Before each lecture, I will mention (well in advance) what you need to be familiar with to follow the lecture. I will also post resources which will help you gain familiarity. Not only that, I am most happy to engage with you outside class to discuss those concepts and help you. During the actual class, I might give brief introductions to those concepts, but can make no promise about it. It would be best if you are prepared that I will assume familiarity with those concepts.
Date | Prerequisites | Topics | Notes | Post lecture remarks |
---|---|---|---|---|
Week 1 (Mar 19) | basic algebra, dealing with variables, solving a small system of linear equations | algorithms, solving system of linear equations using Gaussian elimination, determinant of a matrix, computing the determinant, permanent of a matrix, complexity of computing the permanent | notes | |
Week 2 (Mar 26) | general mathematical maturity | Grobner Basis: definition of ideal, computation of S-polynomials, Buchberger's algorithm; applications of Grobner bases: solvability of polynomial systems (e.g. Sudoku), ideal membership, elimination, syzygies, de Rham Cohomology, etc. | ||
Week 3 (Apr 2) | general mathematical maturity | randomized algorithm for testing equalilty of polynomial expressions, polynomial identity testing |