Next quarter, starting March 30, I will be teaching “Math 247B: Classical Fourier Analysis” here at UCLA. (The course should more accurately be named “Modern real-variable harmonic analysis”, but we have not gotten around to implementing such a name change.) This class (a continuation of Math 247A from previous quarter, taught by my colleague, Monica Visan) will cover the following topics:

- Restriction theory and Strichartz estimates
- Decoupling estimates and applications
- Paraproducts; time frequency analysis; Carleson’s theorem

As usual, lecture notes will be made available on this blog.

Unlike previous courses, this one will be given online as part of UCLA’s social distancing efforts. In particular, the course will be open to anyone with an internet connection (no UCLA affiliation is required), though non-UCLA participants will not have full access to all aspects of the course, and there is the possibility that some restrictions on participation may be imposed if there are significant disruptions to class activity. For more information, see the course description. **UPDATE**: due to time limitations, I will not be able to respond to personal email inquiries about this class from non-UCLA participants in the course. Please use the comment thread to this blog post for such inquiries. I will also update the course description throughout the course to reflect the latest information about the course, both for UCLA students enrolled in the course and for non-UCLA participants.

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14 March, 2020 at 9:13 pm

JosephSugarShould participants register for the class, or its open university style?

Given the current announcement from UCLA that teaching is transferring to online through the winter quarter, will it be possible to access other math classes also online? I don’t see why not. Hardly any other university can offer such quality mathematics content as UCLA, and this unfortunate pandemic could be the beginning of a new era of mathematics education.

15 March, 2020 at 7:51 am

Terence TaoAt present, UCLA does not have plans to permanently transition to an online education model; for the spring quarter all classes will be given online, but it is up to each instructor whether to open their course beyond their enrolled UCLA students. In particular there is currently no way for participants not affiliated with UCLA to formally enroll in the course, and some course components (e.g., homework grading) will be restricted to UCLA students enrolled in the course. By the end of the spring quarter there may be more clarity (both with regards to the efficacy of online teaching, and on the state of the coronavirus pandemic) as to how UCLA is to proceed going forward, but at this point there is far too much uncertainty to make any predictions.

15 March, 2020 at 2:10 am

physicslightMr. Tao,

Thank you for sharing this open

It helps in these days to exercise the mind.

Best,

marco

15 March, 2020 at 7:18 am

John Manguala quick library search turns up this expository article about the Waring problem.

https://arxiv.org/abs/1707.00119

There are also some nice – rather technical – articles by Jean Bourgain.

https://arxiv.org/abs/1604.06032

How do we pass between discrete statements over to statements over ? Any time we used symbols like “” or these were certainly limits of some other process.

15 March, 2020 at 8:13 am

Xinwu YangDear Prof. Tao,

I haven’t studied too much about the topics in the prerequisite (i.e. M247A); I did some graduate real analysis before, and we finished Chapter 1-7 in Folland and a bit of distribution theory. I am afraid that they are not enough. Could you help suggest some notes/book/reading for me to get more preparation for M247B? I searched online and found that you also wrote some notes for M247A (https://www.math.ucla.edu/~tao/247a.1.06f/), is it enough for your M247B?

15 March, 2020 at 9:52 am

ZaneFYI this was the class page for last quarter’s 247A taught by Professor Visan.

https://www.math.ucla.edu/~visan/Math247A_W20/

15 March, 2020 at 10:15 am

AnonymousI guess one can say that Monica’s “The lectures are most strongly influenced by the following” list of references in Zane’s link covers almost ALL primary texts in “introductory” harmonic analysis. (I mean, of course, the lecture would/should be strongly influenced by those books. What could else books be?) One may feel lost…

15 March, 2020 at 9:52 am

Terence TaoThat course covered a slightly different set of topics than last quarter’s 247A (that set is now listed in the course description), but either course should be sufficient preparation for 247B (in particular, familiarity with interpolation, Fourier analysis, and estimation of oscillatory integrals (e.g., by the method of stationary phase) will be helpful.)

