Individual #pure_mathematics  the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness
  >part of:  #mathematics__math__maths__math  a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
  >part:  #arithmetic  the branch of pure mathematics dealing with the theory of numerical calculations
     >part:  #algorism  computation with Arabic figures
  >part:  #geometry  the pure mathematics of points and lines and curves and surfaces
     >part:  #elementary_geometry__parabolic_geometry__parabolicgeometry__Euclidean_geometry  geometry based on Euclid's axioms: e.g., only one line can be drawn through a point parallel to another line
     >part:  #non-Euclidean_geometry  geometry based on axioms different from Euclid's
        >part:  #hyperbolic_geometry  a non-Euclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane
        >part:  #elliptic_geometry__Riemannian_geometry  a non-Euclidean geometry that regards space is like a sphere and a line is a great circle
     >part:  #spherical_geometry__sphericalgeometry  the geometry of figures on the surface of a sphere
     >part:  #analytic_geometry__analytical_geometry__coordinate_geometry  the use of algebra to study geometric properties; operates on symbols defined in a coordinate system
     >part:  #plane_geometry__planegeometry  the geometry of 2-dimensional figures
     >part:  #solid_geometry__solidgeometry  the geometry of 3-dimensional space
     >part:  #projective_geometry__descriptive_geometry__descriptivegeometry  the geometry of properties that remain invariant under projection
  >part:  #trigonometry__trig  the mathematics of triangles and trigonometric functions
     >part:  #spherical_trigonometry__sphericaltrigonometry  the trigonometry of spherical triangles
     >part:  #triangulation.trigonometry  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
  >part:  #algebra  the mathematics of generalized arithmetical operations
     >part:  #quadratics  a branch of algebra dealing with quadratic equations
     >part:  #linear_algebra  the part of algebra that deals with the theory of linear equations and linear transformation
     >part:  #vector_algebra  the part of algebra that deals with the theory of vectors and vector spaces
        >part:  #vector_decomposition__decomposition  the analysis of a vector field
     >part:  #matrix_algebra  the part of algebra that deals with the theory of matrices
  >part:  #infinitesimal_calculus__calculus__the_calculus  the branch of mathematics that is concerned with limits and with the differentiation and integration of functions
     >part:  #analysis.infinitesimal_calculus__analysi  a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation
        >part:  #Fourier_analysis__harmonic_analysis  analysis of a periodic function into a sum of simple sinusoidal components
     >part:  #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
     >part:  #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.
     >part:  #calculus_of_variations  the calculus of maxima and minima of definite integrals
  >part:  #set_theory__settheory  the branch of pure mathematics that deals with the nature and relations of sets
  >part:  #group_theory__grouptheory  the branch of mathematics dealing with groups
     >part:  #Galois_theory  group theory applied to the solution of algebraic equations
  >part:  #topology__analysis_situs  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
  >part:  #metamathematics__metamathematic  the logical analysis of mathematical reasoning

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