Review of Introduction to Groups

Introduction to Groups is the first of a series of learning resources designed for individual study of some topics in university level mathematics. Written by David Saunders and published by Symplekta, it aims to provide an introduction to the subject of Groups for Mathematics and is suitable both for University students and for those studying Further Mathematics at A level. The author has also written a follow-up (doing some serious group theory for 1st/ 2nd year university students) and is now starting on a disk introducing matrices. The CD consists of an hour or more of audio tutorial (depending on the user’s speed of progress), animations and interactivity, exercises and a hyper linked glossary. It uses numbers, permutations and the symmetries of geometrical objects to motivate the introduction of group axioms. Concrete examples of small groups are used to illustrate the ideas of subgroup and isomorphism, and a statement of Lagrange’s Theorem is used to motivate the definition of a coset. The proof of Lagrange’s Theorem is covered, together with that of Fermat’s Little Theorem as a corollary.