# mathematics

## English Thesaurus

1. a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement (noun.cognition)

hypernym | : | science, scientific discipline, |

definition | : | a particular branch of scientific knowledge (noun.cognition) |

hyponym | : | pure mathematics, |

definition | : | the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness (noun.cognition) |

hyponym | : | applied math, applied mathematics, |

definition | : | the branches of mathematics that are involved in the study of the physical or biological or sociological world (noun.cognition) |

domain category | : | science, scientific discipline, |

definition | : | a particular branch of scientific knowledge (noun.cognition) |

domain member category | : | rounding, rounding error, |

definition | : | (mathematics) a miscalculation that results from rounding off numbers to a convenient number of decimals (noun.act) |

domain member category | : | truncation error, |

definition | : | (mathematics) a miscalculation that results from cutting off a numerical calculation before it is finished (noun.act) |

domain member category | : | mathematical operation, mathematical process, operation, |

definition | : | (mathematics) calculation by mathematical methods (noun.act) |

domain member category | : | rationalisation, rationalization, |

definition | : | (mathematics) the simplification of an expression or equation by eliminating radicals without changing the value of the expression or the roots of the equation (noun.act) |

domain member category | : | invariance, |

definition | : | the nature of a quantity or property or function that remains unchanged when a given transformation is applied to it (noun.attribute) |

domain member category | : | accuracy, |

definition | : | (mathematics) the number of significant figures given in a number (noun.attribute) |

domain member category | : | balance, correspondence, symmetricalness, symmetry, |

definition | : | (mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane (noun.attribute) |

domain member category | : | asymmetry, dissymmetry, imbalance, |

definition | : | (mathematics) a lack of symmetry (noun.attribute) |

domain member category | : | factoring, factorisation, factorization, |

definition | : | (mathematics) the resolution of an entity into factors such that when multiplied together they give the original entity (noun.cognition) |

domain member category | : | extrapolation, |

definition | : | (mathematics) calculation of the value of a function outside the range of known values (noun.cognition) |

domain member category | : | interpolation, |

definition | : | (mathematics) calculation of the value of a function between the values already known (noun.cognition) |

domain member category | : | recursion, |

definition | : | (mathematics) an expression such that each term is generated by repeating a particular mathematical operation (noun.cognition) |

domain member category | : | invariant, |

definition | : | a feature (quantity or property or function) that remains unchanged when a particular transformation is applied to it (noun.cognition) |

domain member category | : | multinomial, polynomial, |

definition | : | a mathematical function that is the sum of a number of terms (noun.cognition) |

domain member category | : | series, |

definition | : | (mathematics) the sum of a finite or infinite sequence of expressions (noun.cognition) |

domain member category | : | infinitesimal, |

definition | : | (mathematics) a variable that has zero as its limit (noun.cognition) |

domain member category | : | fractal, |

definition | : | (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry (noun.cognition) |

domain member category | : | arithmetic, |

definition | : | the branch of pure mathematics dealing with the theory of numerical calculations (noun.cognition) |

domain member category | : | geometry, |

definition | : | the pure mathematics of points and lines and curves and surfaces (noun.cognition) |

domain member category | : | affine geometry, |

definition | : | the geometry of affine transformations (noun.cognition) |

domain member category | : | elementary geometry, euclidean geometry, parabolic geometry, |

definition | : | (mathematics) geometry based on Euclid's axioms (noun.cognition) |

domain member category | : | euclid's axiom, euclid's postulate, euclidean axiom, |

definition | : | (mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry (noun.cognition) |

domain member category | : | fractal geometry, |

definition | : | (mathematics) the geometry of fractals (noun.cognition) |

domain member category | : | non-euclidean geometry, |

definition | : | (mathematics) geometry based on axioms different from Euclid's (noun.cognition) |

domain member category | : | hyperbolic geometry, |

definition | : | (mathematics) a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane (noun.cognition) |

domain member category | : | elliptic geometry, riemannian geometry, |

definition | : | (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle (noun.cognition) |

domain member category | : | numerical analysis, |

definition | : | (mathematics) the branch of mathematics that studies algorithms for approximating solutions to problems in the infinitesimal calculus (noun.cognition) |

domain member category | : | spherical geometry, |

definition | : | (mathematics) the geometry of figures on the surface of a sphere (noun.cognition) |

domain member category | : | spherical trigonometry, |

definition | : | (mathematics) the trigonometry of spherical triangles (noun.cognition) |

domain member category | : | analytic geometry, analytical geometry, coordinate geometry, |

definition | : | the use of algebra to study geometric properties; operates on symbols defined in a coordinate system (noun.cognition) |

