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  3. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...

  4. Principles and Standards for School Mathematics - Wikipedia

    en.wikipedia.org/wiki/Principles_and_Standards...

    The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]

  5. Spectrum (topology) - Wikipedia

    en.wikipedia.org/wiki/Spectrum_(topology)

    In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem .

  6. Spline (mathematics) - Wikipedia

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

    In the mathematical study of polynomial splines the question of what happens when two knots, say t i and t i+1, are taken to approach one another and become coincident has an easy answer. The polynomial piece P i ( t ) disappears, and the pieces P i −1 ( t ) and P i +1 ( t ) join with the sum of the smoothness losses for t i and t i +1 .

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  8. Spectrum of a matrix - Wikipedia

    en.wikipedia.org/wiki/Spectrum_of_a_matrix

    In mathematics, the spectrum of a matrix is the set of its eigenvalues. [ 1 ] [ 2 ] [ 3 ] More generally, if T : V → V {\displaystyle T\colon V\to V} is a linear operator on any finite-dimensional vector space , its spectrum is the set of scalars λ {\displaystyle \lambda } such that T − λ I {\displaystyle T-\lambda I} is not invertible .

  9. Essential spectrum - Wikipedia

    en.wikipedia.org/wiki/Essential_spectrum

    The essential spectrum () is a subset of the spectrum () and its complement is called the discrete spectrum, so = ().If is self-adjoint, then, by definition, a number is in the discrete spectrum of if it is an isolated eigenvalue of finite multiplicity, meaning that the dimension of the space