Mathematics

Lambda calculus: foundations, concepts, and influence Lambda calculus Lambda calculus is a concise formal system for defining and transforming functions. It underpins computability theory and many functional programming ideas through abstraction, app…

Langlands program: a unifying framework in number theory and representation theory Langlands program A set of deep conjectures and results linking number theory, harmonic analysis and representation theory, generalizing class field theory and predicting correspondences between Gal…

Laplace operator: definition, properties, applications and variants Laplace operator Overview of the Laplace operator (Laplacian): definition, coordinate forms, key properties, role in PDEs and physics, historical origin, discrete and manifold generalizations, and…

Laplace transform: definition, properties, history, and applications Laplace transform Integral transform that converts time-domain functions into complex-frequency functions. Widely used to solve differential equations, analyze systems, and study probability and sig…

Laplace's equation: definition, properties, and applications Laplace's equation Laplace's equation is a second‑order linear partial differential equation whose solutions (harmonic functions) describe steady-state potentials in physics and arise in many mathema…

Las Vegas algorithm: randomized methods that guarantee correctness Las Vegas algorithm A Las Vegas algorithm is a randomized procedure that always returns a correct result (or reports failure) while its running time is a random variable. Contrasts with Monte Carlo al…

LaTeX — document preparation system LaTeX LaTeX is a high-quality digital typesetting system built on TeX, using macros and packages to produce scientific, technical, and general documents. Widely used in academia for its…

Law of large numbers The law of large numbers explains why sample averages converge toward the expected value as the number of independent observations grows; covers weak and strong forms, conditions,…

Law of sines: statement, derivations, uses and the ambiguous case Law of sines The law of sines relates the sides and angles of a triangle: a/sin A = b/sin B = c/sin C = 2R. Article covers statements, derivations, examples, the SSA ambiguous case, history, an…

Laws of Form A concise guide to George Spencer-Brown's Laws of Form: its core idea of distinction, the calculus of indications, historical context, influence, uses, and critical reception.

League (unit of length) League (unit) The league is a historical unit of distance once defined as the distance a person could walk in roughly an hour; its length varied by place and era and survives in literature and o…

Leap year: rules, reason, calendars, and cultural notes Leap year A leap year inserts an extra day or month to keep calendars aligned with the seasons. Explanations, the Gregorian rule, comparisons with other calendars, and social effects of Feb…

Leap year starting on Friday Overview and calendar properties of leap years whose January 1 falls on a Friday in the Gregorian calendar, with examples, holiday placements, and notable patterns.

Leap year starting on Monday Explanation and calendar effects of a leap year whose January 1 falls on a Monday, including holiday placements, Friday the 13th occurrences, examples and ties to the Gregorian cal…

Leap year starting on Saturday Overview of leap years whose January 1 falls on a Saturday: calendar structure, holiday placements, examples in the Gregorian calendar, and notable patterns such as Friday the 13th…

Leap year starting on Sunday Overview of a leap year whose January 1 falls on Sunday: calendar layout, holiday dates, occurrence examples, why it has three Friday the 13ths, and relations to other year types.

Leap year beginning on Thursday (Gregorian calendar) Leap year starting on Thursday Overview and calendar characteristics of leap years whose January 1 falls on Thursday; includes weekday patterns, holidays, Friday the 13ths, examples and how the pattern arises.

Leap year beginning on Tuesday (Gregorian calendar) Leap year starting on Tuesday Overview of the Gregorian leap year that starts on Tuesday: calendar layout, holiday dates, frequency, examples, and notable traits including its single Friday the 13th (in June).

Least squares (method of fitting and estimation) Least squares Least squares is a mathematical procedure to fit functions to data by minimizing the sum of squared residuals. It underpins regression, estimation and many numerical methods, with…

Lemma — mathematics, linguistics, and botany Lemma Lemma: a supporting proposition in mathematics, a citation or base form in linguistics and lexicography, and a bract of a grass spikelet in botany; the term originates in Greek for…

Lemma (mathematics) A lemma is a proven auxiliary statement used to support the proof of a more significant theorem; often technical, it helps structure arguments and isolate intermediate results.

