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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 ...
There is no general consensus about the definition of mathematics or its epistemological status—that is, its place inside knowledge. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. There is not even consensus on whether mathematics is an art or a science.
German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
Schaum's Outlines (/ ʃ ɔː m /) is a series of supplementary texts for American high school, AP, and college-level courses, currently published by McGraw-Hill Education Professional, a subsidiary of McGraw-Hill Education.
The definition and scope of schools self-classified as "free schools" and their associated movement were never clearly delineated, and as such, there was a wide variation between schools. [ 25 ] As an anarchist Leo Tolstoy emphasized the freedom and empowerment of the lower classes through education and the experience of self-organization and ...
Different levels of mathematics are taught at different ages and in somewhat different sequences in different countries. Sometimes a class may be taught at an earlier age than typical as a special or honors class. Elementary mathematics in most countries is taught similarly, though there are differences.
The democratization of knowledge is the acquisition and spread of knowledge amongst a wider part of the population, not just privileged elites such as clergy and academics.
The preceding kinds of definitions, which had prevailed since Aristotle's time, [4] were abandoned in the 19th century as new branches of mathematics were developed, which bore no obvious relation to measurement or the physical world, such as group theory, projective geometry, [3] and non-Euclidean geometry.