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2. Word problem for groups - Wikipedia

   en.wikipedia.org/wiki/Word_problem_for_groups

   Then the word problem in is solvable: given two words , in the generators of , write them as words in and compare them using the solution to the word problem in . It is easy to think that this demonstrates a uniform solution of the word problem for the class K {\displaystyle K} (say) of finitely generated groups that can be embedded in G ...

3. 10 Hard Math Problems That Even the Smartest People in the ...

   www.aol.com/10-hard-math-problems-even-150000090...

   When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...

4. Word problem (mathematics education) - Wikipedia

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

   For instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. 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.

5. Multiple representations (mathematics education) - Wikipedia

   en.wikipedia.org/wiki/Multiple_representations...

   The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.

6. Free group - Wikipedia

   en.wikipedia.org/wiki/Free_group

   In mathematics, the free group F S over a given set S consists of all words that can be built from members of S, considering two words to be different unless their equality follows from the group axioms (e.g. st = suu −1 t but s ≠ t −1 for s,t,u ∈ S). The members of S are called generators of F S, and the number of generators is the ...

7. Word (group theory) - Wikipedia

   en.wikipedia.org/wiki/Word_(group_theory)

   For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2] Words play an important role in the theory of free groups and presentations, and are central objects of study in ...

8. Word problem (mathematics) - Wikipedia

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

   The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]

9. Glossary of mathematical jargon - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_mathematical...

   The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes. There are two canonical proofs that are always used to show non-mathematicians what a mathematical proof is like: