Worth noting before taking this course is that it is mainly taken by graduate students. This has pros and cons: the main pro is (perhaps) that there are a lot of students in the class who don't really seem to care. Sometimes this may be because some of their English isn't stellar; the main con, however, is that this might also be because they already know the material really well. No matter, though, because honestly this was one of the easier classes I have taken here at Columbia. The material totally has the potential to be really hard, but there is a solutions manual that you can Google for the homework, and the exams were the easiest exams I have taken since high school, no joke. They were almost offensively easy. BIG BIG BIG word of advice: Sobel never says this in class, but he will ask A LOT of definitions on exams (literally 25% of the final was f***ing definitions). DEFINITELY know the axioms of probability, that was asked on both the midterm and the final. Sobel himself is not the most personable man you will ever meet. He tended to be really snappy when people asked questions in class, unless of course you're an attractive female. Moreover, he is honestly an awful teacher. I learned approximately 0% of the material from actually attending class, and ended up teaching myself all of the material, which, I reiterate, was honestly not too bad. In class he tends to do a lot of proofs of theorems that we will never use. He does them in a really handwavey way - which might sound appealing to some, but he isn't GOOD at being handwavey, so it just ends up being confusing and annoying. Please don't take my negative review to mean that you shouldn't take this class. This is honestly a great probability class to take if you want a pretty easy grade and are willing to spend some time near exams teaching yourself the material. I know for a fact it was much easier and less work-intensive than 3105 and the IEOR probability class (I have friends that took each of those at the same time I was taking this who confirmed this testimony).
My comments on 4109 in general as well as this particular class: If you can avoid taking 4109, do it. At all costs. Take 4105 and 4107. Not only will you have a more diversified group of students and therefore a more normal distribution of grades, you will have more time to actually learn the material (it's a lot!). In any given 4109 class, you'll find about 85-90% of the students are Chinese, half of which have already taken the material (maybe not all, but a majority of it) in their undergrad program. So don't plan on getting an A in this course unless you already know the material walking into the class on day 1. It's possible, but very difficult. Oh, and then there's the cheating. The MA Stats program is rife with cheating (the Chinese!), and this class was no exception. In every quiz or exam there was a constant flow of whisperings in Mandarin. Some of the more cavalier students even took out their cell phones to search topics or formulas during the actual test! Also, if you don't sit in the first few rows of the class, expect to want to punch half the students around you for constantly chatting (also in Mandarin). The professor can't hear them beyond the first few rows, so unless you mention the issue to him he won't do anything. My comments on Victor: When you boil everything down, Victor is considerate, fair, but a bit disorganized. The lectures consist of him putting his hand-written notes, many of which are riddled with errors, up on the projector while he simply talks through each page. I don't mind this teaching style but, on top of all the errors, his notes don't follow the book (from which I had to base my learning). The homeworks are what help you understand the material, but his quizes/exams are based on his notes, so there will often be test questions that you haven't had any opportunity to practice or understand fully. Another annoying point was that if he deviated from this typical lecture plan, he would often confuse himself, then call a 5 minute break while we, the students, had to explain to him what he was trying to do. He would often say, "I don't do math in public". Many students, including myself, often walked out of a lecture more confused about a topic than when we walked in. Summary: Professors are humans (surprise!), and they make mistakes too. Victor made some mistakes throughout the semester, but we brought them his attention and he tried his best to correct for them. That said, take a different professor. You'll save yourself from a lot of anxiety.
