Discrete Mathematics

$$Discrete$$ $$Mathematics$$

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

Contents

 * /Introduction/

Introductory discrete mathematics

 * 1) /Set theory/
 * 2) /Functions and relations/
 * 3) /Number theory/
 * 4) /Logic/
 * 5) /Enumeration/
 * 6) /Graph theory/
 * 7) /Recursion/
 * 8) /Semigroup/

Upper-level set theory

 * 1) /Axiomatic set theory/
 * 2) /Zermelo-Frankel Axioms/
 * 3) /Topoi/

Upper-level number theory

 * 1) /Number representations/
 * 2) /Modular arithmetic/
 * 3) /Polynomials/
 * 4) /Finite fields/
 * 5) /Arithmetic Functions/
 * 6) /Analytic Number Theory/

Upper-level logic

 * 1) /Godel's incompleteness theorem/
 * 2) /Second order logic/

Abstract algebraic systems

 * 1) Groups
 * 2) Lattice theory
 * 3) Matroids
 * 4) Boolean algebra
 * 5) Category theory

Algebra over other number systems

 * 1) Hypercomplex numbers
 * 2) Rings, fields and modules

Automata

 * 1) /Finite state automata/
 * 2) /Pushdown automata/
 * 3) /Turing machines/
 * 4) /Cellular automata/

Further problems

 * 1) /Selected problems/

Unordered pages

 * 1) /Combinatory logic/
 * 2) /Languages and grammars/
 * 3) /Axiom of choice/
 * 4) /Naive set theory/
 * 5) /Sieve of Eratosthenes/

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