Syllabus for Math 4310 (Introduction to Real Analysis), Fall 2015

TuTh 2-3:15 pm, Dell 2 103.


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. 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. The tentative plan is to cover chapters 1,2,4,7,11 from Rudin's book and some parts of other chapters. The book `Introductory Real Analysis' by Kolmogorov and Fomin will be the main reference for Lebesque integration (roughly the last three weeks of the semester).


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


The format of the exams has not been finalized 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:

All students with special needs requiring accommodations should present the appropriate paperwork from the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.