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Outline of discrete mathematics

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(Redirected from List of basic discrete mathematics topics) 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 – 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.

Concepts in discrete mathematics

Sets

Functions

Arithmetic

Elementary algebra

Elementary algebra – Basic concepts of algebra

Mathematical relations

Mathematical phraseology

Combinatorics

Combinatorics – Branch of discrete mathematics

Probability

Probability – Branch of mathematics concerning chance and uncertainty

  • Average – Number taken as representative of a list of numbers
  • Expected value – Average value of a random variable
  • Discrete random variable – Variable representing a random phenomenonPages displaying short descriptions of redirect targets
  • Sample space – Set of all possible outcomes or results of a statistical trial or experiment
  • Event – In statistics and probability theory, set of outcomes to which a probability is assigned
  • Conditional Probability – Probability of an event occurring, given that another event has already occurredPages displaying short descriptions of redirect targets
  • Independence – When the occurrence of one event does not affect the likelihood of another
  • Random variables – Variable representing a random phenomenonPages displaying short descriptions of redirect targets

Propositional logic

  • Logical operator – Symbol connecting sentential formulas in logicPages displaying short descriptions of redirect targets
  • Truth table – Mathematical table used in logic
  • De Morgan's laws – Pair of logical equivalences
  • Open sentence – Formula that contains at least one free variablePages displaying short descriptions of redirect targets
  • List of topics in logic – Overview of and topical guide to logicPages displaying short descriptions of redirect targets

Mathematicians associated with discrete mathematics

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  • Paul Erdős – Hungarian mathematician (1913–1996)
  • Leonhard Euler - Swiss mathematician (1707-1783)
  • Claude Shannon - American mathematician (1916-2001)
  • Donald Knuth - American mathematician and computer scientist (b. 1938)
  • Aristotle – Ancient Greek philosopher and polymath (384–322 BC)

See also

References

  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.

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