Leonhard Euler: Life, Work, and Legacy Leonhard Euler Comprehensive overview of Leonhard Euler, the Swiss mathematician and physicist: biography, major contributions, notation, applications, and lasting influence on mathematics and sc…

Level — measurement, rank, and meanings Level Comprehensive overview of ‘level’: its senses (measurement tools like spirit and laser levels, elevation/flatness, ranks/stages, and mathematical level sets), history, uses, and im…

Level set (mathematics) Level set A level set is the subset of a domain where a real-valued function attains a fixed value. It appears as contours, surfaces, and plays roles in geometry, differential topology, and…

Limit (mathematics, science, and general concept) Limit A limit denotes a value or boundary approached by a sequence, function, or process, or a constraint that cannot be exceeded; it is central to calculus and appears in law, computing…

Limit (mathematics) A limit is the value that a function or sequence approaches as its argument or index approaches a point. Limits formalize approach and are foundational for continuity, derivatives,…

Limit of a function Description of the mathematical concept of a limit of a function, its formal definitions, variants, techniques for evaluation, examples, and its role in continuity, derivatives and…

Limit of a Sequence An explanation of the limit of a sequence: definition, formal criterion, typical examples and distinctions between convergence, divergence, and oscillation, with historical and pra…

Line (geometry) A basic one-dimensional straight locus of points in geometry: definition, properties, common types, historical context, and practical uses in mathematics and applied fields.

Line segment: definition, properties, and examples Line segment Clear overview of a line segment in geometry: definition, notation, key properties, special cases (chord, side), historical context, and common uses.

Linear algebra: concepts, methods, and applications Linear algebra Overview of linear algebra: fundamental objects (vectors, matrices, vector spaces), solving linear systems, main operations and theorems, history, and applications across science a…

Linear combination A linear combination expresses an element as a sum of scalar multiples of other elements; a central concept in linear algebra with roles in span, dependence, coordinates and applic…

Linear cryptanalysis: statistical attack using linear approximations Linear cryptanalysis Linear cryptanalysis is a statistical method that exploits approximate linear relations between plaintext, ciphertext and key bits to recover key information; it is a major tool in…

Linear equation A linear equation describes a straight line relationship between variables. This article explains common forms, slope and intercept, examples, historical notes, and applications in…

Linear function (affine form and linear mapping) Linear function A linear function commonly means a straight-line rule y = mx + b in elementary math; in higher mathematics it denotes a linear map preserving addition and scalar multiplication.

Linear independence Linear independence describes when vectors (or functions) in a vector space cannot be expressed as nontrivial linear combinations of each other; it underlies bases, dimension, and…

Linear mapping (linear transformation) Linear mapping A linear mapping is a function between vector spaces that preserves vector addition and scalar multiplication. This article explains definition, properties, matrix form, examples,…

Linear programming: theory, methods, and applications Linear programming Linear programming (linear optimisation) studies the maximization or minimization of a linear function subject to linear constraints. It underpins operations research, optimization…

Linear regression: concepts, history, methods, and practical uses Linear regression An accessible overview of linear regression covering its definition, mathematical form, history, assumptions, common estimation methods, extensions, and practical applications.

Linear system: definition, properties, representations and applications Linear system An explanatory article on linear systems: definition, key properties (superposition), common representations (matrices, state-space, transfer functions), uses, history, and distinc…

List of chess openings An organized overview of chess openings: what they are, how they are classified, common types and examples, historical development, practical importance, and study methods.

List of mathematics topics Organized overview of major mathematical branches, common concepts, history, applications, and how topics are grouped for study and reference.

Readability tests: common formulas and their uses List of readability tests Overview of readability tests—formulas that estimate how difficult a text is to read, major indices, how they work, their history, common applications, and limitations.

Litre: definition, history, conversion and common uses Litre The litre (liter) is a metric unit of volume equal to 1,000 cubic centimetres (0.001 m³). This article explains its definition, history, common conversions, notation and typical ap…

Locus Locus — from Latin for 'place' — denotes a position, site, or set of positions. Common uses include mathematics (sets of points), genetics (chromosomal position), psychology (locus…

Locus (mathematics): set of points defined by geometric conditions Locus (mathematics) A locus is the set of all points satisfying one or more geometric conditions. This article explains the concept, common types, historical context, methods of description, and key a…

Log–log graph: definition, interpretation and applications Log-log graph A log–log graph plots both axes on logarithmic scales to linearize power‑law relationships, reveal scaling, and compare multiplicative patterns across many disciplines.

Logarithm — definition, properties, history and common uses Logarithm An accessible overview of logarithms: definition, basic properties and rules, common bases, historical development, practical uses and noteworthy distinctions.