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  2. Topology - Wikipedia

    en.wikipedia.org/wiki/Topology

    A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...

  3. Characteristic (algebra) - Wikipedia

    en.wikipedia.org/wiki/Characteristic_(algebra)

    For example, if p is prime and q(X) is an irreducible polynomial with coefficients in the field with p elements, then the quotient ring [] / (()) is a field of characteristic p. Another example: The field C {\displaystyle \mathbb {C} } of complex numbers contains Z {\displaystyle \mathbb {Z} } , so the characteristic of C {\displaystyle \mathbb ...

  4. Elliptic curve - Wikipedia

    en.wikipedia.org/wiki/Elliptic_curve

    If the characteristic is 2 or 3, then more terms need to be kept: in characteristic 3, the most general equation is of the form = + + + for arbitrary constants b 2, b 4, b 6 such that the polynomial on the right-hand side has distinct roots (the notation is chosen for historical reasons). In characteristic 2, even this much is not possible, and ...

  5. Characterization (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Characterization_(mathematics)

    A reference on mathematical terminology notes that characteristic originates from the Greek term kharax, "a pointed stake": From Greek kharax came kharakhter, an instrument used to mark or engrave an object. Once an object was marked, it became distinctive, so the character of something came to mean its distinctive nature.

  6. 10 Hard Math Problems That Even the Smartest People in the ...

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    When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...

  7. Method of characteristics - Wikipedia

    en.wikipedia.org/wiki/Method_of_characteristics

    Characteristics may fail to cover part of the domain of the PDE. This is called a rarefaction, and indicates the solution typically exists only in a weak, i.e. integral equation, sense. The direction of the characteristic lines indicates the flow of values through the solution, as the example above demonstrates.

  8. Characteristic equation (calculus) - Wikipedia

    en.wikipedia.org/wiki/Characteristic_equation...

    In mathematics, the characteristic equation (or auxiliary equation [1]) is an algebraic equation of degree n upon which depends the solution of a given n th-order differential equation [2] or difference equation. [3] [4] The characteristic equation can only be formed when the differential equation is linear and homogeneous, and has constant ...

  9. A College Student Just Solved a Notoriously Impossible Math ...

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