Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometry
MIT's undergraduate seminar in algebra and number theory, focused for its fall 2008 offering on computational commutative algebra and algebraic geometry. Students read primary and secondary sources on the topic, then take turns presenting material to the class, with the instructor and peers pushing back in discussion. The course doubles as practice in mathematical writing and oral presentation, since each student produces both a written paper and a talk. Some prior experience with proof-based mathematics is expected going in. Materials on MIT OpenCourseWare include the syllabus, topic list, and student presentation schedule, giving a clear picture of how a research-style seminar in computational algebra is run at the undergraduate level. There are no video lectures; the course is built around reading, presenting, and critiquing rather than passive instruction, and it is free to access with no certificate offered.