Math 447 is the first theoretical courses in real analysis offered here. Ideally, a student should leave such a course with not only a basic understanding of the major concepts of the one-dimensional calculus, but an increased facility at reading and writing mathematical sentences, the ability to produce and analyze examples, and some skills at constructing and writing elementary proofs.

The same text is now used in both Math 444 and 447.

Math 447 covers enough metric topology to provide background for other courses such as 448. Students in Math 444 win have more time to investigate examples and master the fundamental concepts.