Group Theory: Finite Discrete Groups And Applications

Symmetry is an essential concept in the understanding of the physical world, leading to the notion of transformations and the branch of mathematics known as Group Theory. This volume focuses on discrete groups, which are countable, usually finite in number, and can be used as a tool for applications. It is not intended for those who would like to just look up a formula or use the results of a table without understanding their derivation.

Format: Hardback
Length: 364 pages
Publication date: 21 July 2023
Publisher: World Scientific Publishing Co Pte Ltd

This book delves into the profound influence of symmetry on our understanding of the physical world, commencing with the concept of geometric symmetries that were explored by ancient Greek philosophers and mathematicians. The recognition of symmetries paved the way for the notion of transformations, which facilitated the transition between different states of a system. It was subsequently discovered that these transformations, when subjected to multiplication, formed a captivating set, leading to the development of the field of mathematics known as Group Theory.

With the advent of quantum mechanics, this theory gained even greater interest, yielding numerous additional applications. Furthermore, the requirement for the description of physical systems with internal degrees of freedom further propelled the theory, transforming the concept of symmetry from a purely geometric notion into a valuable tool for studying all branches of physical sciences.

For practical and pedagogical purposes, Group Theory is typically divided into two main sections. The first focuses on discrete groups, where the group elements are countable and typically limited in number. On the other hand, the second deals with continuous groups, whose elements are dependent on continuous parameters.

This volume specifically concentrates on discrete groups, recognizing the importance of presenting Group Theory from a unified perspective that encompasses both the mathematical rigor and aesthetic beauty of symmetries while also highlighting its practical applications. It is not intended for individuals who seek to merely reference formulas or utilize results from tables without comprehending their underlying derivations.

ISBN-13: 9789811274756