Discrete optimization no relation set theory
Discrete mathematics
Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example is the set of all integers. Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply. Algorithms—especially their implementation and computational complexity—play a major role in discrete mathematics.The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of the 20th century. The P versus NP problem, which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult problems.Discrete mathematics includes:
Combinatorics, the art of enumerating mathematical objects that satisfy some given constraints. Originally, these objects were elements or subsets of a given set; this has been extended to various objects, which establishes a strong link between combinatorics and other parts of discrete mathematics. For example, discrete geometry includes counting configurations of geometric shapes
Graph theory and hypergraphs
Coding theory, including error correcting codes and a part of cryptography
Matroid theory
Discrete geometry
Discrete probability distributions
Game theory (although continuous games are also studied, most common games, such as chess and poker are discrete)
Discrete optimization, including combinatorial optimization, integer programming, constraint programming
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