Group Theory

An Example-Based Introduction
1. Auflage 2027
ISBN: 978-1-041-29519-8
Verlag: Taylor & Francis Ltd

Buch, Englisch, 456 Seiten, Format (B × H): 178 mm x 254 mm

Reihe: Textbooks in Mathematics

Group Theory: An Example-Based Introduction is an introduction to group theory for upper-level undergraduates with prior experience reading and writing mathematical proofs. It covers all the standard topics expected of an introductory text, including cyclic groups, quotient groups, the isomorphism theorems, the structure theorem for finitely generated abelian groups, group actions, and the Sylow Theorems. Throughout the book, abstract ideas are motivated by concrete examples and applications drawn from geometry, number theory, art, puzzles, and coding theory. In addition to the standard curriculum, topics include the classification of isometries of the Euclidean plane, frieze and wallpaper groups, Burnside’s Counting Theorem and its application to the art of Sol LeWitt, the mathematics of the Rubik’s Cube, finite fields and coding theory, and Dickson’s classification of the natural numbers for which every group of that order is abelian or cyclic.

Features

- Includes over 250 examples and 500 exercises to help readers master the material.

- Explores applications of group theory to geometry, number theory, art, puzzles, and coding theory.

- Every chapter ends with suggestions for further reading and the biography of an influential mathematician.

- A solutions guide featuring answers to odd-numbered exercises freely available at www.routledge.com/9781041295198.

Zielgruppe

Undergraduate Core

Autoren/Hrsg.

Linowitz, Benjamin

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

1. Motivation 2. Number Theory 3. What is a Group? 4. Important Families of Groups 5. Lagrange’s Theorem and Cauchy’s Theorem 6. Quotient Groups 7. The Isomorphism Theorems 8. The Structure Theorem for Finitely Generated Abelian Groups 9. Divisible and Torsion Groups 10. Groups Acting on Sets 11. Burnside’s Counting Theorem 12. The Sylow Theorems 13. Geometric Group Actions 14. Frieze Groups and Wallpaper Groups 15. Semidirect Products 16. When is Every Group of Order n 17. The Rubik’s Cube 18. Rings, Fields, and Algebraic Coding Theory

Über Autor(innen)

Benjamin Linowitz is an Associate Professor of Mathematics at Oberlin College. After high school he spent three years active duty in the US Army before receiving a Green to Gold scholarship to attend college. He received his undergraduate degree from the University of Pennsylvania in 2006 and his PhD from Dartmouth College in 2012. Following this, he was an NSF postdoctoral fellow at the University of Michigan. He has authored more than 30 research articles, and his work has been supported by grants from the National Science Foundation and the Simons Foundation. His research focuses on the theory of arithmetic groups, particularly their applications to geometry and topology. A passionate educator, Benjamin enjoys teaching undergraduate courses on abstract algebra, number theory, geometry, and the history of mathematics.