Introduction to Discrete Mathematics

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This book has two primary objectives: It teaches students fundamental concepts in discrete mathematics (from counting to basic cryptography to graph theory), and it teaches students proof-writing skills. Overall, this book is an introduction to mathematics. In particular, it is an introduction to discrete mathematics. All of the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective. While algorithms and analysis appear throughout, the emphasis is on mathematics. Students will learn that discrete mathematics is very useful, especially those whose interests lie in computer science and engineering, as well as those who plan to study probability, statistics, operations research, and other areas of applied mathematics. Key Feature Self Tests: A self test appears at the end of every chapter. The problems are of various degrees of difficulty, and complete answers appear in Appendix B Induction: The sections on mathematical induction have been reworked with new motivational material, more examples, and more problems. The induction section is now essentially independent of the proof by smallest counterexample section New Opening: The introductory section, "Joy," motivates students by describing the pleasure of doing mathematics Proof Templates: Proof templates appear throughout the book and give students the basic skeleton of the proof as well as boilerplate language Hints: Appendix A contains an extensive collection of hints (and some answers when necessary) that point students in the correct direction Table of Contents 1. Fundamentals 2. Collections 3. Counting and Relations 4. More Proof 5. Functions 6. Probability 7. Number Theory 8. Algebra 9. Graphs 10. Partially Ordered Sets Appendices