Overview of and topical guide to 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[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.
Logic – Study of correct reasoning
Modal logic – Type of formal logic
Set theory – Branch of mathematics that studies sets
Number theory – Mathematics of integer properties
Combinatorics – Branch of discrete mathematics
Finite mathematics – Syllabus in college and university mathematics
Graph theory – Area of discrete mathematics
Digital geometry – Deals with digitized models or images of objects of the 2D or 3D Euclidean space
Digital topology – Properties of 2D or 3D digital images that correspond to classic topological properties
Algorithmics – Sequence of operations for a taskPages displaying short descriptions of redirect targets
Information theory – Scientific study of digital information
Computability – Ability to solve a problem in an effective manner
Computational complexity theory – Inherent difficulty of computational problems
Probability theory – Branch of mathematics concerning probability
Probability – Branch of mathematics concerning chance and uncertainty
Markov chains – Random process independent of past history
Linear algebra – Branch of mathematics
Functions – Association of one output to each input
Partially ordered set – Mathematical set with an ordering
Proofs – Reasoning for mathematical statements
Relation – Relationship between two sets, defined by a set of ordered pairs
^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.
^Weisstein, Eric W. "Discrete mathematics". MathWorld.
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