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In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. [1]
Bernoulli number. Agoh–Giuga conjecture; Von Staudt–Clausen theorem; Dirichlet series; Euler product; Prime number theorem. Prime-counting function. Meissel–Lehmer algorithm; Offset logarithmic integral; Legendre's constant; Skewes' number; Bertrand's postulate. Proof of Bertrand's postulate; Proof that the sum of the reciprocals of the ...
The NTF funds the Selfridge prize awarded at each Algorithmic Number Theory Symposium (ANTS) [2] [3] and is a regular supporter of several conferences and organizations in number theory, including the Canadian Number Theory Association (CNTA), [4] [5] Women in Numbers (WIN), and the West Coast Number Theory (WCNT) conference. [1]
Algorithmic Number Theory Symposium (ANTS) is a biennial academic conference, first held in Cornell in 1994, constituting an international forum for the presentation of new research in computational number theory. They are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic ...
James Burton Ax (10 January 1937 – 11 June 2006) [1] was an American mathematician who made groundbreaking contributions in algebra and number theory using model theory.He shared, with Simon B. Kochen, the seventh Frank Nelson Cole Prize in Number Theory, which was awarded for a series of three joint papers [2] [3] [4] on Diophantine problems.
Algorithmic efficiency, the computational resources used by an algorithm; Algorithmic information theory, study of relationships between computation and information; Algorithmic mechanism design, the design of economic systems from an algorithmic point of view; Algorithmic number theory, algorithms for number-theoretic computation
Gregory John Chaitin (/ ˈ tʃ aɪ t ɪ n / CHY-tin; born 25 June 1947) is an Argentine-American mathematician and computer scientist.Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a computer-theoretic result equivalent to Gödel's incompleteness theorem. [2]
William Judson LeVeque (August 9, 1923 – December 1, 2007) was an American mathematician and administrator who worked primarily in number theory.He was executive director of the American Mathematical Society during the 1970s and 1980s when that organization was growing rapidly and greatly increasing its use of computers in academic publishing.