The Discrete Math Hub
Discrete Structures in Mathematics
A ProblemSolving 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 (5Card 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 CounterExamples
(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 OldFashioned 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 MATH270:
Discrete Mathematics, many of whom have reported a typo or two. Thanks very much!

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Last Updated on April 25th, 2018.
