Real analysis

Real analysis puts the tools of calculus on a rigorous footing. The published first unit works through limits, sequences of sets, and an early look at measure. From there the outline continues into the completeness of the real numbers and the role of suprema, the convergence of sequences and series, continuity, and finally differentiation and integration, rebuilding the results of earlier courses from careful definitions and proof.

The problems are the proofs: block-assembled arguments, step-by-step gap fills, and the epsilon and inequality bounds you enter directly, with hints on most. One of the five planned units is published today, which makes this the newest course in the catalog, and the syllabus below will lengthen as the outline fills.