Ebook: Groups and symmetries: From finite groups to Lie groups

Unlike many other texts, this book deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume.

Key Topics:

• Brisk review of the basic definitions of group theory, with examples

• Representation theory of finite groups: character theory

• Representations of compact groups using the Haar measure

• Lie algebras and linear Lie groups

• Detailed study of SO(3) and SU(2), and their representations

• Spherical harmonics

• Representations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group

This book is illustrated with portraits and a few historical remarks. With only linear algebra and calculus as prerequisites, Groups and Symmetries: From Finite Groups to Lie Groups is accessible to advanced undergraduates in mathematics and physics, and will still be of interest to beginning graduate students. Exercises for each chapter and a collection of problems with complete solutions make this an ideal text for the classroom and for independent study.

- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas

- Applies material to physics so students appreciate the applications of abstract mathematics

- Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates

- Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study