professor


May 2015 
Dorian Goldfeld is a great guy! He's one of Columbia's most accomplished math professors, and that definitely bleeds through into the class. Often he'll prove things in nonstandard ways that's he's encountered over the course of his career that are a little nicer than the regular way. One time he showed us a proof for a theorem that he made (and published) by himself, which was far shorter than the regular one. Having said this, some technical stuff will go over your heard. I wouldn't say he races through the material, but he's definitely not slow. This man is so comfortable with the material that he does pretty involved integrals and changeofvariables in a single step. The first part of the course goes over the historical proof of the prime number theorem, and in the process covers an extraordinary amount of mathematical machinery, filled to the brim with incredible tricks I wouldn't have thought of in a million years. I wish at the end he gave a birdseye view of the theorem we spent so long proving, so I could remember exactly how it all fit together. I think it got pretty myopic at points, but I can't say I didn't learn a lot in the process. After the first part of the course I was a litte disillusioned because I felt that I knew a bunch of scattered techniques without feeling I understood the subject from the groundup. This was remedied in the second part of the course, which was primarily focused on modular forms. I gotta admit, I really liked those modular forms. There was definitely an understandable component to them, even if the results got a little crazy at times. The problem sets were actually pretty good. They were all 4 problems long and took over a day or two to complete, but not too much more. I had a really hard time with the first one because I had no idea what analysis was, but after that I was able to attack them with confidence. You'll DEFINITELY need to take good notes in able to do these problems, as they often require a result proved in class. The last problem set was the best, you got to prove a few results that looked like complete blackmagic, and all on your own! The final was reasonable. It too used things proved in class (and how they were proved). It was a takehome final over the weekend that lasted 24 hours. The class was very small, all filled with bright kids who understood mostly everything, and they all got good grades from what I hear. Goldfeld isn't a grade monster. The only prereq for the class is complex variables, but if you know all about the residue theorem and some facts about holomorphic / meromorphic functions, you'll be okay. Furthermore, I think a general mathematical interest is good to have, as he uses some group theory and linear algebra that aren't technically prereqs. Having said all this, the class is mostly selfcontained. Also, a word must be said for Goldfeld the man. He laughs a lot while teaching, and is generally very friendly and lighthearted. He talked to me on a few occasions, and genuinely seemed invested in having his students understanding the material. Sometimes he tells great anecdotes about himself or other mathematicians that bring a great character to the material. I would definitely recommend this class, or any upperlevel class taught by Goldfeld. I think this was a relatively painless and fascinating introduction to Analytic Number Theory, which has become a vast branch of math. You learn a lot of landmark results, and break a lot of ground into the subject. I can read wikipedia articles about the subject matter and understand almost all of it. 10/10
May 2012 
Solid class. Dorian isn't necessarily the friendliest or warmest professor, but he does a good job of explaining some fairly complicated concepts and is fairly reasonable. The class covers cryptography and coding theory and the math behind them  they're fairly interesting topics. He stresses this in the first class and he's right: the class is much harder than the first week or two would make it seem. The first few topics you cover are pretty easy and then things really take off. The sense I get, however, is that it's still easier than most upperlevel math classes, though it's not a walk in the park by any means. One huge plus is that Dorian reviews the material a lot. In addition to the review sessions he gives before the second midterm and the final, he starts off each class by reviewing everything he taught in the previous class. This can be a bit tiresome if you're on top of everything, but it's great if you ever miss a class or just feel like you've fallen behind. He also writes an insane amount of notes on the board.
May 2008 
Dorian Goldfeld is, simply put, the love of my mathlife. His class is possibly the best math class I've ever taken. For the most part, he does a great job of explaining everything. His tests seemed to cover the material in a pretty fair manner, and the grades were curved. A lot.
May 2008 
This class is probably one of the easier higher level math courses offered at Columbia. Number theory isn't a prereq for Codes, and it only crept up a couple of times during the course, and definitely won't ruin your chances of getting a good grade here. Prof Goldfeld writes a copious amount of notes on the boardliterally every word he sayswhich is great when you're falling asleep during some of the less stimulating portions of the lecture. The material is different though and will take some getting used to; just make sure to read the text, and understand the homeworks. Aside from the disproportionate number of grad students taking the course, it's not that bad.
Dec 2006 
Professor Goldfeld is a mild but engaging professor. This class was always the fastest hour and fifteen minute class of my Tuesday or Thursday. His classes are usually all about proving theorems that are either very important or just very interesting to him. He tries to involve the class as much as possible and seems to really care that you understand what's going on. Some of the homework problems will make you rip your hair out because you can't see the proof, but most of them aren't bad at all. Exams are difficult but fair. Our midterm happened to be a particularly tough one but he saw that a lot of people struggled with it and in turn tried to give the final more of a spread of material. He's a brilliant guy and he makes his class really interesting by showing you the applications of a field that many people wouldn't consider very realworld applicable. Good class, and one of the easier advanced classes in the math department.
