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[1] – do not vary smoothly in this way, but have distinct, separated values.[2] 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.

Subjects in discrete mathematics

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.

Concepts in discrete mathematics




Elementary algebra

Elementary algebra

Mathematical relations

Mathematical phraseology





Propositional logic

Mathematicians associated with discrete mathematics

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See also


  1. ^ Richard Johnsonbaugh, Discrete Mathematics, Prentice Hall, 2008; James Franklin, Discrete and continuous: a fundamental dichotomy in mathematics, Journal of Humanistic Mathematics 7 (2017), 355-378..
  2. ^ Weisstein, Eric W. "Discrete mathematics". MathWorld.