domain member category | : | plane geometry, |

definition | : | the geometry of 2-dimensional figures (noun.cognition) |

domain member category | : | solid geometry, |

definition | : | the geometry of 3-dimensional space (noun.cognition) |

domain member category | : | descriptive geometry, projective geometry, |

definition | : | the geometry of properties that remain invariant under projection (noun.cognition) |

domain member category | : | trig, trigonometry, |

definition | : | the mathematics of triangles and trigonometric functions (noun.cognition) |

domain member category | : | algebra, |

definition | : | the mathematics of generalized arithmetical operations (noun.cognition) |

domain member category | : | quadratics, |

definition | : | a branch of algebra dealing with quadratic equations (noun.cognition) |

domain member category | : | linear algebra, |

definition | : | the part of algebra that deals with the theory of linear equations and linear transformation (noun.cognition) |

domain member category | : | vector algebra, |

definition | : | the part of algebra that deals with the theory of vectors and vector spaces (noun.cognition) |

domain member category | : | matrix algebra, |

definition | : | the part of algebra that deals with the theory of matrices (noun.cognition) |

domain member category | : | calculus, infinitesimal calculus, |

definition | : | the branch of mathematics that is concerned with limits and with the differentiation and integration of functions (noun.cognition) |

domain member category | : | analysis, |

definition | : | a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation (noun.cognition) |

domain member category | : | differential calculus, method of fluxions, |

definition | : | the part of calculus that deals with the variation of a function with respect to changes in the independent variable (or variables) by means of the concepts of derivative and differential (noun.cognition) |

domain member category | : | integral calculus, |

definition | : | the part of calculus that deals with integration and its application in the solution of differential equations and in determining areas or volumes etc. (noun.cognition) |

domain member category | : | calculus of variations, |

definition | : | the calculus of maxima and minima of definite integrals (noun.cognition) |

domain member category | : | set theory, |

definition | : | the branch of pure mathematics that deals with the nature and relations of sets (noun.cognition) |

domain member category | : | subgroup, |

definition | : | (mathematics) a subset (that is not empty) of a mathematical group (noun.cognition) |

domain member category | : | group theory, |

definition | : | the branch of mathematics dealing with groups (noun.cognition) |

domain member category | : | galois theory, |

definition | : | group theory applied to the solution of algebraic equations (noun.cognition) |

domain member category | : | analysis situs, topology, |

definition | : | the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions (noun.cognition) |

domain member category | : | metamathematics, |

definition | : | the logical analysis of mathematical reasoning (noun.cognition) |

domain member category | : | binomial, |

definition | : | (mathematics) a quantity expressed as a sum or difference of two terms; a polynomial with two terms (noun.cognition) |

domain member category | : | proof, |

definition | : | a formal series of statements showing that if one thing is true something else necessarily follows from it (noun.communication) |

domain member category | : | equation, |

definition | : | a mathematical statement that two expressions are equal (noun.communication) |

domain member category | : | expression, formula, |

definition | : | a group of symbols that make a mathematical statement (noun.communication) |

domain member category | : | mathematical statement, |

definition | : | a statement of a mathematical relation (noun.communication) |

domain member category | : | recursive definition, |

definition | : | (mathematics) a definition of a function from which values of the function can be calculated in a finite number of steps (noun.communication) |

domain member category | : | boundary condition, |

definition | : | (mathematics) a condition specified for the solution to a set of differential equations (noun.communication) |

domain member category | : | set, |

definition | : | (mathematics) an abstract collection of numbers or symbols (noun.group) |

domain member category | : | domain, domain of a function, |

definition | : | (mathematics) the set of values of the independent variable for which a function is defined (noun.group) |

domain member category | : | image, range, range of a function, |

definition | : | (mathematics) the set of values of the dependent variable for which a function is defined (noun.group) |

domain member category | : | universal set, |

definition | : | (mathematics) the set that contains all the elements or objects involved in the problem under consideration (noun.group) |

domain member category | : | mathematical space, topological space, |

definition | : | (mathematics) any set of points that satisfy a set of postulates of some kind (noun.group) |

domain member category | : | field, |

definition | : | (mathematics) a set of elements such that addition and multiplication are commutative and associative and multiplication is distributive over addition and there are two elements 0 and 1 (noun.group) |

domain member category | : | matrix, |

definition | : | (mathematics) a rectangular array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules (noun.group) |

domain member category | : | diagonal, |

definition | : | (mathematics) a set of entries in a square matrix running diagonally either from the upper left to lower right entry or running from the upper right to lower left entry (noun.group) |

