Discovering group theory a transition to advanced mathematics - Barnard, Tony; Neill, Hugh (Boca Raton, FL CRC Press, Taylor & Francis Group, 2017)
This book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book aims to help students with the transition from concrete to abstract mathematical thinking. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study co-sets and finishes with The First Isomorphism Theorem. Very little background knowledge on the part of the reader is assumed. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. This book is written in a reader-friendly conversational style. Complete solutions are given to all exercises.
1. Proof -- 2. Sets -- 3. Binary operations -- 4. Integers -- 5.Groups -- 6. Subgroups -- 7. Cyclic groups -- 8. Products of groups -- 9. Functions -- 10. Composition of functions -- 11. Isomorphisms -- 12. Permutations -- 13. Dihedral groups -- 14. Cosets -- 15. Groups of orders up to 8 -- 16. Equivalence relations -- 17. Quotient groups -- 18. Homomorphisms -- 19. The first isomorphism theorem.
Previous edition: Mathematical groups / Tony Barnard and Hugh Neill (London : Teach Yourself Books, 1996).
Includes bibliographical references and index.
Keywords: Group theory -- Textbooks; Algebra -- Textbooks; Mathematics -- Study and teaching