Modern Analysis 2

Time and Location

MWF Period 4 (10:40-11:30)   217 Little Hall

Office hours

M6  F5 (primary); M5 F6 (secondary); or by appointment

Text

Walter Rudin, Principles of Mathematical Analysis, Third Edition

Topics

This second-semester course has the same foundational goals as the first, but addresses a different set of topics. In principle, it will cover material from chapters six, seven, eight, and eleven of Rudin, as indicated in the official syllabus: https://math.ufl.edu/first-year-exam-syllabi/maa-5229-modern-analysis-2

Regarding Chapter six, we shall focus primarily not on the Riemann-Stieltjes integral but on the simpler Riemann integral, but incorporating modifications that are attributable to Darboux.

Our study of Chapters Seven and Eight will be rooted in the notion of uniform convergence for sequences of functions, with excursions into approximation theory (via the Weierstrass approximation theorem and its generalizations) and differential equations (via the Arzela-Ascoli theorem on compactness in function spaces).

Taken together, the previous topics are likely to take us a little way past midterm. The remainder of the semester is devoted to Chapter Eleven on the Lebesgue integral; this is perhaps the most demanding part of the course, coverage of which easily deserves half a semester.

Homework problems will be regularly assigned and discussed in class. Some of these problems
will be officially posted to Canvas, collected and graded, with comments; the grading criteria will be discussed
in class at the start of semester. There will also be a midterm (approximately half way through
the semester) and a final; each of these optional tests will serve as practice for the Analysis First-Year
Examination.

Policies

For various matters of policy, please consult ‘Policies plus’ at the Files page.