Math 452
Real Analysis
Prof. Sullivan
Fall 2016

Goals: Develop a rigorous understanding of the real number line, convergence in metric spaces, the formal basis of calculus (review), and uniform convergence. Develop a beginning understanding of function spaces and the measure of subsets of the reals as preparation for a rigorous course in Lebesgue measure theory and integration as well as preparation for applied courses in approximation theory and physics courses that make use of function spaces.

Students will further improve their theorem proving abilities. All proofs are to be written in grammatically correct sentences.

The textbook, see below, is meant to be read carefully. You cannot just skim through for the important parts like with many lower level textbooks. You should read all the exersices not just the asssigned ones. This is holds for most any upper level textbook.

Textbook: Real Mathematical Analysis, 2nd Edition, by Charles Pugh, Springer. You can get it from: Amazon, Springer, Powell's, etc.

Grading: Weekly homework, a midterm, and a final, will each count as one third of the final grade.

Warning: I know solutions can be found on line. I have copies. Do not use them. Do not look at them. The point is to learn how to think for yourself. If you are copying I will ask that you drop the course and I will not grade your work.

Lectures online: Lecture notes and the lectures themselves will be available online. Off campus students will use these instead of coming to class. On campus students can use them if they wish.

Lecture Notes and Videos

Homework Assignments


Supplemental reading

Other textbooks on Real Analysis

Books every serious student of mathematics should have