Introduction to Modern Algebra II

May 2021


May 2021

I love her. She is the kindest professor at this school, and also the best one. Take any class she teaches and give her a diamond nugget!

Apr 2021

Well-structured lectures, well-designed and not too bad weekly psets (we often use results from previous homework in the following class). Perhaps the psets are not overly challenging, but very well suited for a CS person taken this for fun. Very nice, charming, and young professor. The only thing I wish for is some bigger picture aside from abstract theorems, like history and how the theory is developed. I know about the story about Galois (which is the main reason I took the course), and really'd like to learn more about the motivations when the theorems are introduced.

Apr 2021

She is amazing.

May 2017

This class was challenging yet enjoyable. Thaddeus is very thorough, goes at a good pace, and manages to be quite entertaining. He is very clear and efficient in the proofs he gives and draws nice diagrams where appropriate. Where the material was more challenging, e.g. Galois theory, he slowed down to give lots of examples, which was helpful. He tries to encourage participation, which may or may not have been successful, and answers questions effectively, both in class and during office hours. In fact, if you knock on his door anytime, he will take the time to answer your question if it is not too long. My only complaint is that in Algebra I we spent a bit too much time on introductory material (propositional logic, equivalence relations, elementary number theory) so that midterm 1 did not cover groups at all. Nevertheless, probably the best professor to take Algebra with. Everyone in the class really liked him; a lot of us are going on to his Topology class next semester.

May 2015

I can't shake the feeling that Khovanov was a dud. I like the guy, he's sweet, and actually incredibly smart. Look up "Khovanov Homology," he's done a lot of ground breaking research (somehow being used a lot in String Theory). As a Modern Algebra instructor, though, he fell pretty flat. Modern Algebra I is trivial for anyone who's been exposed to a group before. It was weird, somehow it didn't feel like we were ever really doing anything. I think the only interesting stuff was Burnside's Lemma (and group orbits in general), the Sylow theorems and the classification of Abelian Groups. I realized that I was doing fine in the class, but that was just because I had a good idea of how groups worked, not from anything I learned in lecture. The way Khovanov speaks makes it impossible to pay attention. It's not exactly his accent, I can always make out what he's saying at any given point in time, but the way he presents things is just bizarre, and I can't quite explain how. I had no problem paying attention in any other class except for his. Every time I tried to I would lose the thread after 5 - 10 minutes. By the way, this isn't just me: everyone I talked to in the class had the same experience. Modern Algebra II is pretty bizarre. It definitely had a lot more content than Modern Algebra II, going briefly over Ring Theory and then spending a lot of time talking about Fields and Field Extensions, and then finally Galois Theory (apparently there's more to it than the unsolvability of the quintic, who knew?). I was excited to learn about Galois Theory, but now that the course is done, I can't honestly say I have. Sure, I understood the results, as they weren't too crazy, but I didn't really understand the process. The homeworks and tests really only test you on the results. I basically learned exclusively from the textbooks / Friedman's notes, as I wasn't able to pick up anything from the class itself. It's not hard to get an A in Algebra II, but it is pretty hard to understand all the material at a good level. Maybe it's just Khovanov, who knows? When the TA came in to teach as a substitute a few times, it was like the clouds opened up and I understood everything. The weekly homeworks aren't so bad, a lot of them are pretty easy, some of them use results proved in class which make things a bit harrier. The quizzes are all true / false, a few tricky ones, but not THAT tricky. The midterms were pretty easy, but the final wasn't that easy, not because of the questions, but because I had such a poor grasp of the material. So... Algebra... A bit of a let down, not gonna lie.

Dec 2013

Walter Neumann is a really approachable professor who will take time to help you out if you do not understand class material. His exams clearly follow his notes and if you study hard enough, you can scrape by with at least a B regardless of your level of ability. Each problem set he assigns comes with an Extra Credit problem, and if you rack up enough of those (provided you answered them correctly) I think your grade can get bumped up by at least 1 threshold (think B to B+, B+ to A-, etc) Modern Algebra I and II are hard. They demand your time and attention, and Neumann explains the subject well. My only criticism of Neumann is this: he seems to base his lectures on the Dummit & Foote book, but does not follow the book explicitly. This drives me crazy because, having read the book as a study aid myself, I can say that the book is an ENORMOUS help to those who have trouble with M.Algebra, though Neumann seems to dismiss it. I say this is a 'criticism' of Neumann because the way he explains things is not for everybody, and it would've been very helpful to a lot of students in his class to have followed the book, instead of simply trying to absorb Neumann's notes, hoping for the best.

