Discrete and Combinatorial Mathematics

Part 1: Fundamentals of Discrete Mathematics 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 Part 2: Further Topics in Enumeration 8. The Principle of Inclusion and Exclusion 9. Generating Functions 10. Recurrence Relations Part 3: Graph Theory and Applications 11. An Introduction to Graph Theory 12. Trees 13. Optimization and Matching Part 4: Modern Applied Algebra 14. Rings and Modular Arithmetic 15. Boolean Algebra and Switching Functions 16. Groups, Coding Theory, and Polya's 17. Finite Fields and Combinatorial Designs Appendix 1: Exponential and Logarithmic Functions Appendix 2: Matrices, Matrix Operations, and Determinants Appendix 3: Countable and Uncountable Sets Solutions Index