Mathematics and statistics

Hausdorff space

A Hausdorff space, also called a T2 space or separated space, is a topological space in which any two distinct points can be separated by disjoint neighborhoods.

Hausman test

The Hausman test is a statistical specification test in econometrics, introduced by J. A. Hausman in 1978, that compares two estimators and rejects the null when they diverge.

The haversine formula, also known as the haversine distance, computes the great-circle distance between two points on a sphere from their latitudes and longitudes, using the haversine trigonometric function.

Hawkes process

The Hawkes process is a self-exciting point process introduced by Alan G. Hawkes in 1971, in which each event temporarily raises the probability of further arrivals.

Hazard and operability study

A hazard and operability study (HAZOP), also known as Hazard and Operability Analysis, is a structured team technique that uses guide words such as No, More, and Reverse to identify process deviations.

Hazard ratio

The hazard ratio (HR) is a measure in survival analysis that compares the instantaneous event rates of two groups, most often estimated with the Cox proportional-hazards model, and is not a risk ratio.

Health and Retirement Study

The Health and Retirement Study, run by the University of Michigan since 1992, surveys about 20,000 Americans over age 50 every two years on health, work, income, and wealth.

Health geography

Health geography, also called medical geography, is a subdiscipline of human geography studying how place, location, and spatial relations shape disease, well-being, and health care.

Heat equation

The heat equation, also called the diffusion equation, is the partial differential equation describing how temperature or any diffusing quantity evolves in time, formulated by Joseph Fourier in 1807.

Heat map

A heat map is a data visualization that encodes values in a two-dimensional matrix or table as colors, so patterns, clusters, and outliers can be read from shaded cells.

Heaviside step function

The Heaviside step function, also called the unit step function, is a discontinuous function taking the value 0 for negative input and 1 for positive input, named after Oliver Heaviside.

Heavy-tailed distribution

A heavy-tailed distribution is a probability distribution whose tail decays more slowly than any exponential, so extreme values occur far more often than in Gaussian or exponential models.

Hecke algebra

A Hecke algebra is a commutative algebra of operators acting on modular forms, generated by the Hecke operators T_n, which encode averaging over sublattices of a lattice.

Hecke operator

A Hecke operator is a linear operator on spaces of modular forms, introduced by Erich Hecke in 1937, whose commuting eigenvalues decompose them into eigenforms.

Hedonic regression

Hedonic regression is an econometric method that regresses the price of a good on its attributes, such as a house's size, age, and location, to estimate each attribute's implicit price.

Heegaard Floer homology

Heegaard Floer homology is a collection of invariants of oriented 3-manifolds and of knots and links, introduced by Peter Ozsváth and Zoltán Szabó in the early 2000s.

Heegaard splitting

A Heegaard splitting decomposes a closed 3-manifold into two handlebodies glued along a common Heegaard surface, and every closed orientable 3-manifold admits one; diagrams from splittings underlie Heegaard Floer homology.

Heegner number

A Heegner number is a squarefree positive integer for which the imaginary quadratic field Q(√−n) has class number one; there are exactly nine: 1, 2, 3, 7, 11, 19, 43, 67, and 163.

Height function

A height function in Diophantine geometry measures the arithmetic complexity of rational points on a projective variety, and underlies finiteness results such as the Mordell–Weil theorem.

Heightmap

A heightmap, also called a digital elevation model or height field, is a two-dimensional grid storing one elevation value per location, commonly used for terrain in games and GIS.

Heisenberg algebra

The Heisenberg algebra is a nilpotent Lie algebra, formally the Heisenberg Lie algebra, whose brackets encode the canonical commutation relations of quantum mechanics; Hermann Weyl identified it in the 1920s.

Heisenberg group

The Heisenberg group is a nilpotent Lie group of real upper triangular 3 × 3 matrices with ones on the diagonal, named for its role in quantum mechanics.

Held group

The Held group (He) is a sporadic finite simple group discovered by Dieter Held in 1969 while studying groups related to the Mathieu group M24.

Helix

A helix is a smooth space curve that winds around a fixed axis at constant distance while advancing at a constant rate, like a screw thread.

Hellinger distance

The Hellinger distance, or Hellinger metric, is a metric on probability distributions that compares square-root densities, named after Ernst Hellinger and widely used in statistical lower bounds and decision trees.

Helmholtz equation

The Helmholtz equation is the elliptic partial differential equation describing the spatial amplitude of a harmonically oscillating wave; it is the time-independent form of the wave equation.

Hénon map

The Hénon map is a two-dimensional discrete dynamical system introduced by Michel Hénon in 1976, a standard example of chaos with a strange fractal attractor.

Hensel's lemma

Hensel's lemma, or Hensel lifting, is a number theory theorem stating that a simple root of a polynomial modulo a prime p lifts uniquely to a p-adic root.

Henselian ring

A henselian ring, also called a Hensel local ring, is a local ring in which simple roots of polynomials over the residue field lift to roots in the ring.