#mathematics

• To algebraize — To transpose a problem, statement, geometric structure, or scientific theory into algebraic language; to express through equations, polynomials, and abstract symbols specific to algebra. In mathematical epistemology, it refers to the process of structural formalization.
• Algebraization — The act of algebraizing and its result; the process of transposing, reformulating, or expressing concepts, problems, or scientific branches within the language, structures, and equations of algebra. Historically, algebraization represents a crucial stage of abstract formalization.
• Algorithm — A finite, ordered, unambiguous, and rigorous set of rules, instructions, or logical steps that, executed in a specific sequence starting from initial data, systematically lead to solving a problem or achieving a precise result. In computer science, it forms the logical foundation of software.
• Algorithmics — 1. A branch of computer science and applied mathematics dealing with the study, design, structural analysis, and optimization of computing algorithms. 2. The feminine form of the adjective 'algoritmic'. As a discipline, it analyzes the spatial and temporal complexity of logical procedures.
• Aliquot — A fractional part of a whole, representing an exactly measured quantity or volume of a homogeneous sample extracted for chemical or physical analysis without altering the remaining composition. In mathematics, the term describes an aliquot part, meaning a number or quantity that divides another larger quantity exactly without leaving a remainder (e.g., 4 is an aliquot part of 12).
• Aliquant — A fractional part of a whole or of a number that does not divide it exactly, always leaving a remainder after the mathematical division operation. Unlike an aliquot part, an aliquant part is contained within a larger quantity a number of times plus a fraction (e.g., 5 is an aliquant part of 12, because it goes into it twice and leaves a remainder of 2). In old legal terminology, it described an unequal or residual share.
• Aliquot — An admitted orthographic and phonetic variant of the term 'alicotă'; a volumetric portion precisely extracted from a homogeneous mixture in chemical analytical laboratories, or an ideal, abstract, and fixed share of a common or inherited patrimony in civil law. In number theory, it describes a component part that perfectly divides a whole without leaving a remainder.
• Alternate — Succeeding in a regular manner, one element after another; arranged on either side of an axis or line at different points. In botany, it describes leaves set successively on the stem, at different heights, one by one. In geometry, it refers to angles formed by two lines cut by a transversal, located on opposite sides of it.
• Alternating — Succeeding or changing in a regular, alternative, or periodic manner. In mathematics, it describes series or matrices whose elements or signs change regularly. In linguistics, it refers to sounds exhibiting phonetic alternations within the same root. In geology, it describes sedimentary layers subjected to repetitive stratification.
• To amplify — To increase, enlarge, develop, or intensify the volume, power, amplitude, or value of a phenomenon, an electrical or sound signal, or a state; in mathematics, to multiply both the numerator and the denominator of a fraction by the same integer to change its terms without altering its structural value. It represents a fundamental process in electronics for signal processing and in dynamics for expanding physical effects.
• Amplification — The act of amplifying and its result; a physical, electronic, or mathematical process through which the intensity, power, amplitude of a signal or the value of a fraction's terms is increased. In electronics, it represents the boosting of an input quantity using a specialized device that draws from an external energy source, ensuring optimal data transmission and processing.
• Amplified — Having undergone the process of amplification; a signal, sound, or numerical value structurally increased in intensity, volume, or scope. It describes the final state of an element technically processed to be stronger or of a fraction whose component elements have been multiplied by a common factor.
• Analytic — Based on analysis, utilizing analysis as its primary research method, or pertaining to it. In mathematics, it refers to branches that employ algebraic methods and differential calculus (analytic geometry) or to functions that can be expanded into power series. In linguistics, it describes languages in which grammatical relationships are expressed through separate helper words (prepositions, articles, auxiliary verbs) and word order, as opposed to synthetic languages based on inflection.
• Andreian-Cazacu — A compound Romanian surname, globally famous due to the remarkable figure of Cabiria Andreian Cazacu, a renowned Romanian mathematician and honorary member of the Romanian Academy. In the context of scientific and university terminology, this structural name is directly associated with fundamental research in complex analysis, geometric function theory, Riemann surfaces, and quasiconformal mappings.
• Andrica — A Romanian surname structurally derived from a hypocoristic or matronymic form of the given name Andrew, globally famous in academia due to the Romanian mathematician Dorin Andrica. In the context of number theory, the name is directly associated with 'Andrica's conjecture', a famous unsolved mathematical proposition regarding the gaps between square roots of consecutive prime numbers.
• Anticategory — An abstract concept utilized in structural logic or mathematical category theory to denote a dual, inverse, or complementary structure in relation to a standard defined category. In a philosophical sense, it represents a conceptual class constructed through direct opposition or by negating the fundamental attributes of an established ontological category.
• Antilogarithm — A number whose logarithm value in a given base is equal to a considered number; the inverse operation of taking a logarithm, structurally representing the raising of the base to the power indicated by the logarithm. In a functional sense, if log base b of x equals y, then the antilogarithm of y in base b equals x, historically used in complex numerical calculations via tables.
• Anti-logicism — A philosophical movement, critical attitude, or epistemological doctrine opposing logicism (the theory that all mathematics can be structurally reduced to the laws of formal logic); an orientation asserting that mathematics possesses synthetic a priori intuitions or truths independent of the purely analytical structure of logic.
• Antiparallel — Being oriented in the same mathematical or geometric direction, but in a strictly opposite sense; a geometric element, vector, or straight line whose vector orientations mutually cancel each other out through direction reversal. In plane geometry, the term defines two lines that intersect two sides of an angle in such a way that they form equal but antipositioned angles relative to a symmetrical axis or a reference secant.
• Antipedal curve — A plane geometric curve or derived figure obtained as the locus of the feet of perpendiculars drawn from a fixed point (called a pole) onto the normals of a given curve; also, it can define a structural property related to podal curves in higher analytical geometry. This concept is used in studying kinematic properties and complex geometric transformations of lines.