The Discrete Math Hub

Discrete Structures in Mathematics

A Problem-Solving Approach

by Gregory Bard

  • Chapter 0: The Preface (How to Use This Book) (click here)

  • Chapter 1: Set Theory

  • Chapter 2: The Past and Future of Mathematics
    • Module 2.1: Fermat's Last Theorem and Famous Unsolved Problems [Under Major Repairs]

  • Chapter 3: The Basics of Probability
    • Module 3.1: A Formal Introduction to Probability Theory (click here)
    • Module 3.2: Exploring Probability Through Problem Solving (click here)
    • Module 3.3: Expected Value and Insurance [Planned]
    • Module 3.4: You Can't Just Add Probabilities (click here)
    • Module 3.5: The Square Root of NPQ Rule (click here)

  • Chapter 4: The Basics of Combinatorics
    • Module 4.1: The Multiplication and Exponent Principles (click here)
    • Module 4.2: The Permutations and Factorial Principles (click here)
    • Module 4.3: The Combinations and Handshake Principles (click here)
    • Module 4.4: Which Combinatorial Formula Should I Use? (click here)

  • Chapter 5: Advanced Topics in Probability and Combinatorics
    • Module 5.1: Independence and Repetition (click here)
    • Module 5.2: The Binomial Distribution Formula (click here)
    • The Binomial Distribution Formula helper (powered by SageMathCell) (click here)
    • Module 5.3: Probability Tree Diagrams (click here)
    • Module 5.4: Conditional Probability Notation and Bayes' Rule [Planned]
    • Module 5.5: Probability and Dice Games [Underway]
    • Module 5.6: A Combinatorial View of Poker (5-Card Stud) [Planned]
    • Module 5.7: Pascal's Triangle and the Binomial Theorem (click here)
    • Module 5.8: Poisson's Rare Events Theorem [Underway]
    • Module 5.9: Some Advanced Combinatorial Principles [Under Revision]

  • Chapter 6: Logic
    • Module 6.1: Basic Truth Tables [Planned]
    • Module 6.2: The Logic Game: Ten Levels of Problems Toward Mathematical Logic, and Set Theory (without answers) (with answers)
    • Module 6.3: Contrapositives and Converses, and Counter-Examples (click here)
    • Module 6.4: More about Implications [Planned]
    • Module 6.5: Working with Quantifiers [Planned]

  • Chapter 7: Proof Writing Techniques [Planned]

  • Chapter 8: The Theory of Digraphs and Graphs [Planned]

  • Chapter 9: Number Theory and Cryptography

  • Appendix A: Good Old-Fashioned Mathematics
    • Module A.1: Different Number Bases [Planned]
    • Module A.2: Completing the Square [Underway]
    • Module A.3: Cardano's Cubic Formula [Underway]
    • Module A.4: Working in Binary [Planned]
    • Module A.5: Recursive Notation and the Fibonacci/Lucas Sequences [Planned]
    • Module A.6: Injective, Surjective, and Bijective Functions (click here)
    • Module A.7: Equivalence Relations (Reflexive, Symmetric, Transitive) (click here)

  • Appendix B: A Lab about Dijkstra's Algorithm (without answers) (with answers)

Special thanks to my proofreaders:

I am very indebted to my chief proofreader, Joseph Bertino, who has now moved on to much bigger and better things, but who served me well for nine years; my senior proofreaders, Russel Chamberlain and Isaac Quella; and my junior proofreaders, Trevor Kretschmann and Tanner Verber. I must also mention my gratitude for students from MATH-270: Discrete Mathematics, many of whom have reported a typo or two. Thanks very much!

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Last Updated on April 25th, 2018.