# MATH 336

This is my course review page for MATH 336, the third (and final) quarter of the second year of honors accelerated advanced calculus (known as MATH 33X). MATH 336 covers the basics of complex analysis. I took the course in Spring 2016 with James Morrow and TA Will Dana.

I should preface this review by saying that there has been a considerable amount of hype surrounding 336, with both Morrow and the TA repeatedly mentioning how beautiful complex analysis is, and how easy some of the results are to prove (in contrast to real analysis, which he had been doing), and so forth. In fact, I think to a certain extent for some people in the course, MATH 334 and 335 were seen as messy preparation to understand the material of 336.

## Textbook

The course uses Gamelin’s *Complex Analysis*. Most (all?) editions seem to be published in 2001, but there are several different printings of the 2001 edition, where numerous misprints have been corrected in later printings. (I note this here mostly because I found this to be an annoyance when I discovered I was working off an earlier printing even though I was on the same edition as everyone else!) For reference, here are the corrections: changes from first to second printing, corrections for the second and third printings.

On the third week of class, Morrow revealed that Lars Ahlfors’s *Complex Analysis* is “the best book” on complex analysis ever written, and that a lot of the proofs he presents in class (which differ from the ones in Gamelin) will be from Ahlfors’s text. I find it slightly odd that Morrow would even use Gamelin if Ahlfors really is superior, but I suppose he knows what he’s doing since he’s been teaching this sequence for over a decade.

## Notes

As with the previous quarter, I’ll be taking notes as I go along instead of writing a review at the end.

- The second problem set contained the problem of proving that the sequence of complex binomial coefficients \(\left(\binom\alpha n\right)_{n=0}^\infty\) is bounded if and only if \(\mathop{\mathrm{Re}} \alpha \geq -1\). I thought this was one of the more interesting problems encountered this year.