Overview
- Combines geometric intuition with algebra
- Uses computers as a learning aid, via the open source GAP software
- Contains a numerous illustrative examples and practice exercises
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Keywords
- Algebra
- Euclidean geometry
- Hyperbolic Geometry
- textbook on group theory
- Homomorphism
- Quotient group
- Solvable groups
- Infinite groups
- Products of groups
- Permutation groups
- Subgroup
- Finite groups
About this book
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.
Authors and Affiliations
About the author
Stephan Rosebrock is a professor at the Institute of Mathematics and Computer Science of the University of Education in Karlsruhe, Germany.
Bibliographic Information
Book Title: Visual Group Theory
Book Subtitle: A Computer-Oriented Geometric Introduction
Authors: Stephan Rosebrock
Series Title: Springer Undergraduate Mathematics Series
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2024
Softcover ISBN: 978-3-662-69364-3Due: 31 July 2024
eBook ISBN: 978-3-662-69365-0Due: 31 July 2024
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XII, 239
Number of Illustrations: 72 b/w illustrations, 1 illustrations in colour
Additional Information: Translation from the German language edition: "Anschauliche Gruppentheorie. Eine computerorientierte geometrische Einführung" by Stephan Rosebrock. © Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2020