Calculus with Theory
MIT's rigorous take on single variable calculus, covering the same ground as the standard 18.01 course but built around careful proofs rather than routine computation. Topics include limits, continuity, differentiation, integration, and the fundamental theorem of calculus, all developed with formal epsilon-delta arguments and attention to why the techniques work rather than just how to apply them. The course assumes prior exposure to elementary calculus and is aimed at students who want a proof-based foundation before moving into real analysis. Materials on MIT OpenCourseWare include lecture notes, problem sets, and exams with solutions, allowing self-study at your own pace. There is no instructor interaction or certificate, since OCW simply publishes the course materials MIT uses on campus. It suits students bound for pure mathematics who want rigor built in from the start rather than added later.