15 March, 2020 at 10:07 am

AnonymousThis 247B seems to be quite different from the one you offered before: https://www.math.ucla.edu/~tao/247b.1.07w/

15 March, 2020 at 10:34 am

AnonymousWill you put the video online after class? Like youtube

17 March, 2020 at 6:19 am

Terence TaoI have decided not to do this; it may negatively impact class participation, and there are also some non-trivial issues regarding consent and privacy on the part of the students. It is possible these issues are solvable, but the transition to remote teaching is going to be chaotic enough as it is, so I do not want to make things even more disruptive this quarter. However this may be a possibility for future courses for which there is more time available to prepare for such issues.

17 March, 2020 at 8:01 am

AnonymousDo you expect that the participants may exceed the capacity of Zoom?

17 March, 2020 at 2:44 pm

Terence TaoI believe the capacity of our Zoom meeting rooms is 300. I do not anticipate exceeding this limit, but if this becomes the case I will limit attendance to UCLA affiliated participants once one gets close to this limit. (It should be pointed out that this course is a continuation of a previous graduate course at UCLA and may not necessarily be suitable for external participants that do not have the appropriate prerequisites.)

18 March, 2020 at 8:17 am

AnonymousDue to your popularity (see also https://zhuanlan.zhihu.com/p/113528952), I would not be surprised if the number of participants significantly exceeds the limit, even there may be a lot who don’t know much real analysis. On the other hand, serious students who do want to learn would benefit tremendously from being able to sit in the Zoom room or have access to some recordings without compromising the privacy of UCLA students.

15 March, 2020 at 5:22 pm

Dan Asimov—–

* Restriction theory and Strichartz estimates

* Decoupling estimates and applications

* Paraproducts; time frequency analysis; Carleson’s theorem

—–

In my ignorance of what all these specifically are about, my reaction is that these topics sound a great deal more like a workshop for researchers than a course for graduate students.

15 March, 2020 at 6:42 pm

Maitland BowenThank you. I am interested. Please include me on any applicable lists.

Regards, Maitland Bowen.

25 March, 2020 at 6:46 am

AnonymousDear Prof. Tao,

May I ask how can I attend the Zoom lectures?

Is there any kind of registration?

Many thanks,

27 March, 2020 at 6:27 am

Classical Fourier Analysis by Terence Tao (online lecture) – Ghent Analysis & PDEs[…] will be permitted to attend the Zoom lectures and to post comments on the blog (one can use this post in particular for general questions about the […]

30 March, 2020 at 1:17 pm

AnonymousDear Prof Tao,

I think that as the host, you can mute audio(and video) of every participant except your UCLA students. Thank you very much.

30 March, 2020 at 6:04 pm

Xinjie Zhanghow can we find the replay ? as timezoon difference. we can not attend the online class . please see where can we find the record session .thanks a lot.

31 March, 2020 at 7:40 am

Terence TaoFor reasons of privacy, UCLA policy forbids video recordings to be available except to the students enrolled in the class.

2 April, 2020 at 11:07 am

AnonymousCould you post your notes in .pdf format on line? They don’t need to be the final version. It is easier for students to download and take notes.

2 April, 2020 at 12:58 pm

Terence TaoIf you print a blog page to PDF you will get a readable PDF file (with the header, sidebar, etc. stripped)

6 January, 2021 at 2:39 pm

AnonymousIt is also easy to export the file into notes using an iPad. So convenient to go paperless!

2 June, 2020 at 12:37 am

MATH 247B: Modern Real-Variable Harmonic Analysis – Countable Infinity[…] Spring 2020, I took MATH 247B at UCLA, with Professor Terence Tao. The class covered the following […]

6 January, 2021 at 12:54 pm

AnonymousWould it violate the UCLA policy if you upload your notebook (which contains lots of useful pictures you drew in class) somewhere on your webpage?