mathematics_math_glossary

Last updated: 27.7.2026

LETTER A

• Absolute value: the distance of a number from zero, always expressed as a non-negative value.
• Acceleration: the rate at which velocity changes over time.
• Acute angle: an angle measuring less than 90 degrees.
• Algorithm: a step-by-step procedure used to solve a problem or perform a calculation.
• Algebra: the branch of mathematics that uses symbols, variables, and equations to represent relationships.
• Algebraic expression: a combination of numbers, variables, and mathematical operations without an equality sign.
• Algebraic geometry: the branch of mathematics studying geometric objects defined by algebraic equations.
• Algebraic number: a number that is a solution of a polynomial equation with integer coefficients.
• Algebraic structure: a set with defined operations that follow specific mathematical rules.
• Analytic function: a function that can be represented locally by a convergent power series.
• Analytic geometry: the study of geometric objects using algebraic equations and coordinate systems.
• Angle: the amount of rotation between two intersecting lines or rays.
• Angular velocity: the rate at which an angle changes with respect to time.
• Antiderivative: a function whose derivative is another given function.
• Approximation: a value close to an exact value, used when an exact result is difficult to obtain.
• Approximation theory: the study of methods for estimating functions or values using simpler expressions.
• Arc: a curved part of the circumference of a circle.
• Arithmetic: the branch of mathematics involving basic operations such as addition, subtraction, multiplication, and division.
• Arithmetic mean: the average found by adding values and dividing by the number of values.
• Arithmetic progression: a sequence where each term differs from the previous term by a constant amount.
• Associative property: the property stating that changing the grouping of numbers does not change the result.
• Asymptote: a line that a curve approaches but does not necessarily reach.
• Average: a value found by dividing the sum of quantities by the number of quantities.
• Axiom: a statement accepted as true without proof and used as a foundation for reasoning.
• Autonomous equation: a differential equation where the independent variable does not appear explicitly.

• Basis: a set of vectors that can represent every vector in a space through linear combinations.
• Bayes’ theorem: a formula that updates the probability of an event using new information.
• Bernoulli distribution: a probability distribution describing an experiment with two possible outcomes.
• Bernoulli number: a sequence of rational numbers appearing in number theory and calculus.
• Binary: a number system using only two digits, usually 0 and 1.
• Bijection: a function where every input has exactly one output and every output corresponds to exactly one input.
• Binomial: a polynomial containing exactly two terms.
• Binomial theorem: a formula describing the expansion of powers of binomial expressions.
• Bivariate function: a function depending on two variables.
• Boundary: the edge or limit separating one region from another.

• Calculus: the branch of mathematics dealing with change, derivatives, integrals, and accumulation.
• Calculus of variations: a branch of calculus that finds functions optimizing quantities.
• Canonical form: a standard or simplified representation of a mathematical object.
• Cardinality: the number of elements contained in a set.
• Cartesian plane: a coordinate system using two perpendicular axes to locate points.
• Cauchy sequence: a sequence whose terms become arbitrarily close to each other as it progresses.
• Cauchy theorem: a theorem with important results in areas such as group theory and complex analysis.
• Central limit theorem: a theorem stating that averages of many random samples tend toward a normal distribution.
• Characteristic equation: an equation whose solutions determine important properties of a mathematical system.
• Characteristic polynomial: a polynomial derived from a matrix that determines its eigenvalues.
• Chord: a line segment connecting two points on a circle.
• Circle: a shape consisting of all points at an equal distance from a central point.
• Circumference: the total distance around a circle.
• Coefficient: a number multiplied by a variable in an expression.
• Coefficient matrix: a matrix containing the coefficients of variables in a system of equations.
• Combination: a selection of objects where the order does not matter.
• Combinatorics: the study of counting, arrangements, and possible configurations.
• Compactness: a mathematical property describing spaces that behave similarly to finite objects.
• Complex analysis: the study of functions involving complex numbers.
• Complex number: a number containing a real part and an imaginary part.
• Complex plane: a coordinate plane used to represent complex numbers.
• Computability theory: the study of which problems can be solved using algorithms.
• Composite number: a positive integer with more than two factors.
• Constant: a fixed value that does not change.
• Constant function: a function that has the same output for every input.
• Constraint: a condition that limits possible solutions in a mathematical problem.
• Continuous function: a function with no breaks, jumps, or interruptions.
• Contrapositive: a statement formed by reversing and negating an implication.
• Convergence: the process of approaching a specific value or limit.
• Convex function: a function whose graph lies below the line segment connecting any two points on the graph.
• Coordinate: a value used to specify the location of a point.
• Cosine: a trigonometric function equal to the adjacent side divided by the hypotenuse in a right triangle.
• Cotangent: the reciprocal of the tangent function.
• Correlation coefficient: a number measuring the strength and direction of a relationship between variables.
• Covariance: a measure of how two variables change together.
• Cross product: a vector operation producing a vector perpendicular to two given vectors.
• Cubic equation: an equation containing a variable raised to the third power.
• Curve: a continuous line that bends or changes direction.

