Fascination of Groups by Budden (PDF)

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⭐In the preface the author states that this is not a textbook but a companion whose purpose is to enlighten both students and teachers concerned with the application of groups theory. There are many examples of applications in geometry, music, and campanology (i.e. the study of bells). For those that are interested in and fascinated by group theory, this book will be useful for self-study. The contents are as follows:1. Mathematical structure; 2. Putting things together: binary operations on a set; 3. Self-contained systems: closure; 4. Combined Ops: composition of operations; 5. Associativity; 6. Status Quo: identity elements; 7. As you were! – inverses; 8. Groups structure; 9. Properties of groups; 10. Period (or order) of an element: permutations and cycles; 11. Carbon copy groups: abstract groups: isomorphism; 12. Cyclic groups; 13. The dihedral group; 14. Groups within groups; 15. Group specifications: generators and defining relations; 16. Bigger and better groups: direct product groups; 17. Catalogue of groups: symmetry groups; 18. Permutations; 19. Cosets in finite and infinite groups: equivalence classes; 20. Conjugate elements: normal subgroups (1); 21. Homomorphism: quotients groups: normal subgroups (2); 22. Automorphisms; 23. Groups and music; 24. Ringing the changes: groups and campanology; 25. Groups in geometrical situations; 26. Patterns.

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