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  2. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  3. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    On the contrary, many important mathematical results (theorems) are solutions of problems that other mathematicians failed to solve, and the invention of a way for solving them may be a fundamental way of the solving process.

  4. Floating-point arithmetic - Wikipedia

    en.wikipedia.org/wiki/Floating-point_arithmetic

    A common problem in "fast" math is that subexpressions may not be optimized identically from place to place, leading to unexpected differences. One interpretation of the issue is that "fast" math as implemented currently has a poorly defined semantics. One attempt at formalizing "fast" math optimizations is seen in Icing, a verified compiler. [71]

  5. Tower of Hanoi - Wikipedia

    en.wikipedia.org/wiki/Tower_of_Hanoi

    Although the three-peg version has a simple recursive solution long been known, the optimal solution for the Tower of Hanoi problem with four pegs (called Reve's puzzle) was not verified until 2014, by Bousch. [20] However, in case of four or more pegs, the Frame–Stewart algorithm is known without proof of optimality since 1941. [21]

  6. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.

  7. Ordinary differential equation - Wikipedia

    en.wikipedia.org/wiki/Ordinary_differential_equation

    A particular solution is derived from the general solution by setting the constants to particular values, often chosen to fulfill set 'initial conditions or boundary conditions'. [22] A singular solution is a solution that cannot be obtained by assigning definite values to the arbitrary constants in the general solution.

  8. History of mathematics - Wikipedia

    en.wikipedia.org/wiki/History_of_mathematics

    For instance, although Vietnamese mathematical treatises were written in either Chinese or the native Vietnamese Chữ Nôm script, all of them followed the Chinese format of presenting a collection of problems with algorithms for solving them, followed by numerical answers. [123] Mathematics in Vietnam and Korea were mostly associated with the ...

  9. Graduate Record Examinations - Wikipedia

    en.wikipedia.org/wiki/Graduate_Record_Examinations

    Each quantitative section consists of about 8 quantitative comparisons, 9 problem solving items, and 3 data interpretation questions. The changes in 2011 include the addition of numeric entry items requiring the examinee to fill in the blank and multiple-choice items requiring the examinee to select multiple correct responses.

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