03151nam a22005295i 4500 978-3-662-69365-0 DE-He213 20251030112616.0 cr nn 008mamaa 240705s2024 gw | s |||| 0|eng d 9783662693650 978-3-662-69365-0 10.1007/978-3-662-69365-0 doi QA174-183 PBG bicssc MAT002010 bisacsh PBG thema Rosebrock, Stephan. author. aut http://id.loc.gov/vocabulary/relators/aut 80109 Visual Group Theory [electronic resource] : A Computer-Oriented Geometric Introduction / by Stephan Rosebrock. 1st ed. 2024. Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2024. XII, 237 p. 74 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Undergraduate Mathematics Series, 2197-4144 1 Introduction to Euclidean Geometry -- 2 Introduction to Groups -- 3 Subgroups and Homomorphisms -- 4 Group Operations -- 5 Group Presentations -- 6 Products of Groups -- 7 Finite Groups -- 8 Abelian and Solvable Groups -- 9 The Hyperbolic Plane -- 10 Hyperbolic Groups. 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. Group theory. 70149 Geometry. 68763 Geometry, Hyperbolic. 80110 Group Theory and Generalizations. 70154 Geometry. 68763 Hyperbolic Geometry. 80111 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783662693643 Printed edition: 9783662693667 Springer Undergraduate Mathematics Series, 2197-4144 75368 https://doi.org/10.1007/978-3-662-69365-0 ZDB-2-SMA ZDB-2-SXMS 61381 61381