Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves
An MIT undergraduate seminar built around the theory of elliptic curves and rational points, based on the classic text by Silverman and Tate. Students, not the instructor, prepare and deliver the lectures, working through topics such as the group law on cubic curves, the Mordell-Weil theorem, points of finite order, and connections to number theory including the congruent number problem. MIT OpenCourseWare provides the syllabus, reading assignments, and presentation schedule used to run the seminar, along with notes on how presentations are structured and evaluated. No prior lecturing experience is required, only a solid background in algebra. The course suits math majors who want hands-on experience explaining advanced material rather than just absorbing it, and it doubles as an accessible route into a central topic of modern number theory.