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^[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