MATH V3386

A few very long problem sets assigned the first half of the semester, all graded pretty leniently by the TA. A midterm and a final. The midterm and final had a lot of pretty straightforward but long and easy-to-fuck-up plug and chug type problems (finding metrics, curvatures, Christoffel symbols, lengths, and areas), interspersed with a few really hard problems that probably no one without some previous knowledge of the topics got. Grading is generous, but nothing is assured.

I had really low expectations coming in to this class given the previous reviews, but I thought I'd give it a shot since I'm really interested in differential geometry and it ended up being the only math elective I could fit in my schedule. I can at least say it wasn't as bad as I expected. In fact, I'd say the first half of the class was just like any math course and Hamilton was on the ball. He would come in and lecture, regularly put notes up on courseworks, and assign really long problem sets that I thought I got a lot out of. After the midterm however he didn't assign any more problem sets and I (and many in the class) slowly drifted away from any idea of what was going on. As far as the content: one big problem was that there was no syllabus or outline of the course, and the book he assigns is pretty random; it is very hard to make any connection between the book and his lectures. The order in which he presents topics is actually very logical, but I have not found any book that does it this way. It was like we started from the middle of most books with Reimannian metrics, and worked our way back. Most books start with curvature, which didn't come up until the end of the course. My friends and I used several references throughout the semester, and I think the book closest to Hamilton's treatment is "Elementary Differential Geometry" by Pressley, which really isn't that cl…

No homework, no exams. Everyone got an A.

I read the review from the poor individual below who is reconsidering his or her career goals as a mathemetician because of taking Hamilton's class, and I had to offer encouragement (I hope that person is reading!). True, Hamilton is a great mathematician, but his talent has little or no bearing on the class because he doesn't apply himself to the task of teaching undergrads. Maybe he's used to teaching grad students who sort of know what he's talking about already and who are motivated enough to do work on their own, but he lectures at such a high level that we were completely lost, with no textbook to help guide us and no collected homework to test our understanding. There is a reason that every math class you've ever taken had regular homework assignments and at least one exam: you learn by doing, and I for one did no work for this class (besides taking notes) and got a meaningless A. Hamilton is a nice guy and an important mathematician, but when someone gives you a job to do, you should at least try to do it right, and he completely blew off his responsibilities as a teacher for this class. If you got nothing out of DiffGeo, don't blame yourself, and don't be discouraged; I got nothing out of it either, and I still plan to become a mathematician. P.S. For a real class in Differential Geometry, try W4081, Differentiable Manifolds. You may want to take Topology first though.

So far as I can tell, there is none. Let's hope it stays that way, and we all get free As just for attending the lectures.

It's hard to explain what taking a class with Prof. Hamilton is like. On the one hand, you are given the incredible privilege of learning from one of the world's greatest living geometers. On the other hand, all that you will learn, really, is that mathematics is probably the most difficult field of inquiry to pursue, period. Coming into this class, I had planned on becoming a mathematical logician of some kind. Now, I'm not so sure that I can handle a career in mathematics at all. If you thought that "AP Calculus" was a hard class, I strongly suggest that you steer clear of Hamilton's "Differential Geometry" class. Hamilton is one of the most brilliant individuals I have ever met, and if you have an appreciation for analytical skills, in every lecture his will blow you away. Each meeting of the class is a problem-solving tour de force that few if any of the students appear to follow throughout. Indeed, the problems are sometimes so involved and complicated that even Hamilton loses his train of thought, causing him to pause for a few minutes while he attempts to work through the whole problem again in his head. Approximately twenty-four students signed up for the course initially. Today, there are fewer than ten students remaining, and two of them are well into their forties. That is a vivid reflection, I think, of the intensity of the lectures, which are often much too intens…

Not much, which means YOU must do problems on your own. This is what being a student is about after all!

Man, there are sure a lot of whining little babies on here complaing about Dr. Hamilton. Bottom line, Hamilton is a genius who loves teaches, gave his time to students, and unlike too many other faculty in Columbia completely devoid of pretense and snobbery truly worthy of punishment. If any student did poor, it was because they were simply lazy and didn't take the steps to amend any problems with understanding material. That said, it is true that Dr. Hamilton did not follow the text or assign regular assignments. But he did follow an outline that students had, and moreoever he gave ample references of books to either purchase or take out from the library and gave what I consider to be the best advise to any student: Study on your own and do as many problems as you can stand and then some! You learn math by doing it. These accusations of him being a disorganized and unclear lecturer are simply outright lies. Some professors truly fall into that category, but not Richard Hamilton.

What workload? He handed out two problem sets, neither of which he made any effort to collect, and a single midterm near the beginning because he was thinking about giving two but was too lazy to make up a second one.

This man is apparently one of the most brilliant geometers in the world, and he is also a very nice guy. Put him in front of a chalkboard, however, and horror results. He never prepared any notes or xeroxed our problem sets for us, or ever handed anything back! I'm still waiting on a problem I handed in a month ago and a midterm I took at the beginning of October! His lectures are a mess. He just stands in front of the class solving equations without giving any explanation at all about what the terms he is using mean. He usually gets lost near the end of every class, and spends the last five or ten minutes trying to figure out where he made a mistake. He only successfully proves about half of the theorems he presents. And he's been teaching this course for years, not to mention that this is his field of research. The fact that he picked out such an awful waste of money for a textbook when there are so many fantastic differential geometry books out there indicates his enormous lack of interest. For some reason the math department also unleashes him on the freshman in honors math, many of whom tell me that he scared them away from math completely! This man must be stopped before he does further harm to the young minds of the future.