Introduction to Arithmetic Geometry
Arithmetic geometry sits at the intersection of algebraic geometry and number theory, and this MIT OpenCourseWare course builds the tools needed to study classical Diophantine problems from that modern viewpoint. Topics include affine and projective varieties, schemes, the theory of elliptic curves, and reduction mod p, working toward results like the Mordell-Weil theorem and the study of rational points on curves. Materials include full lecture notes covering the semester's topics and problem sets that develop the algebraic geometry machinery alongside number-theoretic applications. The course assumes prior exposure to algebraic geometry and abstract algebra and is aimed at graduate students or advanced undergraduates. As with other MIT OpenCourseWare offerings, all materials are free to access and there is no certificate. This is a rigorous, self-contained treatment of the subject rather than a survey, suited to students planning further work in number theory or arithmetic geometry.