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Groups and Symmetries: From Finite Groups to Lie Groups (Universitext)
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Beginning with a review of the basic definitions and results of group theory, this volume illustrates definitions with examples important to the study of symmetry. With only linear algebra and calculus as prerequisites, this book will be widely accessible.
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Product details
Series: Universitext (Book 261)
Paperback: 212 pages
Publisher: Springer; 2010 edition (October 28, 2009)
Language: English
ISBN-10: 0387788654
ISBN-13: 978-0387788654
Product Dimensions:
6.1 x 0.5 x 9.2 inches
Shipping Weight: 13.4 ounces (View shipping rates and policies)
Average Customer Review:
4.0 out of 5 stars
1 customer review
Amazon Best Sellers Rank:
#1,823,948 in Books (See Top 100 in Books)
be forewarned that this very concise book is not an easy read, except for someone with a very solid background in abstract and advanced linear algebra. It deserves 5 stars for the lucidity of the mathematical presentation, but I deducted 1 star as a heads up because despite its claim to be aimed at advanced undergraduates / beginning graduates in math *or* physics, I think the book would be tough going for many readers who fit that description. As a math-degree-less autodidact, I found the book very challenging in places. To be fair, I found Chapter 2, Representations of Finite Groups, the most difficult chapter, and this no doubt colored my perception of the book as a whole. So if you can power through that chapter, you might well find the rest fairly smooth sailing.One major plus is that there are a large number of problems and complete solutions (pp 129 - 183).For me, the most outstanding feature -- and the reason I read the book - is that it explains in very clear, mathematically rigorous terms the basic group-theoretic math behind the standard model of elementary particle physics. If you make it through to the end, then you'll come to understand in a mere 100 pages, what, mathematically speaking, the Eightfold Way and quarks really are! This is quite an accomplishment. I have not found any other introductory book that does this except Frankel's The Geometry of Physics: An Introduction, Second Edition, which, although a superb book for self-study, is a very long read. There are also a number of well-written books aimed at physicists like Sternberg's Group Theory and Physics or Ramond's Group Theory: A Physicist's Survey that deal with the topic in some detail and are well worth studying, but no introductory book on the standard model I've consulted, e.g., Griffiths' Introduction to Elementary Particles, even attempts to address the issue. (If you know of one that does, please leave me a comment informing me.)In sum, this is a very clear but ultra-concise exposition of the essential mathematics needed to understand mathematically what those diagrams of representations of groups you see in physics books on the standard model really mean. But if you're not 100% comfortable with very condensed mathematical presentations, this book is probably not the right first book._________________P.S. If you'd like a succinct but clear introduction to the more basic mathematics used in this text or e.g. in Robinson's exceptionally well written but more informal Symmetry and the Standard Model: Mathematics and Particle Physics, check out Tapp's Matrix Groups for Undergraduates (Student Mathematical Library,) or Stillwell's Naive Lie Theory (Undergraduate Texts in Mathematics).
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