1
Front Matter
6 chapters2
Part I: Logic and Proof
8 chapters- Part I: Logic and Proof
- Chapter 1: Propositional Logic
- Chapter 2: Predicate Logic and Quantifiers
- Chapter 3: Rules of Inference
- Chapter 4: Proof Strategies I — Direct Proof and Contraposition
- Chapter 5: Proof Strategies II — Contradiction and Cases
- Chapter 6: Mathematical Induction
- Chapter 7: Strong Induction, Well-Ordering, and Recursive Definitions
3
Part II: Structures
8 chapters4
Part III: Counting and Probability
8 chapters- Part III: Counting and Probability
- Chapter 15: The Basics of Counting
- Chapter 16: Permutations and Combinations
- Chapter 17: Advanced Counting
- Chapter 18: Recurrence Relations
- Chapter 19: Solving Recurrence Relations
- Chapter 20: Discrete Probability
- Chapter 21: Conditional Probability and Bayes' Theorem
5
Part IV: Number Theory and Cryptography
6 chapters6
Part V: Graph Theory
9 chapters- Part V: Graph Theory
- Chapter 27: Introduction to Graphs
- Chapter 28: Graph Representations, Traversal, and Search
- Chapter 29: Weighted Graphs and Shortest Paths
- Chapter 30: Euler Paths, Hamilton Paths, and the Traveling Salesman Problem
- Chapter 31: Trees
- Chapter 32: Spanning Trees, Minimum Spanning Trees, and Network Design
- Chapter 33: Graph Coloring, Planarity, and the Four Color Theorem
- Chapter 34: Network Flow and Matching
7
Part VI: Advanced Topics and Synthesis
7 chapters- Part VI: Advanced Topics and Synthesis
- Chapter 35: Automata and Formal Languages
- Chapter 36: Computability and the Halting Problem
- Chapter 37: Introduction to Complexity Theory — P, NP, and the Biggest Open Problem in CS
- Chapter 38: Coding Theory — Error-Correcting Codes
- Chapter 39: Capstone — Applying Discrete Mathematics to a Real Computing Problem
- Chapter 40: Where Discrete Math Goes Next
8
Appendices
14 chapters- Appendix A: Notation and Symbols
- Appendix B: Python Setup and Reference
- Appendix C: Proof Techniques Cheat Sheet
- Appendix D: Math Foundations Refresher
- Appendix E: Big-O and Complexity Reference
- Appendix F: Graph Algorithms Reference
- Appendix G: Number Theory Reference
- Appendix H: Combinatorics Formula Sheet
- Appendix I: The Discrete Math Toolkit (Full Code)
- Appendix J: Resources and Communities
- Glossary
- Answers to Selected Exercises
- Index
- Bibliography
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