Discrete Math
Introduction
Basic Math Structures
Logic
- Propositional Logic
- Predicates
Proof Basics
- Basic Language
- Overview of Proof Types
- Direct Proofs
- Contraposition
- Contradiction
- Equivalence
- Bad Proofs
Induction Proofs
- Basic Induction
- Strong Induction
- Strengthening the IH
- 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
- Cryptograpy
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 Math
- Useful Functions
- Powers of Two
Outside Resources

Proof by Induction

Proofs for predicates over ordered sequences

Note

Material under development.

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