Discrete and Combinatorial Mathematics - An Applied Introduction

1. Fundamental Principles of Counting
2. Fundamentals of Logic
3. Set Theory
4. Properties of the Integers: Mathematical Induction
5. Relations and Functions
6. Languages: Finite State Machines
7. Relations: The Second Time Around
8. The Principle of Inclusion and Exclusion
9. Generating Functions
10. Recurrence Relations
11. An Introduction to Graph Theory
12. Trees
13. Optimization and Matching
14. Rings and Modular Arithmetic
15. Boolean Algebra and Switching Functions
16. Groups Coding Theory and Polya's Method of Enumeration
17. Finite Fields and Combinatorial Designs