Introduction to Modern Algebra I

Dec 2020

As previous reviews have stated, Prof. Friedman is not human. His lectures move at a breakneck pace, and there's no way a mere mortal would be able to write so quickly; surely their forearms would cramp. The online semester actually saved me here, since I could go back and rewatch lectures at .75x, which still required pausing to write everything down. He is a good and incredibly thorough teacher; you'll never need to ask him to go deeper. There is a problem set due on EVERY Monday, regardless of exams or holidays, for a total of 14. These are long and difficult, but do enhance your understanding of the material and are sufficient preparation for exams. I didn't think the exams (2 midterms and a final) were particularly difficult if you did the homework honestly. Prof. Friedman does not use a textbook and instead typesets his own notes, which he uploads after most lectures. They are beautiful and incredibly thorough, and reading through them makes you question whether he is a human or a publishing company. I want to emphasize the pace of the class again. It was not forgiving, and he didn't even afford us the liberty of dropping the lowest homework. Gods like Prof. Friedman do not need to drop homework since they never have a rough week, but we mortals do. All in all, I did pretty well in the class, but I was decently traumatized.

Dec 2020

Explains group theory without a textbook in his own concise narrative. Lots of guidance written into difficult exercises on homework. His own typed-up notes are thorough and provided at the end of lectures that go over the material covered in the lectures. Overall, an excellent course on introductory group theory.

Dec 2020

This class was taxing. Is Friedman a great professor? Sure, he teaches the concepts well. However, as an earlier review said, he speaks faster than the disclaimers at the end of medicine commercials! In the words of a fellow student "Friedman's lectures are like drinking out of a firehose." Are you hydrated? Sure, have you also been drowned? Also yes. I feel like I learned a lot but he made the class over the top rigorous. The problem sets took years off my life. They were significantly harder than what you would expect from an intro to group theory class. As for his exams: the two midterms and the final exam were very fair but also incredibly difficult. Like the kind of exams where you recognize everything and then suddenly you're on part 7 of a question and you're entirely lost on how to finish it. I found the final to be extraordinarily difficult but that was because I was so exhausted by his class that I had no energy left to try. TLDR: Friedman is a nice guy, the class is like drinking from a fire hose, and above all this class reminded me to take my psychiatric medication every day :)

Dec 2019

Do not take Modern Algebra with Professor Siegel if you're someone who's completely new to group theory and the ideas behind it. Now, part of the reason I struggled in this class was because I didn't really try to understand the material from the get-go, so when it was time to buckle down, I was completely lost. However, that is not to say Professor Siegel tried to make the class easy. First of all, he graded our midterms with a guessing penalty on the true or false section, meaning that if you got the right answer, you got 2 points, but if you got the wrong answer, you got -3 points. The class was already hard on its own, but this guessing penalty just made it even harder to try to get a decent grade. Additionally, he tended to introduce new ideas and theorems in the homework without ever going over them in class. However, those same concepts would then show up on the midterms, meaning if you didn't get them on the homework, you were basically on your own. Finally, he did a really poor job with giving us answer keys for the homework to study. He would either post only part of the solution to the homework problems or blame it on the TAs, though all of the teachers I've had in the past have been good about posting the answer keys at a reasonable time. Some people liked Professor Siegel - I did not. If you don't want to be stressed out of your mind in this class, don't take it with him.

