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Synopsis
Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. Until now, however, there have been virtually no accessible treatments of group theory that include representations and characters. The classic works in the field require a high level of mathematical sophistication, and other texts omit representations and characters.
Groups and Characters offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, this unique text emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The author presents group theory through the Sylow Theorems and includes the full subgroup structure of A5. Representations and characters are worked out with numerous character tables, along with real and induced characters that lead to the table for S5.
The text includes specific sections that provide the mathematical basis for some of the important applications of group theory in spectroscopy and molecular structure. It also offers numerous exercises-some stressing computation of concrete examples, others stressing development of the mathematical theory.
Groups and Characters provides the ideal grounding for more advanced studies with the classic texts, and for more broad-based work in abstract algebra. Furthermore, physical scientists-whose experience with groups and characters may not be rigorous-will find Groups and Characters the ideal means for gaining a sense of the mathematics lying behind the techniques used in applications.
Booknews
Hill (mathematics, Williams College, Massachusetts) introduces the theory of group and group characters at an easier level of mathematics than the classic works by Curtis and Reiner. He addresses undergraduate or beginning graduate mathematics students who want to get their feet wet before plunging into the subject; students in chemistry, physics, or geology who might encounter groups and characters is such areas as crystallography or quantum mechanics; and physical scientists whose exposure to the techniques has been less than rigorous and would like to understand the mathematics behind them. Annotation c. Book News, Inc., Portland, OR (booknews.com)