Group Theory

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, Burnsideâs Counting Theorem and its application to the art of Sol LeWitt, the mathematics of the Rubikâs Cube, finite fields and coding theory, and Dicksonâs classification of the natural numbers for which every group of that order is abelian or cyclic. FeaturesIncludes 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.