Analysis I
A rigorous introduction to real analysis from MIT OpenCourseWare, covering metric spaces, convergence of sequences and series, continuity, differentiability, and the Riemann integral. The course also treats sequences and series of functions, uniform convergence, and the conditions under which limit operations can be interchanged, topics that separate careful analysis from the calculus most students learn first. Materials include lecture notes, problem sets, and exams drawn from MIT's undergraduate mathematics curriculum, following the OpenCourseWare model of self-study without instructor interaction. No enrollment or certificate is offered; the value is the primary course materials themselves, the same ones used in MIT's classroom sequence. Suited to students who have finished single-variable calculus and want the proofs behind it, this is foundational material for anyone heading toward pure mathematics, graduate study, or a deeper theoretical grounding in the subject.