A–Z Math Terms & Definitions

Poset

A poset is a set together with a partial order relation.

Power Set

The power set of A is the set of all subsets of A.

Predicate

A predicate is a statement containing variables that becomes a proposition when values are assigned or quantified.

Number Theory

Prime Number

A whole number greater than 1 with exactly two positive divisors: 1 and itself.

Probability measures how likely an event is, from 0 for impossible to 1 for certain.

Probability Distribution

A probability distribution specifies probabilities or densities for the possible values of a random variable.

Calculus

Product Rule

The product rule differentiates the product of two functions.

Proper Subset

A proper subset contains only elements of another set but is not equal to that set.

Proposition

A proposition is a declarative statement that is either true or false.

Geometry

Pythagorean Theorem

For a right triangle, a² + b² = c², where c is the hypotenuse.

Algebra

Quadratic Equation

An equation in the form ax² + bx + c = 0, where a is not zero.

Quartile

Quartiles divide ordered data into four parts.

Calculus

Quotient Rule

The quotient rule differentiates one function divided by another.

Random Experiment

A random experiment is a process whose exact outcome is uncertain even though the possible outcomes are known.

Random Variable

A random variable assigns a numerical value to each outcome of a random experiment.

Functions

Range

The range of a function is the set of output values the function can produce.

Linear Algebra

Rank

The rank of a matrix is the dimension of its row space or column space and measures the number of independent directions.

Number Theory

Rational Number

A rational number can be written as a ratio of two integers with a non-zero denominator.

Recurrence Relation

A recurrence relation defines terms of a sequence using earlier terms.

Functions

Recursive Function

A recursive function is defined using values of the same function on smaller inputs together with a base case.

Relation

A relation from A to B is any subset of the Cartesian product A × B.

Numerical Methods

Relative Error

Relative error compares absolute error with the magnitude of the exact value.

Sample

A sample is a subset of a population used to estimate or study the whole population.

Sample Space

A sample space is the set of all possible outcomes of a random experiment.

Linear Algebra

Scalar

A scalar is a single numerical value used to scale quantities such as vectors or matrices.

Numerical Methods

Secant Method

The secant method approximates a root using a line through two recent function values instead of an explicit derivative.

Sequence

A sequence is an ordered list of values, often indexed by integers.

Set

A set is a well-defined collection of distinct objects called elements.

Set Difference

The set difference A − B contains elements in A that are not in B.

Graphics & Machine Learning Math

Sigmoid Function

The sigmoid function maps a real number to a value between 0 and 1 using an S-shaped curve.

Geometry & Trigonometry

Sine

In a right triangle, sine of an angle equals opposite side divided by hypotenuse.

Standard Deviation

Standard deviation is the square root of variance and measures spread in the original units.

Statistical Range

The statistical range is the difference between the maximum and minimum values in a dataset.

Strong Induction

Strong induction assumes all earlier cases up to n are true to prove the next case.

Subset

A set A is a subset of B when every element of A is also an element of B.

Algorithm Math & Complexity

Summation

Summation notation compactly represents the addition of a sequence of terms.

Geometry & Trigonometry

Tangent

Tangent is a trigonometric function equal to opposite divided by adjacent in a right triangle.

Tautology

A tautology is a logical expression that is true for every possible truth assignment.

Calculus

Taylor Series

A Taylor series represents a smooth function near a point using an infinite polynomial built from derivatives.

Graph Theory & Trees

Topological Ordering

A topological ordering is a linear order of vertices in a directed acyclic graph where every edge points forward in the order.

Graphics & Machine Learning Math

Transformation Matrix

A transformation matrix represents operations such as rotation, scaling or translation in matrix form.

Linear Algebra

Transpose

The transpose of a matrix swaps its rows and columns.

Graph Theory & Trees

Tree

A tree is a connected undirected graph with no cycles.

Truth Table

A truth table lists the truth value of a logical expression for every possible combination of inputs.

Graph Theory & Trees

Undirected Graph

An undirected graph has edges with no direction.

Union

The union of two sets contains every element that appears in either set.

Universal Quantifier

The universal quantifier states that a predicate is true for every element in a domain.

Universal Set

The universal set contains all objects under consideration in a particular context.