Serial	Week	Topic
1	Jan 21-25	Introduction, sequential and parallel computation, modular arithmetic, chinese remaindering and applications.
2	Jan 28-Feb 1	Fields, rings and groups. Fundamental algorithms: multiplication and gcd.
3	Feb 4-8	Review of linear algebra: matrices and their eigenvalues. Fast parallel matrix inversion
4	Feb 11-15	Polynomials and their properties. Reed Solomon codes and Welch-Berlekamp decoding
5	Feb 18-22	Polynomial Identity Testing. Perfect matching in parallel.
6	Feb 25-29	Primality Testing and Integer Factorization. RSA cryptosystem.
7	Mar 3-7	Factoring univariate polynomials over rationals and over finite fields.
8	Mar 10-14	Factoring multivariate polynomials. List decoding of Reed Solomon Codes
9	Mar 17-21	Spring Recess
10	Mar 24-28	Hilbert's Nullstellensatz and Bezout's Theorem.
11	Mar 31-Apr 4	Arithmetic circuit lower bounds.
12	Apr 7-11	Quantifier elimination over complex numbers
13	Apr 14-18	Real root finding for univariate polynomials.
14	Apr 21-25	Decidability of euclidean geometry.