A Gentle Introduction to Group Theory

The book is intended to serve as an introductory course in group theory geared towards second-year university students. It aims to provide them with the background needed to pursue more advanced courses in algebra and to provide a rich source of examples and exercises. Studying group theory began in the late eighteenth century and is still gaining importance due to its applications in physics, chemistry, geometry, and many fields in mathematics.

Format: Hardback
Length: 417 pages
Publication date: 01 June 2023
Publisher: Springer Verlag, Singapore

The book is designed to serve as an introductory course in group theory, specifically geared towards second-year university students. Its primary objective is to provide the necessary background and foundational knowledge for students to pursue advanced courses in algebra and to serve as a comprehensive resource for examples and exercises. The study of group theory has a rich history dating back to the late eighteenth century, and it continues to gain importance due to its wide-ranging applications in physics, chemistry, geometry, and various branches of mathematics.

The text is structured into three main parts. The first part focuses on establishing the prerequisite knowledge required to study group theory. This includes topics such as set theory, geometry, and number theory. Each chapter concludes with a combination of solved and unsolved exercises designed to reinforce the concepts covered. By incorporating these exercises, the authors aim to bridge the gaps between different branches of mathematics that are interconnected with group theory.

The second part of the book constitutes the core of the material, delving into various topics related to groups, semigroups, symmetric groups, subgroups, homomorphisms, isomorphisms, and Abelian groups. Each topic is presented in a clear and concise manner, with detailed explanations and illustrative examples. The authors have carefully crafted the content to ensure that students can grasp the fundamental principles and apply them to solve practical problems.

The third and final part of the book introduces SAGE, a powerful mathematical software tool widely used in group theory. This section provides an in-depth explanation of the key commands and functionalities of SAGE, enabling students to utilize it effectively for solving complex group theory problems. Numerous examples and exercises are included to reinforce the concepts and facilitate hands-on learning.

In conclusion, this book is an invaluable resource for students embarking on a journey into the world of group theory. It offers a comprehensive and well-organized introduction to the subject, covering the essential topics and providing ample opportunities for practice and application. Whether students are aspiring mathematicians, scientists, or engineers, this book will equip them with the skills and knowledge needed to excel in their respective fields.

Weight: 909g
Dimension: 235 x 155 (mm)
ISBN-13: 9789819901463
Edition number: 1st ed. 2023