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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.
The result is that the word problem, here for the cyclic group of order three, is solvable. This is not, however, the typical case. For the example, we have a canonical form available that reduces any string to one of length at most three, by decreasing the length monotonically. In general, it is not true that one can get a canonical form for ...
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.
A function problem consists of a partial function f; the informal "problem" is to compute the values of f on the inputs for which it is defined. Every function problem can be turned into a decision problem; the decision problem is just the graph of the associated function. (The graph of a function f is the set of pairs (x,y) such that f(x) = y ...
The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning ' something learned, knowledge, mathematics ', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning ' mathematical science '. It entered the English language during the Late Middle English period through French and ...
Other formulas, such as the use of the equation of a sine curve to model the movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations. Expressions are distinct from formulas in the sense that they don't usually contain relations like equality (=) or inequality (<).
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields.