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Geometry -- from Wolfram MathWorld Geometry is the study of figures in a space of a given number of dimensions and of a given type The most common types of geometry are plane geometry (dealing with objects like the point, line, circle, triangle, and polygon), solid geometry (dealing with objects like the line, sphere, and polyhedron), and spherical geometry (dealing with
Mathematics -- from Wolfram MathWorld A New Kind of Science Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined Whereas mathematics began merely as a calculational tool for computation and tabulation of quantities, it has blossomed into an extremely rich and diverse set of tools, terminologies, and approaches
Spherical Geometry -- from Wolfram MathWorld The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid geometry In spherical geometry, straight lines are great circles, so any two lines meet in two points
Algebraic Geometry -- from Wolfram MathWorld Algebraic geometry is the study of geometries that come from algebra, in particular, from rings In classical algebraic geometry, the algebra is the ring of polynomials, and the geometry is the set of zeros of polynomials, called an algebraic variety
Hyperbolic Geometry -- from Wolfram MathWorld Hyperbolic geometry is well understood in two dimensions, but not in three dimensions Geometric models of hyperbolic geometry include the Klein-Beltrami model, which consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines
Algebra -- from Wolfram MathWorld Examples of algebras include the algebra of real numbers, vectors and matrices, tensors, complex numbers, and quaternions (Note that linear algebra, which is the study of linear sets of equations and their transformation properties, is not an algebra in the formal sense of the word )
Topology -- from Wolfram MathWorld Topology Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects Tearing, however, is not allowed A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid
Polygon -- from Wolfram MathWorld A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), namely a cyclically ordered set of points in a plane, with no three successive points collinear, together with the line segments joining consecutive pairs of the points
Calculus -- from Wolfram MathWorld References Anton, H Calculus: A New Horizon, 6th ed New York: Wiley, 1999 Apostol, T M Calculus, 2nd ed , Vol 1: One-Variable Calculus, with an Introduction to Linear Algebra