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Discrete Mathematics for Computer Science
307
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66
Chapters
8
Parts
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About This Book
A comprehensive textbook on Discrete Mathematics for Computer Science.
Table of Contents
Front Matter
1.
Discrete Mathematics for Computer Science
2.
Preface
3.
Acknowledgments
4.
How to Use This Book
5.
Prerequisites
6.
Master Outline
Part I: Logic and Proof
1.
Part I: Logic and Proof
2.
Chapter 1: Propositional Logic
3.
Chapter 2: Predicate Logic and Quantifiers
4.
Chapter 3: Rules of Inference
5.
Chapter 4: Proof Strategies I — Direct Proof and Contraposition
6.
Chapter 5: Proof Strategies II — Contradiction and Cases
7.
Chapter 6: Mathematical Induction
8.
Chapter 7: Strong Induction, Well-Ordering, and Recursive Definitions
Part II: Structures
1.
Part II: Structures
2.
Chapter 8: Sets
3.
Chapter 9: Functions
4.
Chapter 10: Cardinality and Infinity
5.
Chapter 11: Sequences and Summations
6.
Chapter 12: Relations
7.
Chapter 13: Partial Orders, Lattices, and Boolean Algebra
8.
Chapter 14: Algorithms and Complexity
Part III: Counting and Probability
1.
Part III: Counting and Probability
2.
Chapter 15: The Basics of Counting
3.
Chapter 16: Permutations and Combinations
4.
Chapter 17: Advanced Counting
5.
Chapter 18: Recurrence Relations
6.
Chapter 19: Solving Recurrence Relations
7.
Chapter 20: Discrete Probability
8.
Chapter 21: Conditional Probability and Bayes' Theorem
Part IV: Number Theory and Cryptography
1.
Part IV: Number Theory and Cryptography
2.
Chapter 22: Number Theory Foundations
3.
Chapter 23: Modular Arithmetic
4.
Chapter 24: Algebraic Structures — Groups, Rings, and Fields
5.
Chapter 25: Cryptography — From Caesar Cipher to RSA
6.
Chapter 26: Hashing, Checksums, and Error Detection
Part V: Graph Theory
1.
Part V: Graph Theory
2.
Chapter 27: Introduction to Graphs
3.
Chapter 28: Graph Representations, Traversal, and Search
4.
Chapter 29: Weighted Graphs and Shortest Paths
5.
Chapter 30: Euler Paths, Hamilton Paths, and the Traveling Salesman Problem
6.
Chapter 31: Trees
7.
Chapter 32: Spanning Trees, Minimum Spanning Trees, and Network Design
8.
Chapter 33: Graph Coloring, Planarity, and the Four Color Theorem
9.
Chapter 34: Network Flow and Matching
Part VI: Advanced Topics and Synthesis
1.
Part VI: Advanced Topics and Synthesis
2.
Chapter 35: Automata and Formal Languages
3.
Chapter 36: Computability and the Halting Problem
4.
Chapter 37: Introduction to Complexity Theory — P, NP, and the Biggest Open Problem in CS
5.
Chapter 38: Coding Theory — Error-Correcting Codes
6.
Chapter 39: Capstone — Applying Discrete Mathematics to a Real Computing Problem
7.
Chapter 40: Where Discrete Math Goes Next
Appendices
1.
Appendix A: Notation and Symbols
2.
Appendix B: Python Setup and Reference
3.
Appendix C: Proof Techniques Cheat Sheet
4.
Appendix D: Math Foundations Refresher
5.
Appendix E: Big-O and Complexity Reference
6.
Appendix F: Graph Algorithms Reference
7.
Appendix G: Number Theory Reference
8.
Appendix H: Combinatorics Formula Sheet
9.
Appendix I: The Discrete Math Toolkit (Full Code)
10.
Appendix J: Resources and Communities
11.
Glossary
12.
Answers to Selected Exercises
13.
Index
14.
Bibliography
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