Concepts in discrete mathematics

Concepts in discrete mathematics

Sets

• Set (mathematics) –
  • 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 –
• 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 map –
• Pigeonhole principle –
• Relation composition –
• Permutations –
• Symmetry –

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 –
• Groups –
• Group isomorphism –
• Subgroups –
• Fermat's little theorem –
• Cryptography –
• Faulhaber's formula –

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

Mathematical phraseology

If and only if –

Necessary and sufficient (Sufficient condition) –

Distinct –

Difference –

Absolute value –

Up to –

Modular arithmetic –

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 –

Contrapositive –

Mathematical induction –

Combinatorics

• Permutations and combinations –
• Permutation –
• Combination –
• Factorial –
• Empty product –
• Pascal's triangle –
• Combinatorial proof –
• Bijective proof –
• Double counting (proof technique) –

Probability

• Average –
• Expected value –
• Discrete random variable –
• Sample space –
• Event –
• Conditional Probability –
• Independence –
• Random variables –

Propositional logic

Logical operator –

Truth table –

De Morgan's laws –

Open sentence –

List of topics in logic –