COURSE DESCRIPTION
We want to count the number of roots of an algebraic system (over finite fields). This is a very difficult question in general (eg. #P-hard). However, there are fast algorithms known for special cases. In this course we will focus on the "2-variable" case, i.e. curves. This case already demands significant theory and has an amazing list of applications in computer science. We will cover some important aspects of the theory in a self-contained way, and see as many applications as time permits.Prerequisites: Theory of Computation, Algebra.
Text Book: Carlos Moreno, Algebraic Curves over Finite Fields (Cambridge Tracts in Mathematics)
RECENT UPDATE
[03-Apr-23] Assignment 4 posted.
[13-Mar-23] Assignment 3 posted.
[21-Feb-23] Mid-Sem Exam posted.
[08-Feb-23] Assignment 2 posted.
[13-Jan-23] Assignment 1 posted.
[06-Jan-23] Course begins on Fri, 06-Jan-23.