The kindest man. He explains number theory concepts so clearly. He makes even the most challenging of proofs feel simple. Workload is super easy and maneagable. There are about 6-7 problem sets per semester, which are fairly challenging, but I believe he grades homework based on effort. The Midterm is super straightforward. He also uploads a practice midterm that’s fairly similar to the actual one. A lot of people got 100s. Coming to class is pretty important, because there’s no textbook, and it’s hard to learn the material on your own. He is bad at updating courseworks, but he’ll always say in class what’s due when or what even the exams are. He is a fantastic lecturer, and even though you probably need to go to class to get a good grade, you’ll enjoy doing so.
Definitely one of the best classes I've taken here at Columbia. Hansen's an excellent lecturer, extremely clear, and best of all he can actually speak English which already makes him more competent than half of the math department. He's super chill, always ready and able to answer any questions that you might have. The class isn't a walk in the park but is easy by math major coursework standards. Only con to taking this class is there isn't much cryptography covered, but I guess there's Making, Breaking Codes if you're more interested in that.
Zhang is a very difficult professor to write an accurate review for. His class could accurately be described as hell, but I don't really think it was his fault. He is both very smart and very funny. My issue was with the textbook - the thing was horrible; it didn't explain anything well, and the homework problems were abstruse. To be fair, Zhang also hated the textbook, and said he would change it up for next semester. Given that, I think this class will be a lot more reasonable in following semesters. Still, be wary. Zhang is kind of a wild card when it comes to out of class accessibility; sometimes he's nice, sometimes he makes fun of you. If you have trouble with proofs or are short on time, I'd probably advise against this class.
He's a brilliant mathematician and quite the nice guy. However, this class was a bit of a failure. He admitted to not having looked much through the textbook, having gotten it via a colleague's recommendation, and as a result was taken aback when it turned out to be far denser than he thought. The course's pacing was off; most of the time we went too slowly. I would feel rather dishonest to say that I know even elementary number theory after this course I'm willing to chalk a bit up to the fact that he's a busy mathematician with other commitments and did not take much time to set up this course. I suspect were he to teach again, he'd pick a different textbook that was more user friendly, as well as spending more time designing the curriculum.
To begin with, this course should be titled "Number Theory" not "Number Theory and Cryptography." Two lectures are spent on "Cryptography," with much of the focus on factoring algorithms. That being the case, the emphasis on Number Theory was interesting. Kerzhner is nice. There's no denying that. But he is not particularly clear as he teaches, and can tend to get annoyed when students arn't willing to participate. On the other hand, participation doesn't seem to be very important, as only 3-4 students attend each lecture. Lectures consist of the professor working through a proof or two, and the tactics behind it. It is interesting to get this insight, however the proofs presented are generally more difficult than those assigned during HW or exams. Overall, this professor is good enough, and besides the stutter, easy enough to understand. He's also willing to be a bit lenient, so one cannot complain too much. Course is mediocre, but not terribly difficult, especially if time is put into each assignment.
THIS MAN SHOULD NOT BE TEACHING. This was the worst class experience of my whole four years at columbia - yes, not just in the mathematics department, but overall. The class has NO organization, the lectures are horrible, and the book assumes that you should know more than what you really know - or at least assumes that you have a decent professor who will fill in the gaps. Unfortunately, Yakov is not that professor. Absolutely HORRIBLE. Never clear with his students - it made me think whether this man had any idea as to how he would teach the course, or if he just thought of the lectures each morning while on his toilet seat. there were 60 people who showed up the first day, and toward the end about 10 people who were scared out of their minds about the final. everyone else either gave up or dropped the class.
DO NOT TAKE A CLASS WITH THIS PROFESSOR! Ladies and Gentlemen I speak to you now from the bottom of my heart. Please, please listen to me, it is dangerous for your health to endure a semester with this man. No math, no matter how interesting or fun, is worth the stress and heartache you will have to endure from this man. He is a terrible, unclear, imprecise teacher. He will present the material in a harrowing and inconsistent manner and he will make you feel terrible for not understanding what is going on. I stuck with this class, because I wanted it for my major and the material was interesting but I tell you now, it has cost me a few years of my life. I implore you to heed my call and avoid this man at all costs!
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.
Lawrence sucks. While the other TA just wrote out proofs for you (which isn't good for your erudition), Lawrence was the exact opposite. Even if you've worked on a proof for hours, he'll rarely give you any new insight to help you get going. "Have you tried some small examples?" or "Maybe you should look at it harder" are standard repertoire.
Yogishwar is pretty good. If he has looked over the problem set before office hours, he'll know exactly how to help you. Most of the time he'll be willing to just write out the proof for you (which is stupid, because what are you really learning if you don't struggle through the proofs yourself). But when he isn't prepared, be ready to sit there in awkward silence while he struggles to come up with a solution. Generally worthwhile to attend his office hours because more often than not he is prepared. Also he is brilliant and funny, so go even if you don't need help with homework.
One of the best teachers ever. Cathy is organized, enthused, and just cool. Her lecture style is very fast--she writes everything she says on the board, so you basically copy it down and try to make sense of it later. Number Theory is an extremely abstract topic, but Cathy does a good job of motivating everything we do. Very accessible after class and during office hours.
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.