Math glossary
Concise definitions for the recurring terms across algebra, trigonometry, calculus, precalculus, statistics and linear algebra.
Algebra
Discriminant The expression Δ = b² − 4ac that determines the nature of the roots of a quadratic equation. Coefficient A constant multiplier in front of a variable or a term of a polynomial. Slope The steepness of a line — its rise over its run. Y-intercept The y-coordinate where a curve crosses the y-axis. Logarithm The inverse of exponentiation: logₐ(x) is the exponent to which a must be raised to get x.
Trigonometry
Sine In a right triangle, the ratio of the side opposite an angle to the hypotenuse. Cosine In a right triangle, the ratio of the side adjacent to an angle to the hypotenuse. Tangent (trig function) The ratio sin θ / cos θ — undefined when cos θ = 0. Radian The natural unit of angle: a full turn is 2π radians. Pythagorean theorem In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.
Calculus
Derivative The instantaneous rate of change of a function at a point. Integral The accumulation of a function — the signed area under its graph between two points. Limit The value a function approaches as the input gets arbitrarily close to a point. Antiderivative A function whose derivative is the given function. Tangent line The line that touches a curve at a point and has the same slope as the curve there.
Precalculus
Binomial theorem A formula that expands (a + b)ⁿ as a sum of terms with binomial coefficients. Complex number A number of the form a + bi, where i is the imaginary unit with i² = −1. Factorial The product of all positive integers from 1 up to n, written n!. Permutation An ordered arrangement of r objects chosen from n. Combination An unordered selection of r objects chosen from n.
Statistics
Mean The arithmetic average of a set of numbers — their sum divided by the count. Standard deviation A measure of how spread out the values in a data set are around the mean. Z-score The number of standard deviations a value lies above or below the mean. Normal distribution The bell-shaped probability distribution defined by a mean and a standard deviation. Correlation coefficient A number between −1 and 1 measuring the strength and direction of a linear relationship.
Linear Algebra
Matrix A rectangular array of numbers arranged in rows and columns. Determinant A single number computed from a square matrix that signals invertibility. Vector An ordered list of numbers representing a point or direction in space. Dot product A single number obtained by multiplying matching components of two vectors and adding the results. Cross product An operation on two 3D vectors that produces a third vector perpendicular to both.