In short Mike Miller is the most committed, kindest, and one of the smartest professors I have had at Columbia. Although our topology class was no joke (especially the algebraic topology section), I ended up learning a lot. The problem sets and curios were something I got to look forward to because they were designed to teach you a lot of the material and ensure you actually knew how to apply these problems to new and difficult situations. My only advice would be to add some easier problems at the start of a problem set just so we can get used to new concepts and definitions since the problem sets always looked very scary at the beginning. However, Professor Miller was always available on the class discord and his office hours were always immensely useful so I never felt stressed about the problem sets. The midterm was well-structured and I ended up learning a lot from the midterm. We were given the option to choose a final project and a final exam. I found the final project to be quite a bit of work but it definitely felt like it was the better option in comparison to the final which would have a lot of algebraic topology and some manifolds. I think the algebraic topology section was a bit too fast-paced for a lot of us. I also think part of the reason why I found it more difficult was because I also had to focus on a final project on a topic not really related to algebraic topology.
The review about 30 hours per week below is no joke! Sometimes even more. But I would say he is really a great professor if you want to learn the material. Sometimes I put in more work and learn less if I have a bad professor but not in this case at least I can say
I am completely new to the topology and I study so hard to catch up with him. I did get great scores... but in order to get great score, I spend 30 hours per week on his stuff. this is ridiculous. And I am pretty sure almost all of my classmate, except one or two who had learn topology and even did some topological research before, were confused and cannot stay with him. I can tell from the last minute question that they ask before the midterm--some of the questions are fundamental (still hard for a neophyte) and they still have trouble with those trivial things(relative to what Dr. Miller give us in the HW and practice exam.) Just let you know. The class begin with 40-ish people after 2 weeks of the shopping period. but now( 10th week?) we only have 23 people in the class. think about it my friend. And by the way, one of my friends, a math major at another Ivy League U, told me that getting to homotopy and stuff in algebraic topology within half a semester is really crazy. it took him 2 and a half semester of topology course to get there. this instructor really need to reschedule his syllabus. But I had to say that he is friendly. And he is very available if you reach out. Just keep in mind. He is so smart. If you are not so sure weather you are ready to take his topology class... then it's very likely that you are not ready. Be careful. As something would cause you several hours to figure out but those results are trivial for him.
Easily the best math professor I've had at Columbia. Assigns a decent amount of work; however, is incredibly devoted to making sure students understand the material and incredibly kind. He wrote probably pages about my proof style etc in response to my midterm and gave very specific reasoning when I was wrong. Additionally, gives guided proofs that he calls "curios" that take you through some interesting implications or alternative definitions of material in class. He never checks or asks if anyone does them so they really are optional, not like "optional," but they're very interesting and rewarding. He also gives helpful visualizations during lectures and talks frequently about common practices in math, textbook choice, etc. He's incredibly available as well. At least this semester, Fall 2020, when most of us aren't on campus, he set up a discord server for the course for him to answer questions outside of Office Hours and he's incredibly responsive and helpful. It has made me feel much more comfortable to ask questions and it means when you want to ask a question outside office hours, you don't need to construct a somewhat stilted email because it's a bit of a more natural format for questions. I also highly recommend going to his office hours because he's really not at all intimidating and is very approachable and often even if your question is somewhat outside course material he'll have interesting reading suggestions, e.g. I went into talk about whether a theorem about unique limits could be more generalized (not really) and he gave me suggestions for readings about some topological properties we'd not talked about in class but were relevant to the problem and then some problems in a textbook that were also helpful. In this specific instance I learned about the "long line" which is now a favorite topological space of mine! I really cannot recommend enough Professor Miller, at least for topology. If you're a math major and you get the opportunity to take his course you really must.
Take Professor Miller's class if you need a Calc III class! I went into this class very hesitantly, having had bad experiences in Calc I and II. I took this in summer 2020, and I can honestly say that I enjoyed this class, which was something I couldn't say of my other college calculus classes. I asked so many questions which I thought were stupid, but he always answered them non-judgmentally, which was really nice. Additionally, he responds to all your questions very quickly regardless of the time of day, gives not one but TWO practice exams with answers for each midterm and the final (as a reviewer below said, if you can do them you'll ace the exam), and increases office hours to almost every day of the week during exam periods (he usually has them three days a week for an hour or so each). Also, his questions never trick you. They'll make you think, but never cry because you can't understand a question. Also, his homeworks are graded on completion only, so if you do all the problems and don't completely bullsh*t them, you'll get a 100%, and still get very detailed comments explaining any errors. On top of that, lowest homework is dropped. I took his class summer 2020, and all the exams were open book and open note. This man deserves his CULPA gold nugget.
He is absolutely the best professor I ever had in Columbia. He is funny, very detailed in class. He is literally so nice, and so patient, it's beyond belief. I literally bugged him with questions 3 hours before the final, and he explained everything to me. He is very understanding of student's situations and really wants you to learn. He is so good that I felt like crying after the class was over. I understood everything in class (which is extremely rare in my case). He kind of gives like AT LEAST 10 questions (usually more) for the weekly homework, but they are really helpful in mastering the content of the class. He gives a couple of practice midterms and finals, which is very similar to the actual tests, so if you do the practice tests, it is very easy to ace every test. He even responds to emails at 3 at night! HE IS SERIOUSLY THE BEST! IF YOU WANT TO TAKE CALCULUS III, HE IS THE PROFESSOR.
Took Calc III with Professor Miller Such a lovely professor Extremely approachable and responsive (responded to my 2 am email in 10 mins) Definitely take him!!!
A new professor but he is worth of a gold nugget. Clear teaching, clear notes, easy hw, easy tests. Most of my friends got a 100% until the final (which is a bit harder but not impossible). A very nice and caring person as well. Take his class if you're just doing it for requirement. His class might be too easy for quantitative majors.
Mike Miller, (aka Stephen Miller on the directory), is amazing. His sense of fashion transcends all other worries. He is a pretty good math teacher. He doesn't teach us material he doesn't think we need to know, so that's pretty cool. His workload is average and midterms are average. I think he's a solid choice because he is very very approachable. If you email him a question, he will respond with a full page answer within 24 hours. He's sweet, kind, volunteers at central park, and more.