Definitions of pure mathematics
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the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness
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types:
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arithmetic
the branch of pure mathematics dealing with the theory of numerical calculations
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geometry
the pure mathematics of points and lines and curves and surfaces
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numerical analysis
(mathematics) the branch of mathematics that studies algorithms for approximating solutions to problems in the infinitesimal calculus
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trig, trigonometry
the mathematics of triangles and trigonometric functions
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algebra
the mathematics of generalized arithmetical operations
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calculus, infinitesimal calculus
the branch of mathematics that is concerned with limits and with the differentiation and integration of functions
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set theory
the branch of pure mathematics that deals with the nature and relations of sets
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group theory
the branch of mathematics dealing with groups
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analysis situs, topology
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
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metamathematics
the logical analysis of mathematical reasoning
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algorism
computation with Arabic figures
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affine geometry
the geometry of affine transformations
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Euclidean geometry, elementary geometry, parabolic geometry
(mathematics) geometry based on Euclid's axioms
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fractal geometry
(mathematics) the geometry of fractals
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non-Euclidean geometry
(mathematics) geometry based on axioms different from Euclid's
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spherical geometry
(mathematics) the geometry of figures on the surface of a sphere
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spherical trigonometry
(mathematics) the trigonometry of spherical triangles
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triangulation
a trigonometric method of determining the position of a fixed point from the angles to it from two fixed points a known distance apart; useful in navigation
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analytic geometry, analytical geometry, coordinate geometry
the use of algebra to study geometric properties; operates on symbols defined in a coordinate system
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plane geometry
the geometry of 2-dimensional figures
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solid geometry
the geometry of 3-dimensional spaces
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descriptive geometry, projective geometry
the geometry of properties that remain invariant under projection
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quadratics
a branch of algebra dealing with quadratic equations
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linear algebra
the part of algebra that deals with the theory of linear equations and linear transformation
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vector algebra
the part of algebra that deals with the theory of vectors and vector spaces
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matrix algebra
the part of algebra that deals with the theory of matrices
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analysis
a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation
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differential calculus, method of fluxions
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
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integral calculus
the part of calculus that deals with integration and its application in the solution of differential equations and in determining areas or volumes etc.
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calculus of variations
the calculus of maxima and minima of definite integrals
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Galois theory
group theory applied to the solution of algebraic equations
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type of:
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math, mathematics, maths
a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
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