As an undergraduate who took this class for practical reasons, I can say this: if you are not excellent at either statistics or rigorous math, expect a low grade in Davis' class (in the B/B+ range if you work hard). This is particularly painful because it's a six-credit class. That being said, if what is important to you is to understand the material thoroughly, and you're willing to suffer a little and get a low grade- take this class. Prof. Davis is an excellent lecturer. He teaches more or less out of the book, but is very clear and his examples are great. He also covers an unimaginable amount of material- partly by filling every minute of his three-hour lectures, and often going 5-10 minutes overtime (which can be exasperating, but I appreciate the fact that he's giving his students their money's worth). So after this class, you'll definitely feel that you've learned a ton. It should also be said that Prof. Davis is very nice and approachable. He has a kind of dry humor that may sound like a put-down, but he really wants his students to do well and was open to ideas. In this section (not sure if this is always true), indeed the vast majority (around 65/70 I'd estimate) were grad students in statistics, which definitely threw off the curve and made it very hard to get anywhere near the average on tests (not to mention homeworks, where the average was probably in the high 90s). So you're really on your own in this class: you can't count on the curve. The curve itself is generous- I think the lower bound for the class is a B-, even with horrendous scores- but the effect is to more or less set you in the B range. Homeworks were due every class, which was very difficult for the Thursday class. Usually the homework was around 30% easy questions, 30% straightforward but needs some working out, and 30% hard. If you go to the TA's office hours, though, you shold be able to do it all. The midterms and final were very tough, but more because the material is hard than due to Prof. Davis' own questions, which often relied on things straight out of the book. One final note on the TA, Diego: He is amazing, really the perfect TA. He was unbelievably helpful, often answering questions by email and once discussing something over his lunch break. He knows the material back and forth and always tries to make sure you understand the process. He's nice and also gives tips for how to do well in the class. No matter what course you take, if Diego's the TA- it's your gain.
hI recommend taking this class with Professor Davis only if you are a master's student in the statistics department. The class is comprised almost entirely of master's students from China, which meant all the communication between the students in the classroom was in Chinese. It was class that this wasn't their first course in probability and statistics, despite this course not having any probability or statistics prerequisite, and this made the course very stressful for the few of us who were trying to learn the material for the first time. Lectures for this class went from 6:10 - 8:55 on Tuesdays and Thursdays, but Professor Davis usually ran about 10 minutes overtime. At the beginning of the semester, the lectures were completely understandable for students who didn't have background in the subject, as the material we covered at the beginning was simple enough: axiomatic probability, counting methods, conditional probability and Bayes' Theorem, continuous and discrete random variables ,and expectation. These were more or less the topics covered before the first midterm. The homework, which came straight out of the book for the entire semester, was very simplistic, with at least half the problems being silly and pointless one line computations. In other words, there really didn't seem like there was anything to worry about. Homework was assigned and due every lecture, but it wasn't challenging enough to concern anybody. That being said, almost everybody received 100 on every homework, so the only way homework could impact your grade was negatively (by getting less than 100). Then came the first midterm, which he said he was writing to take 90 minutes, though we would have the entire class period to eliminate time-pressure. Most found the exam quite challenging and long, with 8 problems, each of which consisted of 3 to 5 parts. Not a single student finished in 90 minutes; in fact, the entire class sat for the entire class period, and many of us still felt pressed for time. Before he handed back the exam, he tried to reassure us by telling us that grading is relatively generous for master's level courses. The exam statistics were a bit surprising: out of 130 points, the mean was a 97, the median was a 104, and the standard deviation was a 23. He drew the distribution on the board, and said that the cutoff for an A- would be around 115. It was clear at this point that the exam statistics were inflated by students who had significant background in the subject. After this midterm, the class got a lot harder. It was once we finished probability with the multivariate normal distribution, the law of large numbers, and the central limit theorem that I began to feel concerned. There were times during lecture when he'd say "I'm going to do this proof for fun, although I don't think most of you know the math that is needed to understand it." Examples became increasingly sparse in the lectures. Then we started the statistics portion of the course, and it seemed that it was going to remain this difficult for the remainder of the semester. The last lecture before the second midterm was on the Rao-Blackwell Theorem, and he did two examples of it, each one taking him 45 minutes to complete. Then he assigned a homework over fall break due the day of the exam, that he said was important to complete before taking the exam. This was probably the most challenging homework all semester, and it turned out that the second exam was heavily based on the concepts from that homework assignment. The second exam was significantly more challenging than the first exam. There were five problems, two of which were reasonably straightforward, and the others were extremely difficult. It took him two hours just to go over the solutions to the exam, and it took everyone the full three hours to complete. This time, out of 100 points, the mean and median were 63, and the standard deviation was 23. The distribution showed that nobody was on the same page in this class; some students scored in the 30s and others scored as high as 98. He said that the cutoff for an A- on this exam would be around an 80. Ultimately, I feel that Professor Davis made this class a lot harder than it needed to be. It would've been more bearable if we didn't have to go into the exams blindly (when students requested a practice exam, he suggested doing problems out of the book). His tendency to try to squeeze difficult results and proofs into the last minutes of lecture (and inevitably run over) was irritating, as lecture lasted long enough as it was. Finally, he often was presumptuous about what we had learned in previous probability and statistics classes, which was really unfortunate for those of us who hadn't taken any probability or statistics before this class. While the syllabus said that no background was required, the instructor occasionally appeared shocked when students didn't know elementary results that we "should've learned in Kindergarten."
