Discrete Math Elements

Richard Hammack

Part I: Systems, Symbols and Sets

	1. What is Discrete Mathematics?	3
	2. Sets	15
	3. Logic	45
	4. Boolean Expressions and Circuits	67
	5 More on Logic: Quantified Statements	91

Part II: Counting and Computing

	6. Counting	107
	7. Discrete Probability	163
	8. Algorithms	203

Part III: Methods of Proof

	9. Direct Proof	239
	10. Contrapositive Proof	255
	11. Proof by Contradiction	271
	12. Proofs Involving Sets	285
	13. Proving Non-Conditional Statements	303
	14. Disproof	317
	15. Mathematical Induction	327

Part IV: Relational Structures and Cardinality

	16. Introduction to Graph Theory (in progress)	355
	17. Relations	373
	18. Functions	399
	19. Cardinality of Sets	427

Part V: Analysis of Algorithms
	20. Review of Functions of a Real Variable	449
	21. Complexity of Algorithms	465
	22. Introduction to NP-Completeness	500

© 2023 by Richard Hammack This work is licensed under the Creative Commons Attribution-Non Commercial-No Derivative Works 3.0 License

Notes:

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For each chapter, solutions to the odd-numbered exercises are found at the very end of the chapter.

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