Computational Number Theory

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In mathematics, computational number theory, also known as algorithmic number theory, is the study of algorithms for performing number theoretic computations. The best known problem in the field is integer factorization.

References

Victor Shoup, A Computational Introduction to Number Theory and Algebra. Cambridge, 2005, ISBN 0-521-85-154-8

Henri Cohen, A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics 138, Springer-Verlag, 1993.

Eric Bach and Jeffrey Shallit, Algorithmic Number Theory, volume 1: Efficient Algorithms. MIT Press, 1996, ISBN 0-262-02405-5

Richard Crandall and Carl Pomerance, Prime Numbers: A Computational Perspective, Springer-Verlag, 2001, ISBN 0-387-94777-9

Hans Riesel, Prime Numbers and Computer Methods for Factorization, second edition, Birkhäuser, 1994, ISBN 0-8176-3743-5, ISBN 3-7643-3743-5

Major topics in Number theory

Algebraic number theory • Analytic number theory • Geometric number theory • Computational number theory • Transcendental number theory

Numbers • Natural numbers • Prime numbers • Rational numbers • Irrational numbers • Algebraic numbers • Transcendental numbers • Arithmetic • Modular arithmetic • Arithmetic functions

Quadratic forms • L-functions • Diophantine equations • Diophantine approximation • Continued fractions

List of recreational number theory topics • List of number theory topics

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