Discrete Mathematics

Discrete Mathematics Tutorials

Note

This set of tutorials is a work-in-progress, with topics rolling out through early 2026. If we haven’t gotten to the topic you’re interested in yet, check back in a few weeks!

Topic outline:

• Introduction
• Basic Math Structures
  • Sets and Sequences
  • Relations
  • Functions
• Logic
  • Propositional Logic
  • Predicates and Quantifiers
• Proof Basics
  • Basic Language
  • Overview of Proof Types
  • Direct Proofs
  • Contraposition
  • Contradiction
  • Equivalence
  • Bad Proofs
• Induction Proofs
  • Basic Induction
  • Strong Induction
  • Strengthening the Induction Hypothesis
  • Bad Induction
• Inductive Definitions
  • Structures (trees, etc.)
  • Recurrence Relations
  • Languages/Grammars
• Number Theory
  • Modular Arithmetic
  • Divisors and Primes
  • Inverses
  • Powers and Fermat’s Little Theorem
  • Chinese Remainder Theorem
  • Application: Cryptography
• Function Growth
  • Asymptotic Notation
  • Application: Time Complexity
• Graphs
  • Definitions
  • Properties
  • Paths
  • Trees and Spanning Trees
  • Planarity
  • Coloring
• Counting
  • Basics
  • Permutations and Combinations
  • Other Scenarios
  • Inclusion/Exclusion
• Basic Probability
  • Probability Spaces
  • Events
  • Common Distributions
  • Expectation

• Miscellaneous Mathematics
  • Useful Functions
  • Powers of Two