domain member category | : | arithmetic progression, |

definition | : | (mathematics) a progression in which a constant is added to each term in order to obtain the next term (noun.group) |

domain member category | : | geometric progression, |

definition | : | (mathematics) a progression in which each term is multiplied by a constant in order to obtain the next term (noun.group) |

domain member category | : | harmonic progression, |

definition | : | (mathematics) a progression of terms whose reciprocals form an arithmetic progression (noun.group) |

domain member category | : | mathematician, |

definition | : | a person skilled in mathematics (noun.person) |

domain member category | : | cardinality, |

definition | : | (mathematics) the number of elements in a set or group (considered as a property of that grouping) (noun.quantity) |

domain member category | : | complex number, complex quantity, imaginary, imaginary number, |

definition | : | (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1 (noun.quantity) |

domain member category | : | radical, |

definition | : | (mathematics) a quantity expressed as the root of another quantity (noun.quantity) |

domain member category | : | mathematical relation, |

definition | : | a relation between mathematical expressions (such as equality or inequality) (noun.linkdef) |

domain member category | : | function, map, mapping, mathematical function, single-valued function, |

definition | : | (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function) (noun.linkdef) |

domain member category | : | expansion, |

definition | : | a function expressed as a sum or product of terms (noun.linkdef) |

domain member category | : | metric, metric function, |

definition | : | a function of a topological space that gives, for any two points in the space, a value equal to the distance between them (noun.linkdef) |

domain member category | : | transformation, |

definition | : | (mathematics) a function that changes the position or direction of the axes of a coordinate system (noun.linkdef) |

domain member category | : | reflection, |

definition | : | (mathematics) a transformation in which the direction of one axis is reversed (noun.linkdef) |

domain member category | : | rotation, |

definition | : | (mathematics) a transformation in which the coordinate axes are rotated by a fixed angle about the origin (noun.linkdef) |

domain member category | : | translation, |

definition | : | (mathematics) a transformation in which the origin of the coordinate system is moved to another position but the direction of each axis remains the same (noun.linkdef) |

domain member category | : | affine transformation, |

definition | : | (mathematics) a transformation that is a combination of single transformations such as translation or rotation or reflection on an axis (noun.linkdef) |

domain member category | : | operator, |

definition | : | (mathematics) a symbol or function representing a mathematical operation (noun.linkdef) |

domain member category | : | parity, |

definition | : | (mathematics) a relation between a pair of integers: if both integers are odd or both are even they have the same parity; if one is odd and the other is even they have different parity (noun.linkdef) |

domain member category | : | transitivity, |

definition | : | (logic and mathematics) a relation between three elements such that if it holds between the first and second and it also holds between the second and third it must necessarily hold between the first and third (noun.linkdef) |

domain member category | : | reflexiveness, reflexivity, |

definition | : | (logic and mathematics) a relation such that it holds between an element and itself (noun.linkdef) |

domain member category | : | additive inverse, |

definition | : | (mathematics) one of a pair of numbers whose sum is zero; the additive inverse of -5 is +5 (noun.linkdef) |

domain member category | : | multiplicative inverse, reciprocal, |

definition | : | (mathematics) one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7 (noun.linkdef) |

domain member category | : | geodesic, geodesic line, |

definition | : | (mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere) (noun.shape) |

domain member category | : | parallel, |

definition | : | (mathematics) one of a set of parallel geometric figures (parallel lines or planes) (noun.shape) |

domain member category | : | upper bound, |

definition | : | (mathematics) a number equal to or greater than any other number in a given set (noun.shape) |

domain member category | : | lower bound, |

definition | : | (mathematics) a number equal to or less than any other number in a given set (noun.shape) |

domain member category | : | ray, |

definition | : | (mathematics) a straight line extending from a point (noun.shape) |

domain member category | : | osculation, |

definition | : | (mathematics) a contact of two curves (or two surfaces) at which they have a common tangent (noun.state) |

domain member category | : | develop, |

definition | : | expand in the form of a series (verb.change) |

domain member category | : | iterate, |

definition | : | run or be performed again (verb.change) |

domain member category | : | rationalise, rationalize, |

definition | : | remove irrational quantities from (verb.change) |

domain member category | : | eliminate, |

definition | : | remove (an unknown variable) from two or more equations (verb.change) |

domain member category | : | extract, |

definition | : | calculate the root of a number (verb.cognition) |

domain member category | : | extrapolate, interpolate, |

definition | : | estimate the value of (verb.cognition) |

domain member category | : | differentiate, |

definition | : | calculate a derivative; take the derivative (verb.cognition) |

domain member category | : | integrate, |

definition | : | calculate the integral of; calculate by integration (verb.cognition) |

