Overview of and topical guide to discrete mathematics
Discrete mathematics is the study of
mathematicalstructures 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.
Pascal's triangle – Triangular array of the binomial coefficients in mathematics
Combinatorial proof – proofs in enumerative combinatorics based on bijections or double countings of combinatorial objectsPages displaying wikidata descriptions as a fallback
Bijective proof – Technique for proving sets have equal size
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