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.

Subjects in discrete mathematics

Logic – a study of reasoning
Modal Logic: A type of logic for the study of necessity and probability
Set theory – a study of collections of elements
Number theory – study of integers and integer-valued functions
Combinatorics – a study of Counting
Finite mathematics – a course title
Graph theory – a study of graphs
Digital geometry and digital topology
Algorithmics – a study of methods of calculation
Information theory – a mathematical representation of the conditions and parameters affecting the transmission and processing of information
Computability and complexity theories – deal with theoretical and practical limitations of algorithms
Elementary probability theory and Markov chains
Linear algebra – a study of related linear equations
Functions – an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)
Partially ordered set –
Probability – concerns with numerical descriptions of the chances of occurrence of an event
Proofs –
Relation – a collection of ordered pairs containing one object from each set

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

Sets

Set (mathematics) –
- Element (mathematics) –
- Venn diagram –
- Empty set –
- Subset –
- Union (set theory) –
  - Disjoint union –
- Intersection (set theory) –
  - Disjoint sets –
- Complement (set theory) –
- Symmetric difference –
Ordered pair –
Cartesian product –
Power set –
Simple theorems in the algebra of sets –
Naive set theory –
Multiset –

Functions

Arithmetic

Probability

Propositional logic

Mathematicians associated with discrete mathematics

References

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.

External links

Archives
Jonathan Arbib & John Dwyer, Discrete Mathematics for Cryptography, 1st Edition ISBN 978-1-907934-01-8.
John Dwyer & Suzy Jagger, Discrete Mathematics for Business & Computing, 1st Edition 2010 ISBN 978-1-907934-00-1.

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[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.