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Sets, Groups, and Mappings
An Introduction to Abstract Mathematics
Andrew D. Hwang
- English
- PDF
- Available on iOS & Android
Sets, Groups, and Mappings
An Introduction to Abstract Mathematics
Andrew D. Hwang
About This Book
This book introduces students to the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students of math education, computer science or physics who are looking for an easy-going entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry. In its presentation, the book takes special care to forge linguistic and conceptual links between formal precision and underlying intuition, tending toward the concrete, but continually aiming to extend students' comfort with abstraction, experimentation, and non-trivial computation.The main part of the book can be used as the basis for a transition-to-proofs course that balances theory with examples, logical care with intuitive plausibility, and has sufficient informality to be accessible to students with disparate backgrounds. For students and instructors who wish to go further, the book also explores the Sylow theorems, classification of finitely-generated Abelian groups, and discrete groups of Euclidean plane transformations.
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Table of contents
- Cover
- Title page
- Contents
- To the Instructor
- To the Student
- Chapter 1. Logic and Proofs
- Chapter 2. An Introduction to Sets
- Chapter 3. The Integers
- Chapter 4. Mappings and Relations
- Chapter 5. Induction and Recursion
- Chapter 6. Binary Operations
- Chapter 7. Groups
- Chapter 8. Divisibility and Congruences
- Chapter 9. Primes
- Chapter 10. Multiplicative Inverses of Residue Classes
- Chapter 11. Linear Transformations
- Chapter 12. Isomorphism
- Chapter 13. The Symmetric Group
- Chapter 14. Examples of Finite Groups
- Chapter 15. Cosets
- Chapter 16. Homomorphisms
- Chapter 17. Group Actions
- Chapter 18. Euclidean Geometry
- Appendix A. Eulerâs Formula
- Index
- Back Cover