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How to Solve It suggests the following steps when solving a mathematical problem: . First, you have to understand the problem. [2]After understanding, make a plan. [3]Carry out the plan.
Diophantine problems have fewer equations than unknowns and involve finding integers that solve simultaneously all equations. As such systems of equations define algebraic curves , algebraic surfaces , or, more generally, algebraic sets , their study is a part of algebraic geometry that is called Diophantine geometry .
Social problem-solving, in its most basic form, is defined as problem solving as it occurs in the natural environment. [1] More specifically it refers to the cognitive-behavioral process in which one works to find adaptive ways of coping with everyday situations that are considered problematic.
Post proved the word problem (for semigroups) to be undecidable in general, essentially by reducing the halting problem [7] for Turing machines to an instance of the word problem. Concretely, Post devised an encoding as a finite string of the state of a Turing machine plus tape, such that the actions of this machine can be carried out by a ...
The General Problem Solver (GPS) is a particular computer program created in 1957 by Herbert Simon, J. C. Shaw, and Allen Newell intended to work as a universal problem solver, that theoretically can be used to solve every possible problem that can be formalized in a symbolic system, given the right input configuration.
In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors , direct methods would deliver an exact solution (for example, solving a linear system of equations A x = b {\displaystyle A\mathbf {x} =\mathbf {b} } by Gaussian elimination ).
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