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 2016

I couldn't imagine a more straight forward class. Or a more clear professor. Friedman adheres to Chekhov's Gun Principle in all his lectures. He'll mention some tidbit at the beginning; you won't understand it. An hour will pass. You will have scribbled five pages of notes that seem to have no connection from one line to the next. Then with five minutes left, he fires Chekhov's gun, weaves the lecture right back to the tidbit he dropped in the first five minutes. And your newly-connected synapses will high five each other. You will realize pure math is beautiful. The best part of this course was stepping into deeper levels of abstraction week to week. Take quotient groups for example. You start with (Z/nZ) in an isolated case; you learn some rules for (Z/nZ), learn some proofs, and think that's it. Then three weeks later you learn about cosets and quotient groups and realize (Z/nZ) is just one instance of a quotient group. Sure, he could teach about general quotient groups then give Z/nZ as an example. But it's so much cooler to step back from your one example and have all the theorems make sense a month later. Chekhov's gun, people. He types up a great sheet of notes so about half the class skips lecture. Don't do this. He won the Van Doren teaching award for a reason; spending three hours per week in his class is worth it. I devoted every Sunday to the problem sets. The entire Sunday. Then I'd take any questions I had to the TA help room Monday morning; the TA from Taiwan is really great, though I can't remember his name. The problem sets are graded pretty harshly; expect points of unless you're perfect, another reason to go to office hours. I changed my major from CS to math because of this class. I'm taking his Algebra II course next semester as well because he is stellar. Take anything he offers.

May 2015

Friedman is a polarizing guy- just look at the all-or-nothing reviews below this one. Yet, I'm pretty split on him. If Friedman is (in)famous for anything, it's for talking faster than the disclaimers at the end of a medicine commercial. While this isn't untrue, he doesn't actually move through material as quickly as one would expect by counting his words-per-minute, instead drawing out the obvious and writing out every detail to the extent that his proofs are nearly computer-checkable. This isn't entirely bad, especially if modern algebra is your first real proof-based class, but it makes the class appear to move a lot faster than it does and there were some topics we didn't have time to do. For instance, we did very little with symmetries of geometric solids, which is traditionally an important application of group theory. The bright side is that Friedman is pretty devoted to this class. He wrote up solutions for the problem sets, posted review sheets, and held review sessions all to help us prepare for exams. I think he even knows my name but I haven't found a way to test this theory. The exams themselves are all straightforward. He sometimes takes ideas from the homeworks, so doing them is advisable just in case you were on the fence.

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.

May 2014

Modern Algebra 1 with Professor Neumann was a pleasant and fairly easy class (and I say that as a CS major -- math majors presumably breeze through), although it may be tougher in semesters where one particular student doesn't hold up the entire class with dumb questions. Neumann prepares well for lecture, doesn't make mistakes, and is reasonably engaging. He only kinda-sorta follows the textbook (Dummit & Foote) which can get frustrating at times, but normally he's just skipping the toughest material. He'll often provide lecture notes along with the week's homework assignment, and the homework often consists of things that are proved in the book, so just digging about a bit will give you the answer. That said, it's worth doing the homework to make sure you're familiar with the material.

Dec 2013

Anand deserves a gold nugget!!! He is the best professor I have had a Columbia. Modern Algebra is an awesome class, and Anand made it thoroughly enjoyable. This guy is a fantastic teacher, and seems to do his best to ensure that every student understands what's going on at any given point during the lecture before he moves on. Plus he manages to do it all without notes, which is incredible. He is very approachable, and I encourage anyone who takes a class with him to go to office hours all the time. I was always amazed by his ability during office hours to clearly present one way to prove something, and then find some other beautiful way to prove it that made it even more clear. But the best thing about Anand is how openly he loves the material, and I found his enthusiasm to be contagious. Overall, I totally encourage anyone to take this class, and I feel bad for anyone who doesn't get the chance to take it with Anand!

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.

Jan 2013

Professor Friedman is absolutely brilliant. So brilliant, that he lectures at an insane pace because he assumes that everyone knows exactly what he's talking about. Which is probably about right. The lecture speed takes a little time to getting used to, but maybe that's because he has so much material to cover in a semester. He mentioned at the beginning of the semester, if you want to slow him down, ask questions. The bane of this class is the problem sets. The problem sets are tremendously long and difficult, and if you leave it to the last day to finish, I can guarantee you will be emailing him about an extension. Definitely work in groups, and make use of the TA's office hours and the math help room. The problem sets are incredible though when you figure them out, and they contribute greatly to your understanding of the material. I cannot stress this enough. Some of the examination questions are based off material found in the homeworks. It's very crucial to study each problem closely before each midterm. Know your vocabulary. To the letter. The vocabulary is a huge foundation of the material and he begins every examination with definitions. Memorizing definitions goes a long way to helping you cope with the difficulty of this class. Friedman is very receptive during office hours and although it may be a tad intimidating speaking to him one-on-one because of his brilliance, he's very helpful and interested in each student. He is a fantastic professor, and if you are willing to put in the time and effort, you will come out with a greater understanding of algebra. If you're a genius at math you will probably find little to no issues with this class. But if you're like me and you're not gifted at math, then prepare to put in long hours into this class.

