[COMS W3203] Discrete Mathematics

Professor Cannon is great. While his lectures aren't always structured like they're coming from an outline you can copy down, they aren't boring and they do get the information across. The point of Discrete Math is to make you learn to think through problems, and few problems in the real world just appear in your head with a clear path to get you from A-B-C-D-E. If it were that easy, it wouldn't be a problem that you needed to learn how to solve. When he lectures, he doesn't just go A-B-C-D-E, he tries to get you to think about the process behind getting to E.

The class covered a lot of material very fast, and it definitely helped if you had a rudimentary familiarity with things like statistics, logic, and counting. But if you didn't he gave enough information that you should have been fine.

His lecturing style is a bit free flowing. He seems to have an ordered list of a dozen or so things to get through each lecture, and will work through them. He does enjoy occasional diversions to related topics. He clearly likes the material and manages to keep what could be a very dry topic interesting. He welcomes questions, and is one of the best professors I've seen at being able to explain concepts multiple ways when people don't grasp them. If you ask a stupid question, he won't sugar-coat his response, but he won't out-right mock you either. And in one-on-one interactions, he's great. Very approachable.

On the downside, he was usually 5 minutes late to class, and there was a very long lag time for homework to be graded and returned.

And he LOVES his definitions. Make sure to copy them down and memorize them for the exams. You'll need them both for the terms section and also for the proofs. They're the keys to the kingdom.

I have to disagree on most accounts with the below polemic on Adam Cannon. There are two separate issues needing to be addressed here. First, whether or not Adam Cannon taught the class well, and second whether or not it was hard and time-consuming.

I can say that I thoroughly enjoyed the class and, as usual, found Adam Cannon to be an engaging and witty lecturer. It is true, he wasn't on cruise control as he is while teaching 1004, but he was still very good. His explanations were intuitive and clear and he realized that most people taking the class had not had previous exposure to a higher level of mathematics. As a result, he time again emphasized and explained to us, the importance of thinking truly mathematically as it were. In other words, he taught us to recognize the importance and place of proofs in mathematics and stated that while examples are often helpful, they are simply not adequate to understand abstract concepts completely. He sometimes proved theorems which were not in the book, so be aware of that and occasionally makes notational mistakes on the board so don't be afraid to point them out as he often doesn't notice them afterwards. I felt lost in only one of the lectures which was the one on solving liner homogeneous and non-homogeneous recurrence relations, I don't know what happened there but it seemed like Adam Cannon was having a monologue with the board for 20 minutes.

In class, he asks interesting puzzles related to the material and will always give you an idea about the real-world applications of the concepts being covered. He is also just friendly and approachable. He has 4 office hours a week, which is more than most professors, although there is often a line so go early. Definitely go to office hours if you get stuck on the homeworks, he's more than happy to help. He'll rarely give away an answer but will certainly tell you how to approach any given problem.

For a Discrete Mathematics course I felt that Cannon did pretty good job. He was enthusiastic about the course material and was clear in his presentation of core principles in Discrete Mathematics. His proofs were simpler than the textbook's but they showed the basis for core theorems and for what he expects in proofs. Cannon was also able to effectively condense a 800 page textbook into only a notebook of notes. While the textbook is huge, most of the material in the textbook are proofs and there are only a 100 or so pages of actual definitions, theorems and algorithms that you need to learn. However,I feel that Cannon was irresponsible in frequently arriving late for lecture.

Cannon is definitely NOT a good discrete math teacher by any standard. In fact, he could possibly be the worst discrete math teacher at Columbia. Having had him for 1004, I thought he would be as a great a teacher at discrete math. He cursorily goes over TONS material which he seems not to have mastered well himself, but succeeds at covering it up. He assigns EXTREMELY long problem sets that are proof heavy. Attending class was a major time-sink as he would be late for class, his lectures were unorganized and his class examples trivial, not helpful at all when it came to doing the problem sets.Though discrete math is a useful class, I disagree it is the most important (as Cannon appears convinced) and he should be more considerate of this view.
The midterm for the class was fair, but the final impossible. Of the many faults Cannon's teaching style has, the worst is probably the fact that the final is cumulative, with approximately 700 pages worth of material--including over 300 vocabulary words and proofs--to know by heart.
Strongly consider taking discrete math with another teacher.

God, Professor Gross is wonderful. I want him to be my uncle.

That said... the class was really entertaining, not particularly hard, and basically lots of fun if you go to lecture. Prof. Gross is hilarious and obviously very smart, but he has the best, nerdiest sense of humor (read his quotes page to see what I mean: http://www.cs.columbia.edu/~gross/things_I_said.html) We actually did a demo of the birthday problem in class!!

