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Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
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.
Such questions are usually more difficult to solve than regular mathematical exercises like "5 − 3", even if one knows the mathematics required to solve the problem. Known as word problems , they are used in mathematics education to teach students to connect real-world situations to the abstract language of mathematics.
In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
Pólya lays a big emphasis on the teachers' behavior. A teacher should support students with devising their own plan with a question method that goes from the most general questions to more particular questions, with the goal that the last step to having a plan is made by the student.
On the relation between mathematics and the ordered patterns of Op art: 1965 Aug: Thoughts on the task of communication with intelligent organisms on other worlds: 1965 Sep: The superellipse: a curve that lies between the ellipse and the rectangle: 1965 Oct: Pentominoes and polyominoes: five games and a sampling of problems 1965 Nov
In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational differentiation, [6] [7] is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes ...
Encyclopedia of Mathematics. EMS Press. 2001 [1994]. "Original text of Hilbert's talk, in German". Archived from the original on 2012-02-05 "David Hilbert's "Mathematical Problems": A lecture delivered before the International Congress of Mathematicians at Paris in 1900" (PDF). Mathematical Problems public domain audiobook at LibriVox