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  2. Arithmetic geometry - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_geometry

    In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. [1] Arithmetic geometry is centered around Diophantine geometry , the study of rational points of algebraic varieties .

  3. Algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Algebraic_geometry

    Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.

  4. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    [72] [73] Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra, and geometry for taxation and other financial calculations, for building and construction, and for astronomy. [74] The oldest mathematical texts from Mesopotamia and Egypt are from 2000 to ...

  5. Algebraic geometry and analytic geometry - Wikipedia

    en.wikipedia.org/wiki/Algebraic_geometry_and...

    In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The deep relation between these ...

  6. Algebraic variety - Wikipedia

    en.wikipedia.org/wiki/Algebraic_variety

    The twisted cubic is a projective algebraic variety.. Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics.Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers.

  7. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.

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