• Data set: a collection of values, observations, or measurements used for analysis.
• Decimal: a number written using the base-ten system with digits after a decimal point.
• Deductive reasoning: reasoning that derives conclusions from established principles or assumptions.
• Definite integral: an integral evaluated over a specific interval that gives an accumulated value.
• Degree: a unit for measuring angles, where a full rotation equals 360 degrees.
• Degree of polynomial: the highest exponent of the variable appearing in a polynomial.
• Denominator: the bottom part of a fraction showing the number of equal parts.
• Dependent variable: a variable whose value depends on another variable.
• Derivative: a measure of the rate at which a function changes.
• Derivative operator: a mathematical symbol or operation representing differentiation.
• Determinant: a value calculated from a square matrix that provides information about the matrix.
• Deterministic system: a system where future behavior is completely determined by current conditions.
• Differentiability: the property of a function having a derivative at a point or interval.
• Differential: a small change in a variable used in calculus.
• Differential equation: an equation involving a function and its derivatives.
• Dimension: the number of independent coordinates needed to describe a space.
• Directional derivative: the rate of change of a function in a specific direction.
• Discriminant: a value in a quadratic equation used to determine the number and type of solutions.
• Divergence theorem: a theorem relating the flow through a closed surface to the divergence inside a region.
• Domain: the complete set of possible input values of a function.
• Domain restriction: a limitation placed on the allowed inputs of a function.
• Dot product: a multiplication of two vectors that produces a scalar value.

• Eigenvalue: a scalar showing how much an eigenvector is stretched or compressed by a transformation.
• Eigenvector: a vector that keeps the same direction after a matrix transformation.
• Element: an individual object contained in a set.
• Ellipse: a closed curve where the sum of distances from two fixed points remains constant.
• Elliptic curve: a type of algebraic curve important in number theory and cryptography.
• Embedding: placing one mathematical structure inside another while preserving its properties.
• Empty set: a set containing no elements.
• Equation: a statement showing that two mathematical expressions are equal.
• Equivalence class: a group of objects considered equivalent under a defined relation.
• Euclidean geometry: the study of geometry based on Euclid’s postulates involving points, lines, angles, and shapes.
• Euclidean space: ordinary geometric space described using coordinates and distances.
• Euler characteristic: a number describing important topological properties of shapes and spaces.
• Euler identity: the equation eiπ+1=0e^{i\pi}+1=0eiπ+1=0, connecting fundamental mathematical constants.
• Euler method: a numerical method for approximating solutions to differential equations.
• Exponent: a number indicating how many times a base is multiplied by itself.
• Exponential function: a function where the variable appears in the exponent.
• Expression: a combination of numbers, variables, and operations without an equality sign.

• Factor: a number or expression that divides another number or expression exactly.
• Factorial: the product of all positive integers from 1 up to a given number, written with an exclamation mark.
• Field: a mathematical system where addition, subtraction, multiplication, and division are defined.
• Fourier series: a representation of a periodic function as a sum of sine and cosine waves.
• Fourier transform: a method for expressing functions as combinations of frequencies.
• Fraction: a number representing part of a whole, written as one quantity divided by another.
• Fractal: a complex pattern that repeats itself at different scales.
• Frequency: the number of times an event or value occurs in a data set.
• Fundamental theorem of algebra: the theorem stating that every non-constant polynomial has at least one complex root.
• Fundamental theorem of calculus: the theorem connecting derivatives and integrals.

• Gaussian distribution: another name for the normal distribution, a symmetric probability distribution.
• Gaussian elimination: a method for solving systems of linear equations using row operations.
• Geometric mean: the average found by multiplying values together and taking the appropriate root.
• Geometric progression: a sequence where each term is found by multiplying the previous term by a constant ratio.
• Geometric sequence: a sequence where consecutive terms have a constant ratio.
• Gradient: the rate and direction of change of a function, often represented as a vector.
• Gradient field: a vector field created from the gradient of a scalar function.
• Graph: a visual representation of mathematical relationships, points, or connections.
• Group: a set with an operation satisfying properties such as closure, associativity, identity, and inverses.
• Group theory: the study of algebraic structures based on symmetry and operations.

