Visual Group Theory : A Computer-Oriented Geometric Introduction

Stephan Rosebrock

ISBN 10: 366269364X / ISBN 13: 9783662693643

Published by Springer, Springer, 2024

About this Item

Druck auf Anfrage Neuware - Printed after ordering - This textbook provides an introduction to group theory starting from the basics, relying on geometry to elucidate its various aspects.Groups naturally manifest as symmetries of geometric shapes, such as reflections and rotations. The book adopts this perspective to provide a straightforward, descriptive explanation, supported by examples and exercises in GAP, an open-source computer algebra system. It covers all of the key concepts of group theory, including homomorphisms, group operations, presentations, products of groups, and finite, abelian, and solvable groups. The topics include cyclic and symmetric groups, dihedral, orthogonal, and hyperbolic groups, as well as the significant notion of Cayley graphs.Self-contained and requiring little beyond high school mathematics, this book is aimed at undergraduate courses and features numerous exercises. It will also appeal to anyone interested in the geometric approach to group theory.

Seller Inventory # 9783662693643

Bibliographic Details

• Title: Visual Group Theory : A Computer-Oriented Geometric Introduction
• Publisher: Springer, Springer
• Publication Date: 2024
• Language: English
• ISBN 10: 366269364X
• ISBN 13: 9783662693643
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 14D millimeters 235 millimeters width by 155 millimeters height by 14 millimeters depth
• Weight: 388 grams

About this title

Synopsis

This textbook provides an introduction to group theory starting from the basics, relying on geometry to elucidate its various aspects.

Groups naturally manifest as symmetries of geometric shapes, such as reflections and rotations. The book adopts this perspective to provide a straightforward, descriptive explanation, supported by examples and exercises in GAP, an open-source computer algebra system. It covers all of the key concepts of group theory, including homomorphisms, group operations, presentations, products of groups, and finite, abelian, and solvable groups. The topics include cyclic and symmetric groups, dihedral, orthogonal, and hyperbolic groups, as well as the significant notion of Cayley graphs.

Self-contained and requiring little beyond high school mathematics, this book is aimed at undergraduate courses and features numerous exercises. It will also appeal to anyone interested in the geometric approach to group theory.

About the Author

Stephan Rosebrock is a professor at the Institute of Mathematics and Computer Science of the University of Education in Karlsruhe, Germany.