Glosarium

Bayes' Theorem

A formula for updating the probability of a hypothesis given new evidence, foundational to statistical inference.

Big O Notation

A mathematical notation describing the upper bound of an algorithm's time or space complexity as input size grows.

Binomial Distribution

Binomial Probability Distribution

A discrete probability distribution modeling the number of successes in a fixed number of independent yes/no trials.

Combination

A selection of elements without regard to order — n choose r equals n!/[r!(n-r)!].

Correlation

Statistical Correlation

A measure of the linear relationship between two variables, ranging from -1 (inverse) to +1 (direct).

Cross Product

Vector Cross Product

An operation on two 3D vectors producing a vector perpendicular to both, with magnitude equal to the parallelogram area they span.

Entropy (Information)

Shannon Information Entropy

A measure of uncertainty or information content in a dataset, calculated as the negative sum of probabilities times their logarithms.

Exponential

Exponential Function

A function where the variable appears as an exponent (e.g. e^x), modeling rapid growth or decay processes.

Factorial

Factorial (n!)

The product of all positive integers up to n (e.g. 5! = 120), used in combinatorics and probability.

Fibonacci Sequence

A sequence where each number is the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8, 13, ...).

Matrix

Mathematical Matrix

A rectangular array of numbers arranged in rows and columns, used in linear algebra and transformations.

Determinant

Matrix Determinant

A scalar value computed from a square matrix that indicates whether the matrix is invertible and describes scaling.

Mean

Arithmetic Mean

The average of a set of numbers, calculated by dividing the sum of all values by the count of values.

Median

Statistical Median

The middle value in a sorted dataset, separating the higher half from the lower half.

Standard Deviation

A measure of how spread out values are from the mean — low values indicate data clustered near the average.

Percentile

Statistical Percentile

A value below which a given percentage of observations fall (e.g. 95th percentile means 95% of values are lower).

Logarithm

The inverse of exponentiation — log base b of x equals the power to which b must be raised to yield x.

Prime Number

A natural number greater than 1 divisible only by 1 and itself (e.g. 2, 3, 5, 7, 11, 13).

GCD

Greatest Common Divisor

The largest positive integer that divides two or more numbers without leaving a remainder.

LCM

Least Common Multiple

The smallest positive integer that is divisible by two or more given numbers.

Permutation

An ordered arrangement of elements — the number of permutations of n items taken r at a time is n!/(n-r)!.

Derivative

Calculus Derivative

The instantaneous rate of change of a function with respect to its variable, representing the slope of the tangent line.

Integral

Calculus Integral

The accumulation of a quantity over an interval, geometrically representing the area under a curve.

Radians

Radian Measure

An angle measurement where one radian equals the angle subtended by an arc equal in length to the radius.

Modular Arithmetic

A system of arithmetic where numbers wrap around after reaching a modulus (e.g. 17 mod 5 = 2).

Eigenvalue

A scalar that, when a matrix is applied to its eigenvector, scales the vector without changing its direction.

Fourier Transform

A mathematical operation decomposing a signal into its constituent frequencies, fundamental to audio and image processing.

Variance

Statistical Variance

The average of squared deviations from the mean, measuring how far data points spread from the average.

Mode

Statistical Mode

The most frequently occurring value in a dataset, useful for categorical data where mean is meaningless.

Regression

Regression Analysis

A statistical method for modeling the relationship between a dependent variable and one or more independent variables.

Normal Distribution

Normal (Gaussian) Distribution

A symmetric bell-shaped probability distribution where about 68% of values fall within one standard deviation of the mean.

Sigmoid Function

An S-shaped function mapping any real number to a value between 0 and 1, widely used in logistic regression and neural networks.

Interpolation (Math)

Mathematical Interpolation

Estimating unknown values between known data points using methods like linear, polynomial, or spline interpolation.

Dot Product

Vector Dot Product

An operation on two vectors returning a scalar equal to the sum of element-wise products, measuring alignment.

Boolean Algebra

A branch of algebra operating on true/false values using AND, OR, NOT operators, foundational to digital logic.

Euler's Number

Euler's Number (e)

The mathematical constant e (approximately 2.71828), the base of natural logarithms, central to calculus and compound growth.

Pi

Pi (Circumference Ratio)

The mathematical constant representing the ratio of a circle's circumference to its diameter, approximately 3.14159.

Complex Number

A number of the form a + bi where i is the imaginary unit (square root of -1), used in signal processing and physics.

Set Theory

A branch of mathematics studying collections of objects, with operations like union, intersection, and complement.

Taylor Series

Taylor Series Expansion

An infinite sum of polynomial terms that approximates a function around a point, used in calculators and numerical methods.

Gradient

Mathematical Gradient

A vector of partial derivatives indicating the direction and rate of steepest ascent of a multivariable function.

Monte Carlo Method

Monte Carlo Simulation

A computational technique that uses repeated random sampling to estimate numerical results for problems that are difficult to solve analytically.

Least Squares

Least Squares Method

A curve-fitting method that minimizes the sum of squared differences between observed data points and a model's predictions.

Hamming Distance

The number of positions at which corresponding bits or symbols of two equal-length strings differ, used in error detection and coding theory.

Newton's Method

Newton-Raphson Method

An iterative algorithm for finding roots of equations by successively improving an estimate using the function's derivative.

Z-Score

Standard Score (Z-Score)

The number of standard deviations a data point lies from the mean, used to compare values across different distributions.

Pythagorean Theorem

The relation a^2 + b^2 = c^2 in a right triangle, where c is the hypotenuse.

Probability Distribution

A mathematical function describing the likelihood of different outcomes in a random experiment (e.g. normal, Poisson).