Algorithms for multiplication, division, greatest common divisors and factorization over the integers, finite fields and polynomial rings. Basic tools include modular arithmetic, discrete Fourier transform, Chinese remainder theorem, Newton iteration, and Hensel techniques. Some properties of finite fields and applications to cryptography. Prerequisite(s): MATH 2108 or MATH 3101 or MATH 2100, or permission of the School.Lectures three hours a week, tutorial/laboratory one hour a week.

MATH 3819 [0.5 credit] Modern Computer Algebra

Algorithms for multiplication, division, greatest common divisors and factorization over the integers, finite fields and polynomial rings. Basic tools include modular arithmetic, discrete Fourier transform, Chinese remainder theorem, Newton iteration, and Hensel techniques. Some properties of finite fields and applications to cryptography. Prerequisite(s): MATH 2108 or MATH 3101 or MATH 2100, or permission of the School.Lectures three hours a week, tutorial/laboratory one hour a week.





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