Portal:Discrete mathematics

• Wikipedia portals:
• Culture
• Geography
• Health
• History
• Mathematics
• Natural sciences
• People
• Philosophy
• Religion
• Society
• Technology

edit  

Discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete in the sense of not supporting or requiring the notion of continuity. Discrete objects can be enumerated by integers. Topics in discrete mathematics include number theory (which deals mainly with the properties of integers), combinatorics, logic, graphs, algorithms, and formal languages.

Discrete mathematics has become popular in recent decades because of its applications to computer science. Discrete mathematics is the mathematical language of computer science. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in all branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are tremendously significant in applying ideas from discrete mathematics to real-world applications, such as in operations research.

The set of objects studied in discrete mathematics can be finite or infinite. In real-world applications, the set of objects of interest are mainly finite, the study of which is often called finite mathematics. In some mathematics curricula, the term "finite mathematics" refers to courses that cover discrete mathematical concepts for business, while "discrete mathematics" courses emphasize discrete mathematical concepts for computer science majors.

edit  

Selected article

Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics. Aspects of combinatorics include "counting" the objects satisfying certain criteria (enumerative combinatorics), deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and finding algebraic structures these objects may have (algebraic combinatorics).

Combinatorics is as much about problem solving as theory building, though it has developed powerful theoretical methods, especially since the later twentieth century (see the page List of combinatorics topics for details of the more recent development of the subject). One of the oldest and most accessible parts of combinatorics is graph theory, which also has numerous natural connections to other areas.

...Archive

Read more...

edit  

WikiProjects

The Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's talk page.

Project pages

• Participants
• Current activity
• Manual of style
• Conventions

Essays

• Advice on using Wikipedia for mathematics self-study
• Proofs

Subprojects

• PlanetMath Exchange (Talk)
• Graphics (Talk)
• Article assessment (Talk)

Related projects

Computer science | Cryptography | Game theory | Numbers | Physics | Science | Statistics

edit  

Selected picture

A Penrose tiling, an example of a tiling that can completely cover an infinite plane, but only in a pattern which is non-repeating (aperiodic).

...Archive

Image credit: xJaM

Read more...

edit  

Did you know?

• ...that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.
• ...that the Catalan numbers solve a number of problems in combinatorics such as the number of ways to completely parenthesize an algebraic expression with n+1 factors?

edit  

Categories

Coding theory • Combinatorics • Digital systems • Discrete geometry • Factorial and binomial topics • Finite differences • Graph theory • Permutations • Symmetric functions

edit  

Topics in Discrete mathematics

Major areas	Combinatorics	Graph Theory	Game theory
Automata theory Combinatorics Combinatorial topology Computational geometry Digital geometry Discrete geometry Graph theory Information theory Optimization Order theory Game theory	Combinatorics Combination Permutation Enumerative combinatorics Pascal's triangle Combinatorial proof Bijective proof List of combinatorics topics	Graph theory Glossary of graph theory Graph coloring Network Network theory List of network theory topics Hypergraph List of graph theory topics	Game theory Extensive form game Normal form game Non-cooperative, Cooperative games Symmetric game Zero-sum Sequential game Perfect information Determinacy Strategy Solution concept Nash equilibrium Backward induction Glossary of game theory List of games in game theory

edit  

Related portals

Algebra	Analysis	Category theory	Computer science	Cryptography	Discrete mathematics	Geometry

Logic	Mathematics	Number theory	Physics	Science	Set theory	Statistics	Topology

edit  

Wikimedia

• What are portals?
• List of portals
• Featured portals