May 2006 
This is the most relaxing math class that I have ever had at Columbia. You feel that you really can just be yourself and not suppressed by tons of definitions, lemmas and theorems that are shooting out from a fire hose. Because the stuff is so effortlessly taught and learnt. We only had three homework sets. As a result, we have more motivation and more interest for the material and therefore more memory retained :) The professor speaks in a very calm pace, which is extremely nonintimidating. You have plenty of time to absorb the meanings of the definitions before the statements of the theorems. Other attractions: There is a class dinner (which I unfortunately had to miss) that I heard was great; a genuine friendly feeling among classmates rather than competitiveness; a 15 minute presentation in lieu of midterm (there is nothing better than this :) and even better than all the above (pardon my inconsistency on what is the best) is the danger of being inspired!!! In this class, you will feel that math is not combing through tangled hair in a rush, which might make you look neat but how tedious and painful that is, nor is it a race to satisfy some weekly deadlines, and especially not a practice for law school. Instead, you will have fun.
Apr 2005 
He's a pretty standard math teacher, though not so engaging with the lectures. The tests given are slightly on the difficult side, though entirely doable if you know the stuff. The biggest thing I had a problem with is webworks, though its really such a small part of your final grade.

Jan 2005 
Professor Goldfeld is simply phenomenal. You'd be really, really foolish not to take this class. Not only is his English perfect, but he's a brilliant mathematician as well. I went to his office hours once and not only did he help me with 2 homework problems, but he even offered me a chocolate truffle at the end! Study hard and you're basically guaranteed an A.
Dec 2004 
What can I say? I chose him because he was the only prof available that spoke English. I ended up not going to class, so it didn't matter anyway. As far as math professors go, he was an alright guy, and if you need to go to class to learn the materia, he explains things pretty well. . The second midterm and especially the final are hard to study for; they're insane "trick" questions. You don't have to get them all, though, to get an A; he curves to a B on the tests, no matter how bad the students do. Why oh why do Calc II professors have to give Webworks? I hate them so. In fact, one time I spent hours trying to figure out a single problem, only to find out later that the problem was messed up!
Dec 2004 
Goldfeld speaks fluent English and I hear that that is a rarity in the Math department. I have no idea how to rate Goldfeld compared to other math teachers, but just be prepared to come to class, take notes, and then come back to your room and teach yourself the material. The examples done in class are way easier than those on the homework. However, if you do all of the assigned work, you should be very prepared for the test. The tests are harder, but, then again, everything is curved. Goldfeld is a nice guy though and very willing to meet up and help you. If you're going to take Calc II (it's hard!), take it with Goldfeld. The class is doable if you make it a priority.
Nov 2004 
Funny, entertaining (the infamous laugh), nice, approachable, willing to help, clear lectures, good curve on midterms (just be sure to study the book, not webworks), speaks English perfectly, highly recommended!
May 2004 
Dorian has a...different sense of humor. You laugh because he says some pretty funny stuff, but also sometimes just because of the face he makes. He gives a LOT of notes, which are very helpful. You can understand him perfectly, which is a rare case in the math department here. His exams are challenging yet very straightforward. Study a lot and you'll get an A.
May 2004 
Funny little man who is a decent teacher. Sometimes he likes to go into tangents, and doesnt always explain things that well, but overall...a good teacher. I mean, at least his English is understandable.
Dec 2003 
Not bad at all. His lectures are clear and straightforward, though his examples in class are much much easier than those you see on the midterms and final exams. Also, he sometimes goes pretty slowly, so you don't cover the homework material during class, effectively forcing you to teach yourself. The workload's not too bad, homework each week, 2 midterms, 1 final. However, the webworks sometimes takes forever depending on the week. For the most part, a pretty good teacher. Plus, he can speak English, which is saying something.
Nov 2003 
Overall, a pretty good professor. He explains the material well and fairly methodically, sometimes too methodically perhaps but he made sure we understood. Some complaints 1. His examples in class are nothing like the exams or the HW in terms of level of difficulty  they're deceivingly easy 2. Sometimes, because he went so slowly, he would make us do HW problems over topics we hadn't covered. However, on the upside, he's quirky and nerdy, always nervously snickering at something unfunny, so he's always amusing if nothing else. Seriously though, I think he's a pretty good choice in the Math Department.
Jan 2000 
Yes, he is one of the authors of that awful textbook some of us used for Calculus 2S and 3S. In person, though, it's a whole other story. He is definitely one of the better professors in the math department. He has a way of making hard proofs easy to understand. He also does a lot of examples which helps further understanding. There are 3 midterms (lowest grade is dropped) that count for 60% and a final which counts for 40%. Homework is assigned and graded but it only counts if your grade is borderline. The tests are not that hard, but he grades them carefully and does not give any partial credit for bs proofs. The final is also not that difficult. The only downside is that he sometimes doesn't prepare lectures and messes up in class which leads to long pauses. But the class had a lot more upsides than downsides and it is definitely recommended.