The work is on the easy side, but laughably easy. It's a smorgasbord of fun, interesting stuff. This is DEFINITELY a recommended class for those of you who need tech electives.

Don't know why the CS department did this, but Abishek was a grad student when he taught this class. First time teaching.

Not the greatest teacher in my opinion; but for the first time teaching, not the worst. He stated repeatedly that he was limited by the lecture notes, that he was told by the Professor Gross to go straight from his lecture notes. Which he did. He did a decent number of examples, but he didn't do them very well, i.e. skipped a lot of steps. The concepts didn't really stick. If you wanted something clarified, however, he was very good at answering questions.

The things he covered in class often carried over to the test, but never to the homework. What the lectures were doing and what the book/homework emphasized were completely different. They didn't have much overlap.

He had abnormal ways of going about tests. He experimented with different ways to do review sessions over the web, i.e. TokBox, Google Wave. It was effective enough, I suppose. He answered the questions that people came up with, but it wasn't as easy to understand; it would've been easier if he did it on a chalkboard. Additionally, the way he grades: if you improve from the first test to the second test by at least 15 points, he'll take the higher of the two. But if you had higher on the first than the second, he won't change the scores. If he is your teacher, I would recommend going to class. Looking at the lecture notes tends not to be enough: he'll go into tangents, which he'll end up testing.

Haven't taken the final, but it seems he plans to curve to either a B+ or an A-.

He has a tendency to go a bit too much into his personal life. He's also always telling you good courses to take.

I'm definitely not the only student with a love-hate relationship with this class. On the one hand, much of the material was fascinating in and of itself (NP-completeness, probability tips and tricks, graph theory) and tied in well with 1007 material; on the other hand, I couldn't draw any connection between units and if I didn't understand one intuitively (which did happen) I never really got it (which happened more often).

Gross is great and I enjoyed his lectures, though they were at times dry. He really knows his stuff, and loves tangents about the material we're learning (almost all of which helped us understand said material).

I'm keeping the text and lecture notes, all of which I'm sure I'll dig out in a few years with intense regrets about not paying more attention during class.

A strange, infuriating, wonderful class. Almost certainly my favorite class this whole semester, but I can't quite figure out why.

Gross is absolutely brilliant -- there's no question about that. He just radiates a sort of aura of genius while he lectures. The class inevitably brings up questions about things that are peripheral to the course material: the incompleteness theorem, decidability, complexity, topology -- Gross can explain it all. But the CS department here is full of brilliant people, and none of them have (yet) inspired the same kind of reaction from me that Gross did.

His lectures and course notes are fantastic. Clear, concise, elegantly typeset -- you could learn all the material from only reading the online notes, or from only going to class and reading nothing at all. But Blaer is a great lecturer, and Allen's notes are just as good; again, I never looked forward to either of their classes as much.

He's digressive, but...actually, I don't think there's another lecturer in the department quite as digressive as Gross. And maybe that's the point. When your question about the well-definedness of negative moduli launches a fifteen minute discussion of how humans understand made-up words (and no answer to your question), you're learning. When you're treated to a lengthy description of the mechanisms used to solve the four-color problem or the Poincare conjecture, you're learning. The main content of his lectures teaches you discrete math, but the digressions teach you to think like a computer scientist.

I think CS students here have a tendency to underestimate the usefulness of this class. If you are planning on doing anything in real computer science (and to a certain extent, even software engineering) discrete math is absolutely crucial. If you can't put together a proper inductive proof, you can't do CS Theory, and you can't do Analysis of Algorithms. If you can't reason about graphs, then you'll never really understand what's going on in Data Structures or in Networks. I would have been helpless on the first Linear Algebra homework this semester were it not for the tools I picked up in this class...you get the point.

This is powerful stuff. Learn it from Gross.

Hui is a very good TA for Professor Grinspun. He held a quite helpful review session that clarified many of our questions about Midterm 1. Hui is willing to stay late to explain the subject for us, and is very patient with students. During office hours he is knowledgeable and clear. In my experience, Hui's grading of assignments has been meticulous, and assignments were returned in a timely fashion. Hui seems to be doing well in all aspects of his TA responsibilities.

Etienne is great. As a TA for Professor Grinspun, his performance is consistently above and beyond the call of duty. He routinely stays long past his posted office hours to finish addressing our questions, and sometimes holds extra office hours as needed (including after class). Etienne is one of the few TAs I've seen who actually takes the trouble to attend Professor Grinspun's lectures. The occasional course lectures he has given are as clear as the professor's, and it would be hard to improve on that level of clarity. Etienne's other responsibilities include writing the homework assignments. He is very good at making homeworks appropriately difficult (challenging but not impossible) and using homework to supplement the educational content of the lectures. He is also patient about clarifying our questions. The homeworks prepared us well for the exams, which Professor Grinspun wrote.

