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  2. Mathematical problem - Wikipedia

    en.wikipedia.org/wiki/Mathematical_problem

    A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems. It can also be a problem referring to the nature of ...

  3. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    Closer to the Collatz problem is the following universally quantified problem: Given g, does the sequence of iterates g k (n) reach 1, for all n > 0? Modifying the condition in this way can make a problem either harder or easier to solve (intuitively, it is harder to justify a positive answer but might be easier to justify a negative one).

  4. Problem solving - Wikipedia

    en.wikipedia.org/wiki/Problem_solving

    Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue ...

  5. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    Equation solving. The quadratic formula, the symbolic solution of the quadratic equation ax2 + bx + c = 0. An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values ( numbers, functions, sets, etc.) that fulfill the condition stated ...

  6. How to Solve It - Wikipedia

    en.wikipedia.org/wiki/How_to_Solve_It

    Genre. Mathematics, problem solving. Publication date. 1945. ISBN. 9780691164076. How to Solve It (1945) is a small volume by mathematician George Pólya, describing methods of problem solving. [1] This book has remained in print continually since 1945.

  7. Computational problem - Wikipedia

    en.wikipedia.org/wiki/Computational_problem

    Computational problem. In theoretical computer science, a computational problem is a problem that may be solved by an algorithm. For example, the problem of factoring. "Given a positive integer n, find a nontrivial prime factor of n ." is a computational problem. A computational problem can be viewed as a set of instances or cases together with ...

  8. Extraneous and missing solutions - Wikipedia

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

    In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process. Both situations frequently result from performing operations that are not invertible for some or all values ...

  9. Mathematical optimization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_optimization

    Feasibility problem. The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as the special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal.

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