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  2. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    The section As a parity sequence above gives a way to speed up simulation of the sequence. To jump ahead k steps on each iteration (using the f function from that section), break up the current number into two parts, b (the k least significant bits, interpreted as an integer), and a (the rest of the bits as an integer

  3. Equating coefficients - Wikipedia

    en.wikipedia.org/wiki/Equating_coefficients

    A similar problem, involving equating like terms rather than coefficients of like terms, arises if we wish to de-nest the nested radicals + to obtain an equivalent expression not involving a square root of an expression itself involving a square root, we can postulate the existence of rational parameters d, e such that

  4. Graph of a function - Wikipedia

    en.wikipedia.org/wiki/Graph_of_a_function

    Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.

  5. Big M method - Wikipedia

    en.wikipedia.org/wiki/Big_M_method

    If the problem is of minimization, transform to maximization by multiplying the objective by −1. For any greater-than constraints, introduce surplus s i and artificial variables a i (as shown below). Choose a large positive Value M and introduce a term in the objective of the form −M multiplying the artificial variables.

  6. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.

  7. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    Multiplying a row by a non-zero scalar. Adding a scalar multiple of one row to another. If the matrix is associated to a system of linear equations, then these operations do not change the solution set. Therefore, if one's goal is to solve a system of linear equations, then using these row operations could make the problem easier.

  8. Polynomial long division - Wikipedia

    en.wikipedia.org/wiki/Polynomial_long_division

    Divide the highest term of the remainder by the highest term of the divisor (3x ÷ x = 3). Place the result (+3) below the bar. 3x has been divided leaving no remainder, and can therefore be marked as used. The result 3 is then multiplied by the second term in the divisor −3 = −9. Determine the partial remainder by subtracting −4 − (− ...

  9. Extraneous and missing solutions - Wikipedia

    en.wikipedia.org/wiki/Extraneous_and_missing...

    One of the basic principles of algebra is that one can multiply both sides of an equation by the same expression without changing the equation's solutions. However, strictly speaking, this is not true, in that multiplication by certain expressions may introduce new solutions that were not present before. For example, consider the following ...