List of basic discrete mathematics topics - Definition and Overview

This is a list of basic discrete mathematics topics, by Wikipedia page. Included here is much of the standard mathematical language, used in university-level courses and routinely in research papers. This is not, however, intended as a complete glossary of mathematical terms; just a selection of typical terms of art that may be encountered.

Sets

• Set
  • 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

• Function
• How to specify a function
• Domain of a function
• Codomain
• Range of a function
• Image (mathematics)
• Injective function
• Surjection
• Bijection
• Function composition
• Partial function
• Multivalued function
• Binary function
• Floor function
• Sign function
• Inclusion (mathematics)

Operations

• Binary operator
• Associativity
• Commutativity
• Distributivity

Arithmetic

• Decimal
• Binary numeral system
• Divisor
• Division by zero
• Indeterminate form
• Empty product
• Euclidean algorithm
• Fundamental theorem of arithmetic
• Modular arithmetic
• Successor function

Elementary algebra

• Left-hand side and right-hand side of an equation
• Linear equation
• Quadratic equation
• Solution point
• Arithmetic progression
• Recurrence relation
• Finite difference
• Difference operator

Mathematical relations

• Binary relation
• Mathematical relation
• Reflexive relation
• Reflexive property of equality
• Symmetric relation
• Symmetric property of equality
• Antisymmetric relation
• Transitivity (mathematics)
  • Transitive closure
  • Transitive property of equality
• Equivalence and identity
  • Equivalence relation
  • Equivalence class
  • Equality (mathematics)
    • Inequation
    • Inequality
  • Similarity (mathematics)
  • Congruence (geometry)
  • Equation
  • Identity
    • Identity element
    • Identity function
  • Substitution property of equality
  • Graphing equivalence
  • Extensionality
  • Uniqueness quantification

Mathematical phraseology

• If and only if (iff)
• Necessary and sufficient
  • Sufficient condition
• Distinct
• Difference
• Absolute value
• Up to
• Modulo
• Characterization (mathematics)
• Normal form
• Canonical form
• Without loss of generality
• Vacuous truth
• Contradiction, Reductio ad absurdum
• Counterexample
• Sufficiently large
• Pons Asinorum
• Table of mathematical symbols

Combinatorics

• Permutations and combinations
• Permutation
• Combination
• Factorial
  • Empty product
• Pascal's triangle

Probability

• Average
• Expectation
• Discrete random variable

Propositional logic

• Logical operator
• Truth table
• De Morgan's laws
• Open sentence
• List of topics in logic

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.

• Automata theory
• Combinatorics
• Combinatorial geometry
• Computational geometry
• Discrete geometry
• Graph theory
• Mathematical logic
• Combinatorial optimization
• Set theory
• Combinatorial topology