Discrete Mathematics, as taught by Professor Grinspun, is a CS prerequisite I am very happy to be taking. Professor Grinspun's computer graphics research is really cool, but that is outside the scope of this review. The main strength of COMS W3203 is clarity. Professor Grinspun's lectures are so understandable that I have not usually needed to read the textbook in depth. If anything, they are too basic and move too slowly, although there is plenty of time to ruminate on the materials in class. The textbook (by Kenneth Rosen) is also excellent, being both engaging and informative. The difficulty and pacing of the course changed relatively little as the semester progressed, a teaching accomplishment in itself.

The curriculum focuses roughly equally on proof-writing and problem-solving--a fair division, although I wish there had been more discussion of how Discrete Math can be applied.

The homework was where most of my learning took place, and it would have been a mistake not to do it as thoroughly as possible even if each assignment is only 4 percent of the grade. (Not everyone does their homework thoroughly.) Homework is ABSOLUTELY ESSENTIAL for preparing for the three exams, which are long and complicated exercises in problem-solving and proof-writing speed. As a warning, almost no one could finish the second midterm exam. This includes some of the best remaining students. Fortunately, the exams' open-book nature and the grading curve meant they were actually easier than exams in many other classes. The 6 homework assignments were 9 to 20 handwritten pages each, and each one usually took me 10-20 hours to finish. Many questions were difficult, and office hours often saved me.

This course has a high attrition rate--perhaps one-third to more than half of the original students choose to drop it after the first lecture, including some of Columbia's best and brightest. There might be several reasons for this. Professor Grinspun calls on students unannounced and does not hesitate to embarrass them (although I never saw him embarrassing anyone unprovoked). Homework 1 was as difficult as the other assignments, which may have led some students to believe the course would be more demanding than it actually was. The heavily proof-oriented nature of Discrete Math may also have scared off some. In my opinion, DROPPING THIS COURSE INSTEAD OF PRESSING THROUGH IS A TERRIBLE MISTAKE. My experience was that around week 4 of the course, proofs suddenly became less intimidating and around week 5 or 6, Professor Grinspun mellowed out. What students contend with is a not especially time-consuming commitment, as CS courses go, and possibly one of the 5 best undergraduate courses in the CS department. I enjoy it, and would strongly recommend it to students with the appropriate background (some introduction to programming such as COMS W1004; pre-calculus or, better yet, calculus; and, if you're really concerned about writing proofs, the supposedly well-taught Introduction to Higher Mathematics).

Great course. Makes a somewhat dry subject incredibly interesting. Very lively lecture... one of the few CS classes I really have enjoyed attending. If you can take this class with Grinspun (he tends to teach in the Spring), so do.

Homework is difficult, but not extraordinarily so. Midterms are very difficult, as they are open book so they test not what you could memorize but how adept you are at solving the problems. It is also possible to recover from a bad midterm... I nearly aced the first midterm (missed one or two points), but the second midterm I don't think I managed to get more than 20/90, but with a decent score on the final I still ended up with an A-.

Not to mention, the questions on the homework and exams are actually somewhat fun (interesting questions, not dull or boring ones for the most part), which is always a plus.

Gross (pronounced the way it's spelled) is a guy devoted to his work. He's decently approachable in class (especially if you're in the 10 or so who actually go) and he's full of fun stories.

He wrote the study-guide for the book that you'll use.
That book actually is pretty good and I'll be keeping it for future reference.

The stuff you'll be doing will be probability, recursion, recurrence relations (kind of like ODE material at times), relations, and most fun was Graph Theory.

Gross tends to like tangents especially if they relate to his line of work - Graph Theory. The amount of material this guy knows is simply astonishing and he delivers it well. If you can imagine a sweet grandfather figure that would likely be Jonathan Gross. Unfortunately you're either so bored because he goes through the material so slowly or you're bored at his new anecdote.

Take this class. Its average but worth your time.

Good professor overall. Entertaining in class, made a potentially dry subject quite interesting. Overall workload easier than one would expect; while each HW assignment was reasonably challenging and lengthy, there were only 6 of them in the whole semester. Material was pretty easy, and it would have been useful if we could have moved along a bit faster. Midterms were challenging, but were also open-book which means you wouldn't have to memorize stuff.

Recommended, but they should probably make the class a bit faster. And maybe spend some time showing where the knowledge can be applied.