• Harmonic mean: an average calculated using the reciprocals of values.
• Hyperbola: a conic section formed by points with a constant difference of distances from two fixed points.
• Hyperbolic geometry: a non-Euclidean geometry where parallel lines behave differently from Euclidean geometry.
• Hypotenuse: the longest side of a right triangle, opposite the right angle.
• Hypothesis: a proposed statement or assumption that can be tested mathematically or scientifically.

• Identity: an equation that is true for all possible values of its variables.
• Imaginary number: a number involving the square root of a negative number, usually written using iii.
• Improper integral: an integral involving infinite intervals or points where the function is undefined.
• Independent variable: a variable that is controlled or chosen and affects another variable.
• Indeterminate form: an expression such as 0/00/00/0 that requires further analysis to determine its value.
• Induction: a proof method that shows a statement is true for all natural numbers by proving a base case and a general step.
• Inequality: a mathematical statement comparing values using symbols such as <<<, >>>, ≤\leq≤, or ≥\geq≥.
• Inner product: a generalization of the dot product used to measure lengths, angles, and orthogonality.
• Integer: a whole number that can be positive, negative, or zero.
• Integral: a mathematical operation used to find accumulated quantities, areas, volumes, or antiderivatives.
• Interpolation: the process of estimating values between known data points.
• Invariant: a quantity or property that remains unchanged under a transformation.
• Inverse function: a function that reverses the effect of another function.
• Inverse matrix: a matrix that reverses the effect of another matrix.
• Irrational number: a number that cannot be written as a ratio of two integers.
• Isosceles triangle: a triangle with at least two equal sides.

• Jacobian: a matrix containing partial derivatives used in multivariable calculus and transformations.
• Jacobian matrix: another name for the matrix of partial derivatives of a vector-valued function.

• Kernel: the set of vectors that a linear transformation maps to zero.
• Knot theory: a branch of topology studying mathematical knots and their properties.

• Laplace transform: a transformation that converts functions into another form to simplify differential equations.
• Law of large numbers: a theorem stating that averages become closer to expected values as sample sizes increase.
• Least squares: a method for finding the best-fitting model by minimizing the sum of squared errors.
• Lebesgue integral: a more general form of integration used in advanced analysis.
• Limit: the value a function approaches as the input approaches a certain point.
• Limit point: a point that can be approached by other points in a space.
• Linear combination: an expression formed by multiplying vectors by scalars and adding them together.
• Linear equation: an equation where variables have a maximum power of one.
• Linear independence: a property where vectors cannot be written as combinations of other vectors.
• Linear transformation: a function between vector spaces that preserves addition and scalar multiplication.
• Logarithm: the inverse operation of exponentiation that finds the power needed to produce a number.

• Maclaurin series: a Taylor series centered at zero.
• Magnitude: the size or length of a quantity, especially a vector.
• Manifold: a space that locally resembles ordinary Euclidean space.
• Matrix: a rectangular arrangement of numbers used to represent data, transformations, and systems of equations.
• Maximum: the greatest value in a set or function.
• Mean: the average value found by adding values and dividing by their count.
• Median: the middle value in an ordered data set.
• Metric space: a set equipped with a distance function that defines how far apart elements are.
• Minimum: the smallest value in a set or function.
• Mode: the value that appears most frequently in a data set.
• Modular arithmetic: arithmetic where numbers repeat after reaching a fixed modulus.
• Modulus: another term for absolute value; it can also describe the size of a complex number.
• Monomial: a polynomial containing exactly one term.
• Multiple: a number produced by multiplying another number by an integer.
• Multivariable calculus: calculus involving functions with two or more variables.

• Natural logarithm: the logarithm with base eee, where eee is approximately 2.718.
• Natural number: a positive counting number such as 1, 2, 3, and so on.
• Negative number: a number less than zero.
• Normal distribution: a symmetric probability distribution shaped like a bell curve.
• Normal vector: a vector perpendicular to a line, surface, or plane.
• Number line: a straight line showing numbers arranged by increasing or decreasing value.
• Number theory: the branch of mathematics studying integers and their properties.
• Numerator: the top part of a fraction showing how many parts are being considered.

• Operator: a mathematical rule or symbol that transforms one object into another.
• Optimization: the process of finding the best possible solution under given conditions.
• Ordinary differential equation (ODE): an equation involving derivatives of a function with respect to one variable.
• Orthogonal: describing objects that are perpendicular or have a zero inner product.
• Orthogonal basis: a basis consisting of mutually perpendicular vectors.

