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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.
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]
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 ...
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
[2] [6] The "discount rate" is the rate at which the "discount" must grow as the delay in payment is extended. [7] This fact is directly tied into the time value of money and its calculations. [1] The present value of $1,000, 100 years into the future. Curves representing constant discount rates of 2%, 3%, 5%, and 7%
For the hyperbolic model using g(D), the discount for a week from now is () =, which is the same as for f in the exponential model, while the incremental discount for an additional week after a delay of D weeks is not the same: (+) = + From this one can see that the two models of discounting are the same "now"; this is the reason for the choice ...
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