Volume: 39; 2019; 304 pp; Hardcover
MSC: Primary 20; Secondary 11; 00
Print ISBN: 978-1-4704-4932-2
Product Code: AMSTEXT/39
List Price: $82.00
AMS Member Price: $65.60
MAA Member Price: $73.80
Electronic ISBN: 978-1-4704-5352-7
Product Code: AMSTEXT/39.E
List Price: $82.00
AMS Member Price: $65.60
MAA Member Price: $73.80
Supplemental Materials
Sets, Groups, and Mappings: An Introduction to Abstract Mathematics
Share this pageAndrew D. Hwang
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.
Readership
Undergraduate students interested in the introduction to proofs and elementary concepts in abstract algebra.
Table of Contents
Table of Contents
Sets, Groups, and Mappings: An Introduction to Abstract Mathematics
- Cover Cover11
- Title page i2
- Contents v6
- To the Instructor ix10
- To the Student xiii14
- Chapter 1. Logic and Proofs 118
- Chapter 2. An Introduction to Sets 1532
- Chapter 3. The Integers 3350
- Chapter 4. Mappings and Relations 4764
- Chapter 5. Induction and Recursion 7188
- Chapter 6. Binary Operations 93110
- Chapter 7. Groups 107124
- Chapter 8. Divisibility and Congruences 125142
- Chapter 9. Primes 135152
- Chapter 10. Multiplicative Inverses of Residue Classes 145162
- Chapter 11. Linear Transformations 159176
- Chapter 12. Isomorphism 181198
- Chapter 13. The Symmetric Group 193210
- Chapter 14. Examples of Finite Groups 209226
- Chapter 15. Cosets 225242
- Chapter 16. Homomorphisms 237254
- Chapter 17. Group Actions 253270
- Chapter 18. Euclidean Geometry 275292
- Appendix A. Euler’s Formula 297314
- Index 299316
- Back Cover Back Cover1322