I read some of his earlier reviews, and I am slightly disappointed by how many great professors get bad reviews for not teaching Calculus well to students who probably take the course hoping for an easy A, but end up getting disappointed when the professor actually makes the class challenging.
Anyway, I took Algebraic Number Theory with Prof. Fedorchuk, and so far it has been one of my favorite courses in Columbia. This class was at 9am, and I never wake up on time for 9am classes. But, I attended the lectures regularly, which is a fair indication of just how good a lecturer Prof. Fedorchuk is. Even though we had a great text for this course, and Prof. Fedorchuk followed it pretty closely, yet his proofs were often shorter and clearer than the ones given in the book. That in itself says a lot, as we were following a book by a master expositor. What I liked about his lecturing style was that even though he prepared notes for himself for each lecture, he rarely looked at them while he lectured. This meant that his lectures were less mechanical. I think this was one the few times when I took a class where I felt I actually got something out of the lectures. More often than not, I have taken classes where I spent time reading the material on my own rather than attending the lectures. Prof. Fedorchuk always lectured at a comfortable pace, giving us enough time to copy whatever he wrote on the blackboard. This was fortunate as we were in a classroom with only two boards.
I have seen a few professors who get flustered when they realize that they made an error in their lecture notes (which is understandable because it is hard to rethink a proof when you are lecturing and are under a time constraint), but on the rare occasions that this happened with Prof. Fedorchuk, he always managed to rethink the proof within a few minutes, sometimes taking suggestions from students. This shows that he knew the material well, even though, to my knowledge he does not work in Algebraic Number Theory.
He encouraged class participation, and was very patient with students when they asked him questions. Another of his qualities is that he is very approachable and friendly, and always asks students how they are doing. This is really helpful, as it makes it easier for students to approach him with questions. He also gave us extensions on home works, which were moderately difficult, but built on the material in the lectures. He often went through the more difficult problems in class, before home works were due. Perhaps the only shortcoming of this class was the TA who was too busy completing his Phd thesis, and so failed to grade home works on time.
His exams were fair and computation based. I previously had professors who gave proof based questions in their exams, so I was a bit startled by the midterm, and did not do well. But, he was understanding, and told me to do well in the final, which I did. His exams are not difficult if you have been paying attention to what he teaches in class. Most of the computational questions he gave were variations of problems he had explicitly solved as examples in class. His exams were also open book, which though not a huge advantage for a 75 minute midterm, is quite helpful in a 3 hour final. It meant that we did not have to memorize some complicated formulas. That makes sense, because Algebraic Number Theory is an upper level undergraduate course, and unless you work in this field, you will end up forgetting those formulas anyway. And, if you do end up working in the field, you can always look up the more complex results from books. No mathematician can remember everything that he/ she reads.
All in all this was a great course taught by a very intelligent professor. Prof. Fedorchuk wanted us to get an understanding of what Algebraic Number Theory is all about, and I think he was successful in his goal. The course has inspired me to take the graduate Algebraic Number Theory course in spring. I just wish Algebraic Number Theory were a two semester course so that I could learn from Prof. Fedorchuk. I know he will be leaving Columbia next fall, which is unfortunate for Columbia as they will lose a great teacher who cares about his students.