I'm an undergraduate with some measure and integration theory background. The undergrad analysis course I took at my institution covered the equivalent of the first two chapters of Folland's Real Analysis (ie introductory measure theory constructions, the convergence theorems for Lebesgue intergrals and Fubini-Tonelli) along with parts of chapters 5 and 6 on Elementary Functional Analysis and Lp Spaces. I was told that with some preparation I could probably take the second semester graduate introductory course on Functional Analysis that follows the first semester measure theory course. However, I am not certain what exactly I am to focus on in my preparation. Currently, I intend to do:

1) Chapter 3 of Folland which covers the Lebesgue Differentiation and the Radon-Nikodym Theorems since this appears to be the one major area which the intro grad course covered but I didn't.

2) Review Point Set Topology from say, Munkres (I'm mostly familiar with this up till Arzela Ascoli and Stone-Weierstrass).

3) Read an undergrad book like Kreyzig's.

Is there anything else I should focus on?

The Functional Analysis course will be using Functional Analysis, Sobolev Spaces and Partial Differential Equations by Brezis. We probably won't cover the entire book.

Thanks in advance.


closed as off-topic by Jack, Alex Ortiz, k170, Stella Biderman, J. M. is a poor mathematician Dec 29 '16 at 5:07

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  • $\begingroup$ Why not ask this question to the person who suggested that you prepare for this course? Or to the person teaching the course? They know what they expect students to know a lot better than we do. $\endgroup$ – Milo Brandt Dec 29 '16 at 4:41
  • $\begingroup$ @MiloBrandt Thanks for your response. The person who recommended the course to me at the time gave me vague recommendations along the lines of what I have mentioned as my intended topics of focus. He's not quite available anymore and so I decided to seek this forum's help with more specificity. The instructor hasn't been reachable. $\endgroup$ – user247381 Dec 29 '16 at 7:28

I would say to mostly focus on Folland. It's specifically mentioned as one of the books that would provide good background. Chapter 4 has enough topology, and Munkres will take quite some time, and it seems like Kreyszig will be somewhat redundant.

I am running under the assumption that the Brezis course is this coming semester (you'll be starting in the 2 weeks). If you'll be doing it at a later point, then going through more slowly could be a good choice. Still, make sure that by the time you start, you know the prerequisite material from Folland well.

  • $\begingroup$ Thanks. The course starts in 20 days. So, thought that might be a good amount of time to squeeze in some preparation. $\endgroup$ – user247381 Dec 29 '16 at 7:26
  • $\begingroup$ Alright, I think you'd be best off getting comfortable with what you've done already + chapters 3-4 of Folland. $\endgroup$ – Daminark Dec 29 '16 at 7:42

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