Think long and hard before taking this class. Not because it's bad, but because it requires a serious commitment of your time and effort. This class is really two classes in one -- it covers two semesters of material (all of 3105/4105 and all of 3107/4107) plus the classes are 2hr 45min twice a week. Also, it's impossible to get ahead of your work, because there's always another problem set due in just a few days (see the workload below). Of course, it's also worth six credits, so you'll be rewarded for your efforts, especially if you can pull off a good grade. But just appreciate how long you'll be spending in each class and doing problem sets and just generally doing probability/statistics. In addition, IMO, the fact that this class goes at double-speed makes it more than twice as difficult. For example, if you were to ever miss a class or ever be unfocused during class, you're suddenly way behind. Furthermore, there's less time to let the often difficult concepts sink in before you've moved onto concepts which build on top of those concepts. If you're confused about anything, going to office hours is very important, otherwise you may stuck behind for a while. Two other important details to realize about the class: (1) It's almost entirely master's students, many of them getting master's in statistics. So the people in this class are bound to be pretty smart and you can't really count on much of a curve. (2) It's fairly theoretical and proof-based. So it may be an an adjustment if you're not used to that type of course. Very few of the problem set questions or the exam questions were purely computational. As far as Liam himself is concerned, I have a generally positive review. First of all, he's definitely a nice guy, and really does want people to come to his office hours. Second of all, he's very relaxed, especially as a lecturer, which can sometimes make it a little tough to focus for such a long time, but it also makes it a far more pleasant experience overall. Finally, he always gives a break at the halfway point in class, and more often than not finishes class early, sometimes even by a half hour. I think he does a decent, but not spectacular job of teaching the material. He admitted on the first day that he's not as strong at probability (and especially combinatorics) as he is at statistics and I think that I may have, in fact, found things a bit clearer in the second half of the course. He goes at a pretty reasonable pace and always stopped to ask if there were any questions. One major flaw of his was that he sometimes kept things too abstract and failed to give more concrete examples to help clarify things. Additionally, though he repeatedly tried to get the class to participate, he usually failed, and classes ended up being almost entirely lectures. However, the fact is, this stuff is difficult and yet in the end, most students seemed to get it. I found that I ended up teaching myself some stuff from the textbook, but most of my understanding of the material came from the lectures. In particular, I sometimes found that Liam helped me get what was going on conceptually while the textbook helped with the actual steps that needed to be done (though the textbook wasn't great -- it may be worthwhile to use other statistics textbooks to supplement it). Overall, I'd say you should take this class if you are either very into probability/statistics or need to get the statistics requirements very difficult. If you don't fit into one of these two categories, you may be better off taking 3105/4105 and then 3107/4107. If you've settled on taking 4109, Liam is a solid choice.
Great teacher! He explains everything well in fluent English (a plus for any statistics course), and he cares. He is readily available for any extra help you might need. However, there is homework due every class. They don't count for much, but if you do bad on the exams they will help you. The class is 6 points so you already know that you have to commit extra time to it. Don't expect a curve because the grad students do ruin it by getting perfect scores. The class is 3 hours long, but he usually lets you out around 8.
A difficult 6 point class for the unprepared and unmotivated. If you don't do the homeworks, you will ultimately fail the class. And homework is due each class session. Professor Rabinowitz speaks fluent English, a treat for any Statistics major. However, be aware that the material covered is extremely difficult, and the textbook is not easy to read. Also, the grad students will ruin the curve with perfect scores. The professor is quite reasonable and paces the class accordingly. Prior to each exam, the professor will hold a two hour review session covering the material from the practice exam. If you can do the practice exam, the exam is a piece of cake. The exams are all open book & open note and allow a calculator. If you work hard to the end, you will have earned that A.