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.

May 2010

Best math professor at this school in my opinion. Quirky, but nice, and brilliant. Waited offsequence to take his class, loved it. It's clear that he really enjoys teaching. He works very hard at making sure you have an in depth understanding of a few key concepts rather than a general knowledge about a variety of concepts. He also makes the classes very interesting, and it's probably the only class I can honestly say I wasn't bored with at any point. It also helps that Modern Algebra is an awesome subject.

May 2009

Dave Bayer is a really awesome person and he will make you love math. Take his class! He's very accessible during his office hours and very good at explaining the material in alternative ways so that everyone understands.

Jan 2009

He's like they used to make 'em: a pure mathematician who understands thoroughly his material, with a British sense of humor to boot. He finds most appealing the concepts rather than the illustration of the concepts through examples. He thinks in theory. Thus the pedagogical approach is unusual, but in the end-- if you'll stick around to it and work hard-- he will make YOU a stronger mathematician, comfortable with hard proofs...

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!

Dec 2008

The man stands in front of the class for 65 minutes (he's always ten minutes late) and rambles on and on about topics. The classes are INCREDIBLY boring and I didn't get anything out of them. There is no text book. Instead, he writes out notes and passes them out during class. A decent amount of people grabbed the notes and left within the first 5 minutes of class. He throws in the occasional witty remark, but is pretty boring for the most part.

May 2007

Prof Neumann is the best. Really. He is always willing to help you out: answer questions before, during and after class and meet during office hours or at another time. He even scheduled an office hour every day of reading week to answer our questions before the final exam. He's also very pleasant and never makes you feel stupid, even if you are completely ignorant about a topic. I came to appreciate and love theoretical mathematics by taking this class.

Dec 2005

Dr. Friedman is an excellent professor who knows his stuff...however be warned! unless you ask questions, he moves very very quickly (so, stop him every once and a while and he'll answer your question without making you feel dumb). The homework is challenging but not mind-blowing. Expect it to take between 1 and 3 hours depending on the length of assignment (and how smart you are!) Most problems are straightforward (even the proofs). My only complaint with this course is that it is not curved, and the tests are very easy (the medians on the midterms were 91 and 88). If you make some stupid mistakes you quickly get bumped below median! (That happened to me twice.)

Feb 2005

Great professor, great class. Though his tone and accent are a little too soothing, he's very clear and understandable when teaching, both in diction and in content. More importantly, he's incredibly accessible outside of class. He will recommend other books if you don't like the textbook's approach, explain things several different ways until you're able to explain them to him just as well, and give leading hints to tricky homework without giving away the farm. He's a very understanding guy, and when I lost confidence in what I was doing towards the end of the semester, he wasn't a jerk when I'd go into his office with my homework done and say, "I did this, and it works, but I'm not sure how or why." To me, it seemed like he really wanted all of his students to understand what they were doing, not just mechanically churn out repetitive proofs week after week. In case you couldn't tell, I really liked Prof. Neumann and wish more professors were as devoted to teaching as he is. The material itself is interesting if you have the slightest logical leaning.

Jan 2005

A very good professor, knows his material very well, can lecture without notes, and is never stumped by a question. A required course for math majors, but not a bad one. Group theory is quite interesting. I would recommend this course even to those who do not have to take it. (Computer Science majors, for instance, would find it very applicable)

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 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 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.