List of basic discrete mathematics topics

Mathematical sets

• Set
  • 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 set theory
• Basic Set Theory

Mathematical functions

• Function
• How to specify a function
• Function domain
• Function codomain
• Function range
• Injective function
• Surjection
• Bijection
• Function composition
• Partial function
• Multivalued function
• Binary function

Operations

• Binary operator
• Associativity
• Commutativity
• Distributivity

Arithmetic

• Decimal
• Binary numeral system
• Divisor
• Euclidean algorithm
• Fundamental theorem of arithmetic
• Modular arithmetic
• Successor function

Elementary algebra

• Linear equation
• Quadratic equation

Mathematical relations

• Binary relation
• Mathematical relation
• Reflexive relation
• Reflexive property of equality
• Symmetric relation
• Symmetric property of equality
• Antisymmetric relation
• Transitive
  • Transitivity
  • 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
• Normal form
• Without loss of generality
• Vacuous truth
• Contradiction, Reductio ad absurdum
• Counterexample
• Table of mathematical symbols

Combinatorics

• 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

Referenced By