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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]
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers , finite fields , and function fields .
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. [1] It is often said to have begun with Peter Gustav Lejeune Dirichlet 's 1837 introduction of Dirichlet L -functions to give the first proof of Dirichlet's theorem on arithmetic progressions.
An Introduction to the Theory of Numbers is a classic textbook in the field of number theory, by G. H. Hardy and E. M. Wright . The book grew out of a series of lectures by Hardy and Wright and was first published in 1938. The third edition added an elementary proof of the prime number theorem, and the sixth edition added a chapter on elliptic ...
Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic methods. Based in part on a course taught at Princeton University in 1961–62, it appeared as Volume 144 in Springer's Grundlehren der mathematischen Wissenschaften series. [2]
Download as PDF; Printable version; Appearance. move to sidebar hide. This is a list of number theory topics. See also: List of recreational number theory topics ...
Multiplicative number theory. Multiplicative number theory is a subfield of analytic number theory that deals with prime numbers and with factorization and divisors. The focus is usually on developing approximate formulas for counting these objects in various contexts. The prime number theorem is a key result in this subject.
Bibliography. Number Theory, An Approach Through History from Hammurapi to Legendre by André Weil, Birkhäuser (December 2006) ISBN 978-0-8176-4565-6. Categories: Mathematics books. 2006 non-fiction books. Mathematics literature stubs.