⊂Discrete Math

Logic, set theory, combinatorics, graph theory

Subfields

Propositions, predicates, proof methods

Set operations, Venn diagrams, axiomatic set theory

Permutations, combinations, binomial theorem, generating functions

Graphs, trees, shortest paths, network flow

Partial orders, total orders, lattices, min/max elements

Lattice structures, distributive lattices, Boolean lattices, abstract algebra

A set is a collection of distinct, well-defined objects. It's one of the most fundamental concepts in mathematics.

A combination is the number of ways to select r items from n items without regard to order.

A permutation is the number of ways to arrange r items from n items where order matters.

A graph is a structure consisting of vertices and edges. It's used to model relationships and networks.

A recurrence relation defines sequence terms using previous terms. It's essential for analyzing recursive algorithm complexity.

Modular arithmetic is a system based on remainders from division. Also called clock arithmetic.

A proposition is a statement that is either true or false. Logical operators combine propositions.

An algebraic system on 0 and 1 (or true and false), fundamental to logic circuits and computer science.

A tree is a connected graph with no cycles. With n vertices, it has n-1 edges.

A formula for expanding powers of binomials using combinations as coefficients.

Asymptotic notation to express time/space complexity of algorithms.