[APMA 4204] Functions of a Complex Variable

Polvani is a great teacher who made complex variables relatively interesting and bearable during the 2.5 hours of weekly lecture, considering that it's late afternoon, when everybody is mentally and physically drained already. He goes through most of the material very thoroughly, minimizing students' pain, by presenting a healthy mix of derivations and applications (+ occasional tangents). He has a cute, but comprehensible, accent and is generally very receptive to questions/comments/corrections to mistakes. He will actually slow down his pace and reiterate certain things depending on people's requests.

Make sure to come to class when he covers CHAPTER 6; otherwise, be prepared to spend a billion hours deciphering the hieroglyphics in the book and still getting confused while doing the long, torturous homework assignment over Thanksgiving break
(i went to lecture, but still spent most of the holiday doing the HW and suffering from the messy algebra).

Be warned that the exams are not simple at all - you need to really know the stuff cold so that time wouldn't be an issue. STUDY, STUDY, and STUDY hard - practice problems, but keep in mind though that understanding of concepts, rather than the ability to perform robotic-like, mindless calculations, is key (think critically!!!).

Also, be heedful of the questions on branch cuts and Mobius transformations -> Lorenzo loves these subjects, but did not provide enough examples, and to make it worse, the text we used, Saff Snider Fundamentals of Complex Analysis, was useless for these topics.

Enjoyable experience overall, to say the least. Very polite, humble, but funny man who respects each student. Only complaint is that we did not get our final course grade until January.

cool guy, cool ish class.

polvani is really, REALLY exuberant about complex variables. he definitely makes the 2.5 hour long class less painful to sit through, and it usually pays off to go to class. the material is a little daunting at first, but the calculations are always simple and solutions are very straight forward. (and there's a solutions manual always floating around that i'm sure you can find.)

this class is required for applied math majors, but i think that other majors could definitely enjoy it as well. you really don't need to know any super advanced math for it anyway.

This past semester, I only went to two classes regularly. One was a lab class so it was mandatory, and the other was this. Professor Polvani makes his weekly 2-hour lectures a breeze; he is so enthusiastic about the subject, it makes you get involved too. He is very thorough in his proofs and examples, pausing often to ask for questions or add quirky remarks. In short, Polvani is awesome.

The homework generally took about 4 hours each for me although there was one that took more than 10 hours, so just look out when he covers chapter six. Otherwise, I found doing the homework really helpful since the exams covered the same material.

The midterm itself was not too difficult since the material covered to that point is largely basic. The final was harder, but not too much so. The curve is not bad, though there were only two A+'s.

By far one of my favorite professors at Columbia. He is completely approachable and very helpful. Also he might be one of the nicest people I have ever met, always encouraging questions during class even though some were really stupid. He is a little scattered and tends to make errors with his calculations on the board but always encourages students to correct him. He makes a difficult subject easy to understand and fun. The only problem I had with the course was that it was a 3 hour lecture on Monday nights. Since I came straight from another class it made for a long day, but he gave the class a break. The lectures aren't mandatory but you should stay. They are usually helpful for an understanding of the subject before attempting the homework and because he is awesome.