MATH 746 Theory of Functions of Real Variable I Fall 2020

Rob Thompson Hunter College
Tuesday--Thursday 7:00-8:15pm Room: Online
August 26-December 20, 2020

Office: Hours: Tuesday and Thursday, 6:00-7:00.

Please Note: This course will be held online. We will have synchronous, live, online classes, using Zoom, during the regularly scheduled time slot for the course. The office hours will also be online. To access my Zoom meeting space go to in your browser and you will be prompted to go to your zoom app. If you do not have a Zoom app installed you will have to do that first. You do not necessarily need to have an account with Zoom to install and use the app. If you go into the Zoom app directly just go to profthompson.

We will have an exam Thursday, 10/22. Topics covered will be Chapter Two, Sections A-D, and Chapter Three, Section 3A.

Here are some Homework solutions/hints.

We will have a quiz Tuesday, 9/22. The topics will be on measure theory.


Here are some practice problems. I will post more.:

Practice problem. This is a multipart problem from Royden that I mentioned in class.

My Office:

My office hours for the fall term will for the most part be Tuesday and Thursday 6:00-7:00 pm. However there will be a couple of days when I have to change this, but I will announce that. You don't need to make an appointment for office hours, you can just drop in. The Zoom address is profthompson.



MATH 351 or the equivalent.

Desired Learning Outcomes:

The student will assimilate the definitions and basic concepts of measure theory, Lebesgue integration, L_p spaces, and Banach spaces. The student will learn the statements of a number of fundamental theorems, and will study their proofs. The student will be doing homework problems which will involve some computations but mostly the proving of various facts. The majority of the assessment will consist of written exams similar to the homework problems.


There will be regularly assigned homework. Most of it will not be handed in, however we will discuss homework problems in class and I will post some solutions. A few homework problems during the semester will be handed in. There will be a short quiz around the end of the second or third week, two exams later in the semester, one of which will probably be a take-home. There will be a final exam on the college scheduled final exam day. Your course grade will be based on the quiz and exams, according to the following rubric: Quiz - 15%, Exams - 25% each, Final - 25%, occasional homework and class participation - 10%.

Recorded Classes

The Homework Assignments

Instructions for submitting the homework:

The homework must be in the form of PDF file


This course is an introduction to Real Analysis, taught at a fairly abstract and conceptual level, with an emphasis on definitions, theorems, and proofs. The students will be doing proofs in the homework, and on exams. Here is a list of topics we hope to cover, roughly keyed to the table of contents of Axler's Book.