00000cam a22000004i 4500 UP-99796217612992207 Buklod 20190405100653.0 a r |||| u| ta 190405s2017 xx d r |||| u| 9781138030169 (pbk.) (iLib)UPD-00398864165 DLC DIM rda eng DMLUC QA 174.2 B37 2017 Barnard, Tony author. Mathematical groups. Discovering group theory a transition to advanced mathematics Tony Barnard, Hugh Neill. Boca Raton, FL CRC Press, Taylor & Francis Group [2017] xii, 219 pages illustrations 24 cm text rdacontent unmediated rdamedia volume rdacarrier Textbooks in mathematics Previous edition: Mathematical groups / Tony Barnard and Hugh Neill (London : Teach Yourself Books, 1996). Includes bibliographical references and index. 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. 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. Group theory Textbooks. Algebra Textbooks. Mathematics Study and teaching. Neill, Hugh author. FO UPD DIM QA 174.2 B37 2017 Book