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Mathematics : A Discrete Introduction
ISBN: 9780534356385 | 0534356389
Edition: 1stFormat: Paperback
Publisher: Brooks Cole
Pub. Date: 1/12/2000
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This book is an introduction to mathematics--in particular, it is an introduction to discrete mathematics. There are two primary goals for this book: students will learn to reading and writing proofs, and students will learn the fundamental concepts of discrete mathematics.
| 1. FUNDAMENTALS | |
| Definition | |
| Theorem | |
| Proof | |
| Counterexample | |
| Boolean Algebra | |
| 2. COLLECTIONS | |
| Lists | |
| Factorial | |
| Sets I: Introduction, Subsets | |
| Quantifiers | |
| Sets II: Operations | |
| 3. COUNTING AND RELATIONS | |
| Relations | |
| Equivalence Relations | |
| Partitions | |
| Binomial Coefficients | |
| Counting Multisets | |
| Inclusion-Exclusion | |
| 4. MORE PROOF | |
| Contradiction | |
| Smallest Counterexample | |
| Introduction | |
| 5. FUNCTIONS | |
| Functions | |
| The Pigeonhole Principle | |
| Composition | |
| Permutations | |
| Symmetry | |
| Assorted Notation | |
| 6. PROBABILITY | |
| Sample Space | |
| Events | |
| Conditional Probability and Independence | |
| Random Variables | |
| Expectation | |
| 7. NUMBER THEORY | |
| Dividing | |
| Greatest Common Divisor | |
| Modular Arithmetic | |
| The Chinese Remainder Theorem | |
| Factoring | |
| 8. ALGEBRA | |
| Groups | |
| Group Isomorphism | |
| Subgroups | |
| Fermat's Little Theorem | |
| Public-Key Cryptography I: Introduction | |
| Public-Key Cryptography II: Rabin's Method | |
| Public-Key Cryptography III: RSA | |
| 9. GRAPHS | |
| Graph Theory Fundamentals | |
| Subgraphs | |
| Connection | |
| Trees | |
| Eulerian Graphs | |
| Coloring | |
| Planar Graphs | |
| 10. PARTIALLY ORDERED SETS | |
| Partially Ordered Sets Fundamentals | |
| Max and Min | |
| Linear Orders | |
| Linear Extensions | |
| Dimension | |
| Lattices | |
| APPENDIXES | |
| A | |
| Lots of Hints and Comments; Some Answers | |
| B | |
| Glossary | |
| C | |
| Fundamentals | |
| Index |
