 Types:
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pure mathematics
the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness

applied math, applied mathematics
the branches of mathematics that are involved in the study of the physical or biological or sociological world

arithmetic
the branch of pure mathematics dealing with the theory of numerical calculations

geometry
the pure mathematics of points and lines and curves and surfaces

numerical analysis
(mathematics) the branch of mathematics that studies algorithms for approximating solutions to problems in the infinitesimal calculus

trig, trigonometry
the mathematics of triangles and trigonometric functions

algebra
the mathematics of generalized arithmetical operations

calculus, infinitesimal calculus
the branch of mathematics that is concerned with limits and with the differentiation and integration of functions

set theory
the branch of pure mathematics that deals with the nature and relations of sets

group theory
the branch of mathematics dealing with groups

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 onetoone correspondence that is continuous in both directions

metamathematics
the logical analysis of mathematical reasoning

linear programming
a mathematical technique used in economics; finds the maximum or minimum of linear functions in many variables subject to constraints

statistics
a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters

probability theory, theory of probability
the branch of applied mathematics that deals with probabilities