Discrete Mathematics

Discrete mathematics is the study of structures which are fundamentally discrete rather than continuous. While many famous results in discrete mathematics pre-date the invention of the digital computer, the field has exploded in our digital age. Computers store data in discrete bits and operate in discrete steps. Discrete mathematics includes the investigation of all structures and algorithms appropriate for the representation and storage of data. The internet, for instance, can be usefully represented as a graph, a fundamental object of this discipline.

Discrete mathematics includes, among others sub-fields, graph theory, combinatorics, coding theory, cryptography, game theory, computational complexity and combinatorial optimization. It makes useful and fascinating connections with fields like group theory, matrix theory and linear programming. It includes the most important unsolved problem in mathematics, the question of whether P = NP. And investigations in many fields, for instance number theory, combine both discrete and continuous tools.