Apr 2012

Many men, mere mortals, have wondered whether Robert Friedman is human, divine, or something else, something more. While we may never know, it hardly matters. Do not – I repeat, do not – miss the opportunity to let this man's radiant brilliance shine forth upon you. Much like, having fallen into the ocean, it is impossible to emerge dry, it is impossible for you not to have become a substantively better human being in every possible respect upon leaving Friedman's classroom after your final exam. Not only will you be an incredible mathematician who will probably solve the 6 remaining Millenium Problems (Friedman already has, he just has no interest in publishing the solutions since he uses them on his problem sets), but you will have the strength of a wild ox, the speed of a cheetah, and will never need to sleep again. I should mention that I told a small lie. You and I can't emerge from the ocean dry. Friedman can.

Jan 2011

Dave is one of the stranger teachers I've ever encountered. His enthusiasm is tangible due to his tendency, as he puts it, to wear his lectures (by the end of each class his clothes and face are invariably covered in chalk dust). His lectures are often hard to follow, which is my one real criticism. He tends to act like he's about to present a theorem, then feint away to an example. Examples are, in fact, his trademark. He believes that it is better to have a handle on a few small examples than to learn all of the abstract theory without knowing how to work with algebraic objects. Perhaps as a result of this, there is no homework. The first semester, he posted a few suggested problems for each topic, but the second semester was much more experimental. To prepare for each midterm, we were just given a selection of old exams and old practice exams. The key, however, was the problem sessions in the week before the exams. In these sessions (which will go until there are no questions remaining) he works through these practice questions, which are just like those on the test, and you will see exactly what he's expecting. The first semester had about 50 people. The second semester had less than half of that, so class got a lot more fun, and he would interact more with the class, posing questions directed at our intuition followed by the inevitable "Why?" to which a satisfactory response need not be perfect; he's seeking to develop a general style of mathematical thinking, so a one word answer may sometimes suffice.

Jan 2009

Seeing as there are no reviews for Bayer's class on the Algebra sequence, and that he's teaching the off track again this spring, this seems necessary. Bayer is a phenomenal teacher but certainly not orthodox: you will not have the 'textbook on the board' style. His lectures are simply inspiring, illustrating not just the many connections in areas of math but also important historical and philosophical development of math and invaluable insight in how to think like a mathematician. Take this course sooner than you think, you can handle it (after calc + lin alg). However, you WILL NOT learn algebra just from him, as he assigns no homework. This might lead to apathy, but if you read the book and do a few problems along the way, you'll have as good a grasp on algebra as the kids who took Gallagher or Neumann's courses. He's using Artin's Algebra, but I also recommend Herstein's Topics in Algebra:take this course!

Apr 2005

As most of the other reviewers have already mentioned, Friedman is one of the clearest and most concise math professors I've had at Columbia. Positives: explains things very clearly and to-the-point, proofs are SO clear because he talks about every step and reasons them out instead of spilling math diarrhea onto the board. Negatives: writing can be hard to read, moves quickly on topics in class, has a tendency to stand in front of whatever he's writing, and then when he moves away he's on the next part of whatever he's talking about. Overall seems like a really nice guy, will occasionally throw things in during lecture about algebraic geometry (his research), and makes the material interesting. Would take another class with him.

May 2004

Professor Neumann means well. He's a nice guy who wants us to learn algebra. Unfortunately half the class never comes to lectures, and the people who come are all dozing off. Neumann is a mediocre teacher - not excellent, but he knows his stuff, knows English, and tries. I was a bit sad that though he was available for office hours and such, he wasn't very helpful - not wanting to just tell me the answers but also not really being good at indepth explaination, he pretty much gave me a slight hint and told me that I'll get better at it if I keep at it. He paces a lot during lecture, which is kinda annoying. The tests are pretty fair (not easy mind you, just fair)- the homework is very time intensive and hard. Personally, I spent a lot of time in the Math helproom, and I saw A LOT of our class there on a regular basis hehe. He grades according to what you did - he won't screw you, but also won't inflate your grade.

May 2004

The subject material is very, very interesting. The professor is very, very boring. However, the textbook you use is enough to learn everything for the course- you DO NOT NEED to go to class. You just need to go to hand in homework and take tests. The subject is still worth learning even if you just read it out of the book. The professor is very, very, very, very boring. The tests and grading are very fair.

May 2002

If you are a (prospective) math major, or just a lover of math, you NEED to take a class with robert friedman. if not, run far, far away! as a fellow number geek, robert friedman rocks my mathematical world. his lectures are engaging and interesting...he goes at a very fast pace, but thoroughly covers the material. he is a fair grader and his exams are straightforward and almost predicatable. if you put a lot of effort into completing and really understanding the homework, you should easily do well on the exams/in the course, since generally the homework is much more difficult than the exams. highly knowledgeable and somewhat quirky, friedman is an excellent prof. although, i would advise any one who is not a math major/who has no interest in mathematics to avoid friedman at all costs.