Chapter 4: Groups, Rings, and Fields

Kapitel in diesem Buch

1. Frontmatter i
2. Contents v
3. Preface xi
4. Chapter 1: A Brief Survey of Elementary Functions 1
5. Chapter 2: Propositional Algebra 27
6. Chapter 3: Naïve and Formal (Axiomatic) Set Theory 51
7. Chapter 4: Groups, Rings, and Fields 67
8. Chapter 5: Predicates and Quantifiers—Algebraic Theory 79
9. Chapter 6: Binary Relations and Relational Databases 93
10. Chapter 7: Combinatorics 117
11. Chapter 8: Elements of Number Theory 139
12. Chapter 9: Boolean Functions 163
13. Chapter 10: Hashing Functions and Cryptographic Maps 171
14. Chapter 11: Generating Polynomials and Inversion Formulas 179
15. Chapter 12: Systems of Representatives 187
16. Chapter 13: Boolean Algebras 193
17. Chapter 14: Combinatorial Circuits 201
18. Chapter 15: Complete Systems of Boolean Functions and Bases 211
19. Chapter 16: Introductory Graph Theory, Euler’s Formula, and Unbreakable Ciphers 225
20. Chapter 17: Trees and Digraphs 245
21. Chapter 18: Computations and Algorithms 263
22. Chapter 19: Finite Automata 271
23. Chapter 20: Introduction to Game Theory 297
24. Chapter 21: Information Theory and Coding 309
25. Chapter 22: Probability Theory with a Finite Sample Space and the Birthday Problem 319
26. Chapter 23: Turing Machines, P and NP Classes, and Other Models of Computation 341
27. Chapter 24: Answers and Solutions to Selected Exercises 351
28. Bibliography 361
29. Index 365