domain member category | : | prove, |

definition | : | prove formally; demonstrate by a mathematical, formal proof (verb.cognition) |

domain member category | : | truncate, |

definition | : | approximate by ignoring all terms beyond a chosen one (verb.cognition) |

domain member category | : | reduce, |

definition | : | simplify the form of a mathematical equation of expression by substituting one term for another (verb.possession) |

domain member category | : | converge, |

definition | : | approach a limit as the number of terms increases without limit (verb.stative) |

domain member category | : | diverge, |

definition | : | have no limits as a mathematical series (verb.stative) |

domain member category | : | osculate, |

definition | : | have at least three points in common with (verb.stative) |

domain member category | : | idempotent, |

definition | : | unchanged in value following multiplication by itself (adj.all) |

domain member category | : | combinatorial, |

definition | : | relating to the combination and arrangement of elements in sets (adj.all) |

domain member category | : | continuous, |

definition | : | of a function or curve; extending without break or irregularity (adj.all) |

domain member category | : | discontinuous, |

definition | : | of a function or curve; possessing one or more discontinuities (adj.all) |

domain member category | : | commutative, |

definition | : | (of a binary operation) independent of order; as in e.g. (adj.all) |

domain member category | : | direct, |

definition | : | similar in nature or effect or relation to another quantity (adj.all) |

domain member category | : | inverse, |

definition | : | opposite in nature or effect or relation to another quantity (adj.all) |

domain member category | : | dividable, |

definition | : | can be divided usually without leaving a remainder (adj.all) |

domain member category | : | indivisible by, undividable, |

definition | : | cannot be divided without leaving a remainder (adj.all) |

domain member category | : | mathematical, |

definition | : | characterized by the exactness or precision of mathematics (adj.all) |

domain member category | : | round, |

definition | : | (mathematics) expressed to the nearest integer, ten, hundred, or thousand (adj.all) |

domain member category | : | representable, |

definition | : | expressible in symbolic form (adj.all) |

domain member category | : | nonlinear, |

definition | : | designating or involving an equation whose terms are not of the first degree (adj.all) |

domain member category | : | nonmonotonic, |

definition | : | not monotonic (adj.all) |

domain member category | : | open, |

definition | : | (set theory) of an interval that contains neither of its endpoints (adj.all) |

domain member category | : | closed, |

definition | : | (set theory) of an interval that contains both its endpoints (adj.all) |

domain member category | : | nonnegative, |

definition | : | either positive or zero (adj.all) |

domain member category | : | positive, |

definition | : | greater than zero (adj.all) |

domain member category | : | negative, |

definition | : | less than zero (adj.all) |

domain member category | : | disjoint, |

definition | : | having no elements in common (adj.all) |

domain member category | : | noninterchangeable, |

definition | : | such that the terms of an expression cannot be interchanged without changing the meaning (adj.all) |

domain member category | : | invariant, |

definition | : | unaffected by a designated operation or transformation (adj.all) |

domain member category | : | affine, |

definition | : | (mathematics) of or pertaining to the geometry of affine transformations (adj.pert) |

domain member category | : | analytic, |

definition | : | using or subjected to a methodology using algebra and calculus (adj.pert) |

domain member category | : | diagonalizable, |

definition | : | capable of being transformed into a diagonal matrix (adj.pert) |

domain member category | : | scalene, |

definition | : | of a triangle having three sides of different lengths (adj.pert) |

domain member category | : | isometric, |

definition | : | related by an isometry (adj.pert) |

domain member category | : | differential, |

definition | : | involving or containing one or more derivatives (adj.pert) |

domain member category | : | rational, |

definition | : | capable of being expressed as a quotient of integers (adj.pert) |

domain member category | : | irrational, |

definition | : | real but not expressible as the quotient of two integers (adj.pert) |

domain member category | : | prime, |

definition | : | of or relating to or being an integer that cannot be factored into other integers (adj.pert) |

domain member category | : | bivariate, |

definition | : | having two variables (adj.pert) |

derivation | : | mathematician, |

definition | : | a person skilled in mathematics (noun.person) |

derivation | : | mathematical, |

definition | : | characterized by the exactness or precision of mathematics (adj.all) |

derivation | : | mathematical, |

definition | : | of or pertaining to or of the nature of mathematics (adj.pert) |

derivation | : | mathematician, |

definition | : | a person skilled in mathematics (noun.person) |

derivation | : | mathematical, |

definition | : | characterized by the exactness or precision of mathematics (adj.all) |

derivation | : | mathematical, |

definition | : | of or pertaining to or of the nature of mathematics (adj.pert) |

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