types:
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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

algorism
computation with Arabic figures

affine geometry
the geometry of affine transformations

Euclidean geometry, elementary geometry, parabolic geometry
(mathematics) geometry based on Euclid's axioms

fractal geometry
(mathematics) the geometry of fractals

nonEuclidean geometry
(mathematics) geometry based on axioms different from Euclid's

spherical geometry
(mathematics) the geometry of figures on the surface of a sphere

spherical trigonometry
(mathematics) the trigonometry of spherical triangles

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

analytic geometry, analytical geometry, coordinate geometry
the use of algebra to study geometric properties; operates on symbols defined in a coordinate system

plane geometry
the geometry of 2dimensional figures

solid geometry
the geometry of 3dimensional spaces

descriptive geometry, projective geometry
the geometry of properties that remain invariant under projection

quadratics
a branch of algebra dealing with quadratic equations

linear algebra
the part of algebra that deals with the theory of linear equations and linear transformation

vector algebra
the part of algebra that deals with the theory of vectors and vector spaces

matrix algebra
the part of algebra that deals with the theory of matrices

analysis
a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation

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

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.

calculus of variations
the calculus of maxima and minima of definite integrals

Galois theory
group theory applied to the solution of algebraic equations