Mathematics: A Discrete Introduction Book

PART I: FUNDAMENTALS. 1. Definition. 2. Theorem. 3. Proof. 4. Counterexample. 5. Boolean Algebra. PART II: COLLECTIONS. 6. Lists. 7. Factorial. 8. Sets I: Introduction, Subsets. 9. Quantifiers. 10. Sets II: Operations. PART III: COUNTING AND RELATIONS. 11. Relations. 12. Equivalence Relations. 13. Partitions. 14. Binomial Coefficients. 15. Counting Multisets. 6. Inclusion-Exclusion. PART IV: MORE PROOF. 17. Contradiction. 18. Smallest Counterexample. 19. Induction. PART V: FUNCTIONS. 20. Functions. 21. The Pigeonhole Principle. 22. Composition. 23. Permutations. 24. Symmetry. 25. Assorted Notation. PART VI: NUMBER THEORY. 26. Dividing. 27. Greatest Common Divisor. 28. Modular Arithmetic. 29. The Chinese Remainder System. PART VII: ALGEBRA. 31. Groups. 32. Group Isomorphism. 33. Subgroups. 34. Fermat's Little Theorem. 35. Public Key Cryptography I: Introduction. 36. Public Key Cryptography II: Rabin's Method. 37. Public Key Cryptography III: RSA. PART VIII: GRAPHS. 38. Graph Theory Fundamentals. 39. Subgraphs. 40. Connection. 41. Trees. 42. Eulerian Graphs. 43. Coloring. 44. Planar Graphs. PART IX: PARTIALLY ORDERED SETS. 45. Partially Ordered Sets Fundamentals. APPENDIX A: LOTS OF HINTS; SOME ANSWERS. APPENDIX B: GLOSSARY. APPENDIX C: FUNDAMENTALS. INDEX.