Visual Group Theory: A Computer-Oriented Geometric Introduction (Springer Undergraduate Mathematics Series)

Visual Group Theory: A Computer-Oriented Geometric Introduction (Springer Undergraduate Mathematics Series)
by: Stephan Rosebrock (Author)
Publisher: Springer
Edition: 2024th
Publication Date: 2024/7/5
Language: English
Print Length: 252 pages
ISBN-10: 366269364X
ISBN-13: 9783662693643
Book Description
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
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. Read more