Representation Theory of Finite Groups An Introductory Approach [Paperback]

This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.This book presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. It can also be used as a reference for academics working in all areas of mathematics and statistics. Includes exercises.-Preface.-Introduction.-Review of Linear Algebra.-Group Representations.-Character Theory.-Fourier Analysis on Finite Groups.-Burnside's Theorem.-Permutation Representations.-Induced Representations.-Another Theorem of Burnside.-The Symmetric Group.-Bibliography.-Index.

From the reviews:

The aim of the author is to give an introductory text on (ordinary) representation theory of finite groups which is accessible for advanced undergraduates already. And Steinberg manages this outstandingly well. & a book which is ideally suited for beginners in math as well as physicists, engineers and so on, who need a concise, well conceived and easy comprehensible introduction into representation theory. (G. Kowol, Monatshefte f?r Mathematik, Vol. 167 (3-4), September, 2012)

Steinberg & provides a one-semester course on representation theory with just linear algebra and lÃ;