Syllabus for Math 5310 (Introduction to Real Analysis), Fall 2014

TuTh 2-3:15 pm, Monroe 118.

Text: Principles of Mathematical Analysis, Walter Rudin, third edition.


Course outline

The main goal of the course is to develop basic notions of mathematical analysis (convergence, continuity, compactness etc.) in the setting of metric spaces. The material in the first half of the course will have some overlap with that of 3310; however, almost everything will be done in greater depth and generality. You should also expect homework exercises to be much more theoretically (rather than computationally) oriented compared to 3310. The second half will cover topics that you most likely have not studied before, including convergence in function spaces, fixed point theorems and Lebesgue integration. Our main textbook will be `Principles of Mathematical Analysis' by Rudin; however, we will not be following it too closely, and I may suggest other reading sources as we progress through the material. The tentative plan is to cover chapters 1,2,4,7,11 as well as parts of chapters 3,5,8 from Rudin's book; we will also cover at least a couple of topics not discussed in Rudin's book.


The course grade will be based on homework, two midterms and the final, with weights distributed as follows:


The format of the exams is open at this point, but most likely the final and the first midterm will be in-class while the second midterm will be take-home. The midterm dates given below are tentative and may be changed later. The date and time of the final exam is determined by the registrar and cannot be changed (in the case of a take-home final it will be due on that date).

Make-up policy


Collaboration policy.


Major announcements will be made in class and also posted on the course webpage. Some other announcements may only be made by e-mail, so check your e-mail account regularly.

Add/drop/withdrawal dates: