Outline of discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics, therefore, excludes topics in "continuous mathematics" such as calculus and analysis.

Included below are many of the standard terms used routinely in university-level courses and in research papers. This is not, however, intended as a complete list of mathematical terms; just a selection of typical terms of art that may be encountered.



Discrete mathematical disciplines
For further reading in discrete mathematics, beyond a basic level, see these pages. Many of these disciplines are closely related to computer science.


 * a study of
 * a study of
 * a study of
 * a study of
 * a study of
 * a study of
 * a study of

Mathematical relations

 * Equivalence and identity
 * Equivalence and identity
 * Equivalence and identity
 * Equivalence and identity
 * Equivalence and identity
 * Equivalence and identity
 * Equivalence and identity
 * Equivalence and identity
 * Equivalence and identity
 * Equivalence and identity
 * Equivalence and identity

Mathematicians associated with discrete mathematics

 * Leonhard Euler - Swiss mathematician (1707-1783)
 * Richard Karp - American computer scientist (b. 1935)
 * Claude Shannon - American mathematician (1916-2001)
 * Donald Knuth - American mathematician and computer scientist (b. 1938)
 * Claude Shannon - American mathematician (1916-2001)
 * Donald Knuth - American mathematician and computer scientist (b. 1938)