#mathematics

• Abelian — A structural mathematical term transposed into neuro-cybernetics and artificial neural network modeling, defining a symmetric operation or structure where the order of components does not change the final result (commutativity). In physiological modeling and neuropsychology, abelian groups or networks are utilized to simulate parallel symmetric processing of sensory stimuli or to map automatic synaptic circuits in the brain where signal synchronization does not depend on the strict sequence of incoming inputs.
• abscissa — (Mathematics) The first coordinate of a point in a plane or spatial Cartesian coordinate system, representing the distance measured from the vertical axis (ordinate) along the horizontal axis (Ox axis).
• Abul Vefa — The Latinized name of Abu al-Wafa al-Buzjani (Muhammad ibn Muhammad ibn Yahya ibn Ismail ibn al-Abbas al-Buzjani), a legendary Persian mathematician and astronomer who flourished in Baghdad during the Islamic Golden Age. He is considered one of the fathers of modern trigonometry, having introduced the secant and cosecant functions, perfected sine and tangent tables, and developed foundational trigonometric identities still used today in complex astronomical and geometric calculations.
• Actuarial science — The science, profession, or institutional department dealing with the application of mathematical and statistical methods to assess risks in the insurance, pension, and finance industries. This structural field analyzes complex demographic and economic models to ensure long-term solvency of companies against uncertain future events.
• Adjacent — Lying near, close, or contiguous; adjoining, neighboring, or situated immediately next to something; in geometry, it describes a structural element that shares a common boundary with another (such as adjacent angles, which have a common vertex and a common side, or adjacent sides of a polygon). This term is essential for defining spatial proximity and topological relationships.
• Dimensionless — Having no physical dimension, or whose fundamental units of measurement cancel each other out through ratio, being expressed as a pure number without an associated unit of measurement; in physics and mechanics, it describes a structural quantity (such as the Reynolds number or friction coefficient) obtained via dimensional analysis to simplify mathematical equations and allow scaled modeling of complex phenomena.
• Addition — The act of adding and its result; a fundamental chemical process through which two or more molecules combine to form a single, more complex product without the elimination of by-products; broadly, it represents the operation of addition, a supplementary element brought to an assembly, or the phenomenon of inserting a segment into a pre-existing structure to modify or improve its properties.
• To add — To perform an operation of addition; to add an element to an existing assembly, to sum up numbers or numerical quantities into a grand total, or to induce a chemical combination whereby extra atoms bind directly to an unsaturated molecular structure.
• Additivity — The property of certain quantities, functions, or systems to have a global value equal to the arithmetic sum of their individual component values. In a structural and mathematical sense, this phenomenon defines linear operators and extensive physical quantities (such as mass, volume, or energy), where the total effect of an assembly is obtained by the simple direct summation of partial effects, without distracting secondary interactions.
• Adjacent — Located in the immediate vicinity, directly neighboring, or attached to something; in geometry, it describes angles that share a common vertex and a common side, lying on opposite sides of that common side. In a general sense, it refers to administrative, structural, or territorial elements that share a common border or are directly connected in a network.
• Adjunction — An operation or relationship of joining or adding an element to a pre-existing structure without altering its basic identity. In linguistics, it refers to the attachment of a syntactic structure to a major constituent, while in mathematics (category theory), it represents a fundamental relation between two parallel functors, termed adjunct functors.
• Ahlfors — The surname of the Finnish mathematician Lars Ahlfors (1907–1996), famous for his fundamental contributions to complex analysis and Riemannian surfaces. He was one of the first two recipients of the Fields Medal in 1936, his name being tightly linked to structural theorems, meromorphic functions, and quasiconformal mappings used in modern geometric topology.
• Ahmes — The name of an Egyptian scribe from the Second Intermediate Period (around 1650 BC), historically recognized as the first mathematician in the world whose name has been documented. He copied and compiled the famous Rhind Mathematical Papyrus, a unique structural collection of ancient Egyptian mathematical and geometric problems including fractions, simple linear equations, and area calculations.
• Random — Depending on a future and uncertain event, determined by hazard or subject to the laws of probability; unpredictable, accidental, random. In computer science and mathematics, it describes a process, variable, or numerical sequence where each outcome has an equal chance of being selected, without any pattern or predetermined order.
• Aleksandrov — 1. A surname of Russian or Bulgarian origin, borne by numerous prominent scholars, such as the mathematician Pavel Aleksandrov (founder of modern topology) or the composer Aleksandr Aleksandrov (author of the Russian national anthem). 2. The designation of several localities and districts within the Russian Federation, historically established as major administrative points.
• Alpha — The first letter of the Greek alphabet (A, α), corresponding to the 'a' sound; by extension, a symbol universally used in mathematics, physics, and chemistry to denote angles, coefficients, radiations, or states of matter. Figuratively or sociologically, the term describes the beginning or origin of something (correlated with 'omega'), or a dominant person or animal that holds a position of leadership and control within a group or social hierarchy.
• Algebra — A foundational branch of mathematics that studies arithmetic operations and structural relations by generalizing the properties of numbers using symbols, letters, and variables. Broadly, it designates the study of abstract structures and polynomial equations.
• Algebraic — Pertaining to algebra; based on or utilizing the principles, rules, or operations of algebra. In mathematics, the term characterizes structures, equations, numbers, or varieties expressed through polynomials and finite arithmetic operations, standing in opposition to transcendental elements.
• Algebraic — A lexicographical variant used as a perfect synonym for 'algebraic'; pertaining to algebra, based on its specific rules, methods, or equations. While modern standards favor 'algebraic', this form frequently appears inside older technical textbooks and scientific literature.
• Algebraically — Algebraically; from an algebraic standpoint or by utilizing methods, rules, and operations specific to algebra. In mathematical problem-solving, it describes finding a solution via equations or symbolic calculus, standing in direct contrast to geometric or graphic approaches.