List of basic discrete mathematics topics

Table of contents

1 Mathematical sets 2 Mathematical functions 3 Operations 4 Arithmetic 5 Elementary algebra 6 Mathematical relations 7 Mathematical phraseology 8 Probability 9 Propositional logic 10 Mathematical disciplines

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

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

• Binary operator
• Associativity
• Commutativity
• Distributivity

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

• Linear equation
• Quadratic equation

• 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)
  • Similarity (mathematics)
  • Congruence (geometry)
  • Equation
  • Identity
    • Identity element
    • Identity function
  • Substitution property of equality
  • Graphing equivalence
  • Extensionality
  • Uniqueness quantification

• 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

• Average
• Expectation

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

• Graph theory
• Combinatorics
• Discrete geometry
• Combinatorial geometry
• Combinatorial optimization
• Combinatorial topology