Discovering Group Theory ─ A Transition to Advanced Mathematics

This book presents group theory to students taking a course to transition to advanced mathematics. The goal is to prepare these students for higher level mathematical study, including advanced algebra courses. The book covers the usual material which is found in a first course on groups. The first three chapters are preliminary. Chapter 4 establishes a number of results about integers which will be used freely in the remainder of the book. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups and groups of residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem.

Tony Barnard has lectured at King's College London on abstract algebra for over 35 years. His research activity was initially in the area of commutative rings and more recently has been in the psychology of mathematics education.? He has worked with school teachers and mathematics educators in developing teaching programmes for elementary geometry and algebraic fluency.? Over the past fifteen years, he has served on several consultative committees of the UK government and learned societies, advising on matters relating to the school mathematics curriculum and university mathematics teaching.
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Hugh Neill started as a school teacher, moved into mathematics teaching at the University of Durham and then became the senior mathematics inspector in schools in Inner London until the Inner London Education Authority was abolished in 1990. During this time he was heavily involved in the design and assessment of mathematics courses for future mathematics teachers. Since 1990 he has been writing mathematics books.