Professor David Blecher
Welcome to Real Variables (Math 6320 - (13175 and 28138))
Time and place : MWF 11:00-12:00 AM on Teams (face-to-face meetings are in SEC204)
Office Hours MF: 12-1 (or by
appointment)
IN PROGRESS: THIS DOCUMENT WILL CHANGE
Upcoming due dates: KEEP WATCHING THIS SPOT SINCE THINGS WILL BE ADDED.
Pace yourself, dont do things at the last moment.
Homework 4 is due November 16 at midnight on the Blackboard site for Chapter 3.
November 17 is the Last Day to Drop a Course with a 'W' or Withdraw.
Please contact me if you want to discuss this.
There will be a short final exam December 14 11 am -1 pm on Teams,
mostly on $L^p$ spaces, and Sections 3.1 and 3.2.
See the "Information and instructions on the test and exam" link below
for more details.
Per request of some in the class, and as mentioned in class,
if you would like an extra credit assignment
please let me know by December 7.
Per request of the class, we will relegate much of the remainder of Chapter 3 to discussion groups, where you all can figure out the math and explain it to each other, and then to the class (in some form—maybe as part of the final exam). At least let us try this and see how it goes. We will remake our 3 groups and ask you to choose one. You can be in more than one group if you are very ambitious.
Please tell me by Monday November 9 which group you wish to join. Elect a group leader, who can inform me on who is
participating. I suggest that you then break up your groups project into smaller subgroups
of people, and explain it to each other.
Group A: Change of variable formula in R^n (3.3.2 and 3.3.4).
Group B: Balls, spheres, and spherical coordinates: 3.3.5-3.3.10.
Group C: Intro to convolutions and the Fourier transform: Section 3.4. (This will be revisited fully in Chapter 8).
There is a small possibility, if you are interested, to do a different project, if I approve it.
Chapter 4. Introduction to Hilbert spaces notes (Chapter 4 Section 1) were distributed and gone through in class
If you would like information on your grades for the final few assignments and final exam, please contact
instructor (the Blackboard gradebook will probably not include these, and havde been superceded by an
Excel spreadsheet maintained by the instructor.
This is the first semester of a 2 semester sequence. This semester we will be developing the basic principles of measure and integration. This body of knowledge is essential to most parts of mathematics (in particular to analysis and probability) and falls within the category of "What every graduate student has to know". The one test and the final exam will be based on the notes given in class, and on the homework.
After each chapter we will schedule a problem solving workshop, based on the homework assigned for that chapter.
You should attempt all homework problems, although it is not expected
that you solve all of them. Most of the problems
are there to help you learn and INTERNALIZE the material.
The most important part of your task as a graduate student in this course is simply to read the class notes
line by line, making sure you understand everything (that is, understand why each line is true,
using the previous line or earlier facts). Please ask me about anything you don't follow. I will refer to this
as `doing your main job', and this is the way a mathematician reads
a mathematics paper or book. The second
most important part of your task is to do as much as possible of the assigned homework.
If you are a new graduate student
taking this class, I suggest reading some material about writing mathematics
and how to prove things.
You can find some books (eg. the one by Krantz)
and plenty of stuff on the web--eg.