Welcome to the homepage of the PRIMES Computer algebra lab! The goals of this program are:

  • To introduce PRIMES participants to fundamtental concepts in abstract algebra, including linear algebra, representation theory, and the theory of rings and modules.
  • To provide PRIMES participants with lectures and hands-on experience using the SAGE computater algebra program to explore and solve problems in modern algebra.
  • To produce student-crafted notes of the lectures, programming workshops, and research projects, with the eventual goal of online publication as a resource to supplement the existing online documentation of SAGE.
  • To complete SAGE-assisted research projects into open problems in algebra, related to research interests of PRIMES staff, MIT faculty, and other contributors.

This being the inaugural year for both PRIMES and the PRIMES Computer algebra lab, the format of lectures and workshops will likely evolve as the year goes on, and be shaped by the input of our participants. Our plan, in the beginning, is that I will conduct weekly lectures on basic topics in algebra, beginning with linear algebra, and moving into representation theory of finite groups.

Each lecture will be supplemented by "pen and paper" homework exercises, in addition to programming projects in SAGE, in which we will demonstrate and elaborate more complicated examples than we could hope to do by hand. At the same time, we will document our programs thoroughly, so that they may serve as a reference for future workshops and researchers.