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  2. Singapore Mathematical Olympiad - Wikipedia

    en.wikipedia.org/wiki/Singapore_Mathematical...

    The paper in Round 1 comprises 5 multiple-choice questions, each with five options, and 30 short answer questions until 2017. From 2018 onwards, The paper has 20 short answer questions instead. The Junior section is geared towards Lower Secondary students, and topics tested include number theory, combinatorics, geometry, algebra, probability ...

  3. Penilaian Menengah Rendah - Wikipedia

    en.wikipedia.org/wiki/Penilaian_Menengah_Rendah

    Penilaian Menengah Rendah (commonly abbreviated as PMR; Malay for Lower Secondary Assessment) was a Malaysian public examination targeting Malaysian adolescents and young adults between the ages of 13 and 30 years taken by all Form Three high school and college students in both government and private schools throughout the country from independence in 1957 to 2013.

  4. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size.

  5. Mathematics of Sudoku - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_Sudoku

    ⌈ x/3 ⌉ = ⌈ x′/3 ⌉ and ⌈ y/3 ⌉ = ⌈ y′/3 ⌉ (same 3×3 cell) The puzzle is then completed by assigning an integer between 1 and 9 to each vertex, in such a way that vertices that are joined by an edge do not have the same integer assigned to them. A Sudoku solution grid is also a Latin square. [9]

  6. Regula falsi - Wikipedia

    en.wikipedia.org/wiki/Regula_falsi

    In addition to sign changes, it is also possible for the method to converge to a point where the limit of the function is zero, even if the function is undefined (or has another value) at that point (for example at x = 0 for the function given by f (x) = abs(x) − x 2 when x ≠ 0 and by f (0) = 5, starting with the interval [-0.5, 3.0]).

  7. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For example, for 2 5 a + 1 there are 3 increases as 1 iterates to 2, 1, 2, 1, and finally to 2 so the result is 3 3 a + 2; for 2 2 a + 1 there is only 1 increase as 1 rises to 2 and falls to 1 so the result is 3a + 1.

  8. Regularization (mathematics) - Wikipedia

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

    In mathematics, statistics, finance, [1] and computer science, particularly in machine learning and inverse problems, regularization is a process that converts the answer of a problem to a simpler one. It is often used in solving ill-posed problems or to prevent overfitting. [2]

  9. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    [2] [3] Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics , most notably in Euclid 's Elements . [ 4 ] Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions ), until the 16th and 17th centuries, when ...

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