Portal:Discrete mathematics

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Discrete mathematics

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Discrete mathematics, also called finite mathematics or decision mathematics, is the study of mathematical structures that are fundamentally discrete in the sense of not supporting or requiring the notion of continuity. Objects studied in finite mathematics are largely countable sets such as integers, finite graphs, and formal languages.

Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasize concepts for computer science majors.

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A 1-forest (a maximal pseudoforest), formed by three 1-trees

In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. That is, it is a system of vertices and edges connecting pairs of vertices, such that no two closed paths of consecutive edges share any vertex with each other, nor can any two such closed paths be connected to each other by a path of consecutive edges. A pseudotree is a connected pseudoforest.

The names are justified by analogy to the more commonly studied trees and forests. (A tree is a connected graph with no cycles; a forest is a disjoint union of trees.) Gabow and Tarjan attribute the naming of pseudoforests to Dantzig's 1963 book on linear programming, in which pseudoforests arise in the solution of certain network flow problems. Pseudoforests also form graph-theoretic models of functions and occur in several algorithmic problems. Pseudoforests are sparse graphs – they have very few edges relative to their number of vertices – and their matroid structure allows several other families of sparse graphs to be decomposed as unions of forests and pseudoforests.

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Penrose tiling 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).
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Categories

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

Major areas Combinatorics Graph 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
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