[shiandow]

The techniques in this article would be considered common knowledge for any of the prerequisite classes you'd need to take to be able to follow a course on Higher order Fourier analysis.

I wouldn't say they're unrelated, but if you want to know whether both uses of the phrase "higher order" have any relation then no.

[gradschoolfail]

Thank you!

I remember seeing in the Tao book a Fourier operator that looks something like the “integral” of exp(ik^2 x).. (or exp(ik x^2), haha)

As a followup, is it possible to ELI5 roughly what Tao meant by “higher-order”?

[coherentpony]

The first paragraph of the preface on page 7 in the book gives an explicit example of “higher order”: https://terrytao.files.wordpress.com/2011/03/higher-book.pdf

[gradschoolfail]

Lollol thats what i half remembered.. i guess then what Terence Tao meant by higher order is lower order in the featured artiicle!