Algorithms in Algebra and Number Theory

MAT482, Fall 2021

Course Info

Instructor: Swastik Kopparty (
Class Time and Place: Mondays 1pm-2pm, Thursdays 2pm-4pm, Northrop Frye Hall 004 (and Zoom)
Office Hours: Wednesdays 11am-12noon (on Zoom)

Please email me if you are not enrolled in the course and would like to sit in. Please email me if you are trying to enroll in the course and would like to be added to the course quercus site in the meantime.

Prerequisites: a solid background in linear algebra, a tiny bit of abstract algebra, mathematical maturity
There is no required book.
References: Lovasz (An Algorithmic Theory of Numbers, Graphs and Convexity), various recent papers available online

This course will study algorithms for dealing with basic objects of algebra and number theory, such as integers, polynomials, rational numbers, matrices, etc. Topics will include: GCDs, continued fractions, lattices, Fast Fourier Transforms, primality testing, integer and polynomial factorization, fast matrix multiplication, and applications to combinatorial algorithms and cryptography.

Syllabus and course policies