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Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values.
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
In 1978, the competition became a nationwide event, and became known as the Australian Mathematics Competition for the Wales awards, with 60,000 students from Australia and New Zealand participating. The competition has spread to countries such as New Zealand , Singapore , Fiji , Tonga , Taiwan , China and Malaysia .
In the present day, the distinction between pure and applied mathematics is more a question of personal research aim of mathematicians than a division of mathematics into broad areas. [ 124 ] [ 125 ] The Mathematics Subject Classification has a section for "general applied mathematics" but does not mention "pure mathematics". [ 14 ]
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.
A well written multiple-choice question avoids obviously wrong or implausible distractors (such as the non-Indian city of Detroit being included in the third example), so that the question makes sense when read with each of the distractors as well as with the correct answer. A more difficult and well-written multiple choice question is as follows:
The deep web is not primarily full of pornography, illegal drug trade websites, and stolen bank details. This information is primarily found in a small portion of the deep web known as the "dark web". Much of the deep web consists of academic libraries, databases, and anything that is not indexed by normal search engines, including most private ...
[7] The interest in the question may suggest some knowledge of the Pythagorean theorem, though the papyrus only shows a straightforward solution to a single second degree equation in one unknown. In modern terms, the simultaneous equations x 2 + y 2 = 100 and x = (3/4) y reduce to the single equation in y : ((3/4) y ) 2 + y 2 = 100 , giving the ...
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