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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]
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
They are used, to some degree, in most subjects, and have widespread use in the math curriculum where there are two major types. The first type of math worksheet contains a collection of similar math problems or exercises. These are intended to help a student become proficient in a particular mathematical skill that was taught to them in class.
[1] [2] [3] Workbooks are usually filled with practice problems, with empty space so that the answers can be written directly in the book. More recently, electronic workbooks have permitted interactive and customized learning. Such workbooks may be used on computers, laptops, PDAs, and may be web-based.
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 ...
The word later came to be used as a noun, first as an abstract noun meaning 'the state or condition of being puzzled', and later developing the meaning of 'a perplexing problem'. The OED ' s earliest clear citation in the sense of 'a toy that tests the player's ingenuity' is from Sir Walter Scott 's 1814 novel Waverley , referring to a toy ...
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