Dorian Goldfeld

Do yourself a favor and do NOT listen to any of these reviews prior to 2012 PLEASE. I thought I would take this class to be an easy A replacement course for calc 2. Wrong. This class was my biggest struggle and most anxiety-inducing class all semester. All I talked about was how much I was worried about Making, Breaking Codes. I'm sure he was once a great professor since he won awards and seemed to have been beloved, but he definitely hit his mark ten years ago. He is a bit hard of hearing and generally tends to be confused, so asking him a question will take 10 minutes of you explaining/repeating it, only to get the vaguest response imaginable. But you'll accept the response anyways because you're so tired of repeating yourself. He doesn't communicate with his TA's either so they can't really help you prepare for exams, and they just tell you to know "everything" (which is a ridiculously large amount). My BIGGEST WARNING is that this is a MEMORIZATION class. NOT A LOGIC class. To my fellow lovely, lovely mathematics majors, you and I are strong in logic. That is where we thrive. This class has none of it.

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 non-standard 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 change-of-variables 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 birds-eye 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 ground-up. This was remedied in the second part of the cours…

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 real-world applicable. Good class, and one of the easier advanced classes in the math department.

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 non-intimidating. 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.

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.

Lots of content in this course, but not conceptually very difficult. Even though many reviews say it is an easy class, I had a tough time memorizing all of the different encryption/decryption algorithms and the various proofs we had to know. There were no cheat sheets allowed and many of the algorithms were multi-step algorithms that we had to know. However, this class is significantly easier than other classes of this level, but I did not enjoy the memorization aspect to it. I also strongly disliked the professor as he has a very condescending tone when answering questions he feels are "obvious", and oftentimes he mishears students questions then answers them in a frustrated manner. Tbh does not make me enjoy being in class with him; wish he had more respect for his students.

4 problem sets (60%), 1 take home final (40%)

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.

mild, but potentially heavy if you are inspired

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!