Discrete Math
Logic, set theory, combinatorics, graph theory
Subfields
Logic
Propositions, predicates, proof methods
Set Theory
Set operations, Venn diagrams, axiomatic set theory
Combinatorics
Permutations, combinations, binomial theorem, generating functions
Graph Theory
Graphs, trees, shortest paths, network flow
Order Theory
Partial orders, total orders, lattices, min/max elements
Lattice Theory
Lattice structures, distributive lattices, Boolean lattices, abstract algebra
Concepts
Sets
★☆☆☆☆A set is a collection of distinct, well-defined objects. It's one of the most fundamental concepts in mathematics.
Combinations
★★☆☆☆A combination is the number of ways to select r items from n items without regard to order.
Permutations
★★☆☆☆A permutation is the number of ways to arrange r items from n items where order matters.
Graph Theory Basics
★★★☆☆A graph is a structure consisting of vertices and edges. It's used to model relationships and networks.
Recurrence Relations
★★★☆☆A recurrence relation defines sequence terms using previous terms. It's essential for analyzing recursive algorithm complexity.
Modular Arithmetic
★★★☆☆Modular arithmetic is a system based on remainders from division. Also called clock arithmetic.
Propositional Logic
★★☆☆☆A proposition is a statement that is either true or false. Logical operators combine propositions.
Boolean Algebra
★★★☆☆An algebraic system on 0 and 1 (or true and false), fundamental to logic circuits and computer science.
Trees
★★★☆☆A tree is a connected graph with no cycles. With n vertices, it has n-1 edges.
Binomial Theorem
★★★☆☆A formula for expanding powers of binomials using combinations as coefficients.
Big O Notation
★★★☆☆Asymptotic notation to express time/space complexity of algorithms.