## 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

**[16-Nov-13]** End-sem exam posted.

**[22-Oct-13]** Assignment 2 posted.

**[20-Sep-13]** Mid-sem exam posted.

**[16-Sep-13]** All lectures are updated online.

**[02-Sep-13]** Assignment 1 posted.

**[29-Jul-13]** Assignment 0 posted.

**[16-May-13]** Course begins on Mon, 29-Jul-13.