Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
== Contents ==
Introduction
=== Introductory discrete mathematics ===
Set theory
Functions and relations
Number theory
Logic
Enumeration
Graph theory
Recursion
Semigroup
=== Upper-level discrete mathematics ===
==== Upper-level set theory ====
Axiomatic set theory
Zermelo-Frankel Axioms
Topoi
==== Upper-level number theory ====
Number representations
Modular arithmetic
Polynomials
Finite fields
Arithmetic Functions
Analytic Number Theory
==== Upper-level logic ====
Godel's incompleteness theorem
Second order logic
==== Upper-level Combinatorics ====
=== Abstract algebra ===
==== Abstract algebraic systems ====
Groups
Lattice theory
Matroids
Boolean algebra
Category theory
==== Algebra over other number systems ====
Hypercomplex numbers
Rings, fields and modules
=== Automata ===
Finite state automata
Pushdown automata
Turing machines
Cellular automata
=== Further problems ===
Selected problems
=== Unordered pages ===
Combinatory logic
Languages and grammars
Axiom of choice
Naive set theory
Sieve of Eratosthenes