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2. Word problem (mathematics education) - Wikipedia

   en.wikipedia.org/wiki/Word_problem_(mathematics...

   In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem. This alludes to how the cognitive skills lead to the development of the mathematical concepts. Some of the related mathematical skills necessary for solving word problems are mathematical ...

3. List of undecidable problems - Wikipedia

   en.wikipedia.org/wiki/List_of_undecidable_problems

   The halting problem for a register machine: a finite-state automaton with no inputs and two counters that can be incremented, decremented, and tested for zero. Universality of a nondeterministic pushdown automaton: determining whether all words are accepted. The problem whether a tag system halts.

4. Word problem (mathematics) - Wikipedia

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

   In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.

5. Word equation - Wikipedia

   en.wikipedia.org/wiki/Word_equation

   One stark difference is that Diophantine equations have an undecidable solubility problem, [2] whereas the analogous problem for word equations is decidable. [ 3 ] A classical example of a word equation is the commutation equation x w = ⋅ w x {\displaystyle xw{\overset {\cdot }{=}}wx} , in which x {\displaystyle x} is an unknown and w ...

6. 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.

7. Exercise (mathematics) - Wikipedia

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

   In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions. Usually instructors prepare students with worked examples: the exercise is stated, then a model answer is provided. Often several worked ...

8. Hilbert's problems - Wikipedia

   en.wikipedia.org/wiki/Hilbert's_problems

   As with the Hilbert problems, one of the prize problems (the Poincaré conjecture) was solved relatively soon after the problems were announced. The Riemann hypothesis is noteworthy for its appearance on the list of Hilbert problems, Smale's list, the list of Millennium Prize Problems, and even the Weil conjectures, in its geometric guise.

9. List of mathematical functions - Wikipedia

   en.wikipedia.org/wiki/List_of_mathematical_functions

   Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function : Number of primes less than or equal to a given number. Partition function : Order-independent count of ways to write a given positive integer as a sum of positive integers.