Difference between revisions of "Combinatorics"
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| − | '''Combinatorics''' is a branch of [[mathematics]] concerning the study of finite or [[Countable set|countable]] discrete structures. | + | '''Combinatorics''' is a branch of [[mathematics]] concerning the study of finite or [[Countable set|countable]] [[Discrete mathematics|discrete]] [[Mathematical structure|structures]]. |
== Description == | == Description == | ||
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* [[Countable set]] | * [[Countable set]] | ||
| + | * [[Discrete mathematics]] | ||
* [[Geometry]] | * [[Geometry]] | ||
* [[Graph theory]] | * [[Graph theory]] | ||
| + | * [[Mathematical structure]] | ||
* [[Mathematics]] | * [[Mathematics]] | ||
Revision as of 14:06, 8 April 2016
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Description
Aspects of combinatorics include:
- Counting the structures of a given kind and size (enumerative combinatorics)
- Deciding when certain criteria can be met
- 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)
- Studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics)
Combinatorial problems arise in many areas of pure mathematics, notably:
Combinatorics has many applications in:
- Mathematical optimization
- Computer science
- Obtain formulas and estimates in the analysis of algorithms
- Ergodic theory
- Statistical physics
Many combinatorial questions have historically been considered in isolation, giving an ad hoc solution to a problem arising in some mathematical context.
In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right.
Graph theory
One of the oldest and most accessible parts of combinatorics is graph theory, which also has numerous natural connections to other areas.
See also
External links
- Combinatorics @ Wikipedia
