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He was a member of the Russian Academy of Sciences from 1921. [4] Uspensky joined the faculty of Stanford University in 1929-30 and 1930-31 as acting professor of mathematics. He was professor of mathematics at Stanford from 1931 until his death. [4] Uspensky was the one who kept alive Vincent's theorem of 1834 and 1836, carrying the torch (so ...
Mathematics. Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [1]
The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.
Lifting-the-exponent lemma. In elementary number theory, the lifting-the-exponent lemma (LTE lemma) provides several formulas for computing the p-adic valuation of special forms of integers. The lemma is named as such because it describes the steps necessary to "lift" the exponent of in such expressions. It is related to Hensel's lemma.
Every textbook on elementary number theory (and quite a few on algebraic number theory) has a proof of quadratic reciprocity. Two are especially noteworthy: Lemmermeyer (2000) has many proofs (some in exercises) of both quadratic and higher-power reciprocity laws and a discussion of their history. Its immense bibliography includes literature ...
Elementary number theory includes topics of number theory commonly taught at the primary and secondary school level, or in college courses on introductory number theory. This category corresponds roughly to MSC 11Axx Elementary number theory; see 11Axx at MathSciNet and 11Axx at zbMATH .
The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory. With the exception of Autolycus' On the Moving Sphere, the Elements is one of the oldest extant Greek mathematical treatises, [9] and it is the oldest extant axiomatic deductive treatment of mathematics.
Elementary number. An elementary number is one formalization of the concept of a closed-form number. The elementary numbers form an algebraically closed field containing the roots of arbitrary expressions using field operations, exponentiation, and logarithms. The set of the elementary numbers is subdivided into the explicit elementary numbers ...