchased a book that I have enjoyed so thoroughly. The day it arrived I read sixty pages in different parts of the book, mostly in the section on Hilbert and Weyl. There are so many branches of advanced mathematics that are tied together here in one place. These different branches, most developed since 1850, are taught as separate subjects nowadays. But in their development they were driven by a small group of scholars and geniuses in a few cities in Europe. I feel as though I'm in Berlin and Paris and Göttingen listening to these great minds as they share ideas, and as one branch of mathematics nourishes and stimulates another. One of the great ideas of Riemann and Hilbert and Weyl is the unity of mathematics, and also physics. This book recaptures that mystical and beautiful unity. I felt like all my Christmases came at once. It was so difficult to choose a section to read that I read many, and have now settled down to read the whole book carefully from cover to cover. | ||