- Paperback: 316 pages
- Publisher: Princeton University Press; New Ed edition (13 Oct 1997)
- Language English
- ISBN-10: 0691057567
- ISBN-13: 978-0691057569
- Product Dimensions: 23 x 15.2 x 2 cm
- Amazon Bestsellers Rank: 1,205,053 in Books (See Top 100 in Books)
- See Complete Table of Contents
| ||||||||||||||||||||||||
Did you know you can trade in your old books for an Amazon.co.uk Gift Card to spend on the things you want? Plus, get an extra £5 Gift Certificate when you trade in books worth £10 or more before June 30, 2012. Visit the Books Trade-In Store for more details. |
Product details |
More About the Author
Product Description
Product Description
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.
Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."
Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.
Inside This Book
(Learn More)
First Sentence
Before we can start talking algebra we must fix the field k of numbers wherein we operate. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Before we can start talking algebra we must fix the field k of numbers wherein we operate. Read the first page
Explore More
Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Tag this product(What's this?)Think of a tag as a keyword or label you consider is strongly related to this product.
Tags will help all customers organise and find favourite items. |
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Reviews
There are no customer reviews yet on Amazon.co.uk.
5 star
4 star
3 star
2 star
1 star
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
3 reviews
27 of 27 people found the following review helpful
Hard-core Group Theory
15 Mar 2001
Format:Paperback|Amazon Verified Purchase
Forget about that pansy abstract axiom approach. This is the WWF of group theory. Weyl will take anyone to the mat with this book. It is packed with detail and demonstrations. He follows the vector space/matrix representation approach common to digital systems, physics and chemistry rather than axiomatic, generators/permutations approach more common in Abstract Algebra courses. This is the lineage that develops matrix transforms as groups starting from "the full group of all non-singular linear transformations and .. the orthogonal groups" (p. vii). The latter chapters cover characters and invariants. Galois and field theory have been vanquished. Chapter 2, "Remembrance of things past" is very entertaining. My favorite quote, "Here there is only one man to mention - Hilbert. His papers (1890/92) mark a turning point in the history of invariants theory. He solves the main problems and thus almost kills the whole subject." It's funny because it's true. This is almost a botanical treatise in which the matrix groups are studied as specimens in the jungle -- "...after all each group stands in its own right and does not deserve to be looked upon merely as a subgroup of...Her All-embracing Majesty GL(n)." (p 136). Historic references throughout provide motivation and entertainment. You couldn't possibly be disappointed with this book.
12 of 12 people found the following review helpful
Great
27 April 2000
Format:Paperback
Although this is a dated work, lacking some of the more modern language, it is still worth owning and reading. It is, after all, a designated "classic." And the material presented has been incorporated within so many aspects of physics that one simply cannot avoid needing a book such as this. There are better books on the subject, for both mathematicians and physicists, but this book still proves its worth.
0 of 4 people found the following review helpful
maybe a liitle more difficult than it has to be?
25 Sep 2009
Format:Paperback
His presentation of simplectic groups ( although short) was helpful.
That said having had Weyl's Space, Time, Matter for many years
I'm used to his notation, but here he is very intense in his presentation
and somewhat less than clear. As he is the founder of gauge group theory
one expects some mathematics, just not where it seems more difficult than necessary?
Also the, now, standard classifications of Cartan groups aren't mentioned ( although might be
because of the original publishing date of 1939?).
I got this book looking for the Weyl root groups used in making Cartan invariant matrices
which I couldn't find.
So on these points the book is a disappointment while still being a classic text.
That said having had Weyl's Space, Time, Matter for many years
I'm used to his notation, but here he is very intense in his presentation
and somewhat less than clear. As he is the founder of gauge group theory
one expects some mathematics, just not where it seems more difficult than necessary?
Also the, now, standard classifications of Cartan groups aren't mentioned ( although might be
because of the original publishing date of 1939?).
I got this book looking for the Weyl root groups used in making Cartan invariant matrices
which I couldn't find.
So on these points the book is a disappointment while still being a classic text.
Were these reviews helpful?
Let us know
Listmania!
Look for similar items by category
Look for similar items by subject
Feedback
- Would you like to update product info or give feedback on images?
- I am the Author, and I want to comment on my book.
- I am the Publisher, and I want to comment on this book.
|
