* SAGE talk on Thur at 5pm in the room by elevator on 4th floor * further discussion about student projects * linalg today -- I'll discuss newforms / oldforms later when they arise naturally. * Ralph talks tomorrow at 4pm: "Elliptic Curves" * I talk tomorrow at 5pm: "How SAGE works" Our schedule: [] Linear algebra 1: computing echelon forms [] Linear algebra 2: decomposition algorithms [] Higher Weight Modular Symbols 1: basic definitions & how to compute [] Higher Weight Modular Symbols 2: Hecke operators on them [] Higher Weight Modular Symbols 3: using to compute modular forms [] Newforms 1: Atkin-Lehner-Li theory [] Newforms 2: Computing (and storing!) systems of eigenvalues [] Special Values of L-functions using modular symbols [] (may 29 -- memorial day holiday) [] Sturm's bound: Congruences between modular forms and gen. Hecke algebras [] Serre's conjectures: more precise statement and computational issues