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Algebra and Number Theory
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Algebra and Number Theory
Roughly speaking, number theory is the study of the integers. Carl Friedrich Gauss is said to have claimed: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." Number theorists are interested in topics like the distribution of prime numbers, the solutions to systems of polynomial equations with integer coefficients, the structure of symmetry groups of the roots of a polynomial, and the very deep generalizations of these topics. Many problems in number theory are simple to state but have surprising solutions that draw broadly from all areas of mathematics, and conjectures in number theory have stimulated major advances in other fields. Number theory is both beautiful in its abstraction and useful in practice: the foundation of modern cryptographic systems rely crucially on the difficulty of certain number theoretic problems.
Members
 Carl Pomerance
 Number theory
 Tom Shemanske
 Number theory
 John Voight
 Number theory; Algebraic geometry; Algebraic computing