• Parameter: a value that controls or defines a mathematical system or function.
• Parallel lines: lines in the same plane that never intersect and remain the same distance apart.
• Partial derivative: a derivative taken with respect to one variable while keeping other variables constant.
• Partial differential equation (PDE): an equation involving partial derivatives of functions with multiple variables.
• Pascal’s triangle: a triangular arrangement of numbers used in combinatorics and probability.
• Permutation: an arrangement of objects where the order matters.
• Perimeter: the total distance around the boundary of a two-dimensional shape.
• Phase space: a space representing all possible states of a mathematical or physical system.
• Plane: a flat, two-dimensional surface extending infinitely in all directions.
• Point: a precise location in space with no length, width, or height.
• Polynomial: an algebraic expression made of variables, coefficients, and non-negative integer powers.
• Power series: an infinite series involving powers of a variable.
• Prime number: a positive integer greater than one with exactly two factors: 1 and itself.
• Primitive function: another name for an antiderivative.
• Probability: the measure of how likely an event is to occur.
• Projection: the process of representing an object or vector on another line, plane, or direction.
• Proof: a logical argument that demonstrates a mathematical statement is true.

• Quadratic equation: an equation containing a variable raised to the second power.
• Quadratic formula: a formula used to solve quadratic equations.
• Quadrilateral: a polygon with four sides and four angles.
• Quotient: the result obtained when one number is divided by another.

• Radius: the distance from the center of a circle to any point on its edge.
• Random variable: a variable whose value depends on the outcome of a random event.
• Rank: the number of linearly independent rows or columns in a matrix.
• Rational number: a number that can be written as a ratio of two integers.
• Real number: any number that can be represented on the number line.
• Rectangle: a quadrilateral with four right angles.
• Recursion: a method where an object is defined using previous cases of itself.
• Regression: a statistical method for modeling relationships between variables.
• Relation: a connection between elements of one or more sets.
• Remainder: the amount left over after division that is not exact.
• Rhombus: a quadrilateral with four equal sides.
• Riemann hypothesis: a famous unsolved problem concerning the zeros of the Riemann zeta function.
• Riemann integral: a formal definition of integration using limits of sums.
• Ring: an algebraic structure with addition and multiplication operations.

• Scalar: a quantity with magnitude but no direction.
• Scalar field: a set of numbers used as scalars in a vector space.
• Secant: a line that intersects a curve, especially a circle, at two points.
• Sequence: an ordered list of numbers or objects following a rule.
• Series: the sum of the terms of a sequence.
• Set: a collection of distinct objects called elements.
• Sine: a trigonometric function relating the opposite side to the hypotenuse in a right triangle.
• Singularity: a point where a mathematical function becomes undefined or behaves unusually.
• Slope: the rate of change of a line, describing its steepness and direction.
• Solution set: the complete set of values satisfying an equation or system.
• Sphere: a three-dimensional shape where all points are the same distance from the center.
• Spectral theory: the study of eigenvalues, eigenvectors, and operators.
• Standard deviation: a measure of how spread out data values are from the mean.
• Subset: a set whose elements all belong to another set.
• Sum: the result of adding numbers together.
• Symmetry: a property where an object remains unchanged under certain transformations.

• Tangent: a line that touches a curve at exactly one point; also a trigonometric ratio.
• Taylor series: an infinite polynomial expansion representing a function near a point.
• Theorem: a mathematical statement proven true using logic and previously established results.
• Topology: the study of properties preserved under continuous transformations.
• Transformation: a change in position, size, shape, or structure of a mathematical object.
• Transcendental number: a number that is not a solution of any polynomial equation with integer coefficients.
• Trapezoid: a quadrilateral with at least one pair of parallel sides.
• Triangle: a polygon with three sides and three angles.
• Trigonometry: the branch of mathematics studying relationships between angles and sides of triangles.
• Turing machine: a mathematical model describing the fundamental principles of computation.

• Uniform convergence: convergence where functions approach their limit at the same rate everywhere.
• Unit circle: a circle with radius one, widely used in trigonometry.

• Variable: a symbol representing an unknown or changing quantity.
• Variance: a measure of how far data values spread from their mean.
• Vector: a quantity with both magnitude and direction.
• Vector field: a function assigning a vector to every point in a space.
• Vector space: a mathematical structure where vectors can be added and multiplied by scalars.
• Vertex: a point where two or more lines, edges, or sides meet.

• Weak convergence: a type of convergence defined through the behavior of functions applied to objects.

• Zeta function: a function important in number theory, especially in the study of prime numbers and the Riemann hypothesis.