Discrete Math Elements

Richard Hammack

Part I: Symbols and Sets and Systems

	1. What is Discrete Mathematics?	3
	2. Sets	15
	3. Logic	41
	4. Boolean Algebra and Logic Circuits	59
	5 More on Logic: Quantified Statements	81

Part II: Counting and Computing

	6. Counting	95
	7. Discrete Probability	139
	8. Algorithms	169

Part III: Methods of Proof

	9. Direct Proof	197
	10. Contrapositive Proof	211
	11. Proof by Contradiction	223
	12. Proofs Involving Sets	233
	13. Proving Non-Conditional Statements	247
	14. Disproof	257
	15. Mathematical Induction	265

Part IV: Relational Structures and Cardinality

	16. Introduction to Graph Theory	285
	17. Relations	311
	18. Functions	331
	19. Cardinality of Sets	353

Part V: Analysis of Algorithms
	20. Review of Functions of a Real Variable	373
	21. Complexity of Algorithms	387
	22. Introduction to NP-Completeness	407

Solutions	431
Index	521

Notes:

This is the latest version of my discrete math textbook. Currently almost 100% complete, modulo copy editing, minor tweaks and polishing.

IMPORTANT: Refresh screen to see latest updates

I am always happy to correct typos and/or mistakes. Please notify me if you find any!

--Thanks, RH

© 2026 by Richard Hammack This work is licensed under the Creative Commons Attribution-Non Commercial-No Derivative Works 3.0 License