Elementary Stochastic Processes

May 2021

Best professor I've had in the stats department, I completely agree with the review below.

May 2021

She's the best and the sweetest! I've had some pretty bad experiences with stats department professors before but she was such a blessing! No doubt the class was hard; I spent 4 hours to understand each 75-minute lecture. But she explained things very clearly with organized slides and some handwritten derivations. She responded on Piazza fairly quickly, and she went to great length to make sure that we understood. There was one time when I posted a question on Piazza--she spent half the next lecture going over that. HWs were not entirely from the textbook and were not easy. However, she would basically go over all the questions in her OH. She posted HW solutions, practice exams, and exam solutions. The structure of the grading, where the final was 50%, was quite stressful, but the exams were pretty fair. None of the questions was meant to trick you, and she tried her best to tell us what we should remember and what kind of questions we needed to know how to solve. An A is very doable and an A+ is possible. Oh she also gave alternative exam-taking times for students on the other side of the globe. Just a considerate thing that not all professors would do.

Dec 2019

I took Professor Rios' STAT4207 (typically taught by Mark Brown) this semester. Reading the other reviews, I was actually quite scared to take his class. However, I had quite a positive experience. He is incredibly approachable, always happy to answer questions during and post-lecture and also in OH, and provide intuition behind the complex math, as well as insight regarding real-world applications in finance/trading. He often said things like: "never be sorry for asking a question" to encourage people to speak up and ask for clarifications. Moreover, the book was often not very easy to follow (examples quickly spiral out of control), but his notes, which he also posted on courseworks, emphasized the concepts that we needed to know for both the assignments and the exams. Though he started every class with a "roadmap" (i.e. what we intend to accomplish during the class, and what we can expect to do in the following class), the class could definitely use a bit more structure, especially when it comes to notifying students of exam scope early enough in advance. Nevertheless, Professor Rios is open to feedback and clearly incorporated students' feedback in shaping the class later on in the semester. TLDR; As the previous review suggests, Professor Rios is clearly improving. He is approachable, responsive, open to feedback, and very capable of explaining complex concepts in very simple language. Would recommend taking a class with him.

Dec 2018

For the love of god. Do not take this class. Required for the Stat major? Change your major. Do a joint Stat major that doesn't require it. Do Comparative Literature, or Biology, or something. The undergrad Statistics department at Columbia is an enormously practical joke, anyway. Mark Brown seems nice enough as a person. He is, by far and away, the worst teacher I have ever had in my entire educational life. The slides, produced in 2016 (this review is being written for Fall 2018), have several typos per lecture, which professor Brown compensates for by uploading a scan of a hand written piece of paper detailing the typos (in no particular order). When it isn't outright wrong, the content in the slides itself is totally meaningless. Concepts and formulas are introduced with little or no explanation, and are completely irrelevant to the skills you need to answer homework and exam questions. Maybe, you say, you could just be part of the 80% (sometimes 90%) of students that skip lecture altogether, and learn by doing practice midterms and exams from previous semesters. While professor Brown does indeed upload several terms worth of previous exams, they are also practically useless. The solution sets, more hand written, difficult to read documents, contain no explanation of how to solve any problems; answers are usually the final number and nothing else, or a single line of equations with 1000 skipped steps. Online learning material to aid you through the course barely exists, since this course is so unorganized. You may even struggle to know what to google. So please. If you are considering taking Elementary Stochastic Processes with Mark Brown. Don't.

Apr 2018

Professor Brown is a nice person, but his class is the worst I have ever taken at Columbia. If your major has something to do with STAT, unfortunately you have to take this class with no choice. But definitely go to his office hours, which would restore some of your trust and hope in this course. That said, this class like many offered by the STAT department is really bad in terms of delivery and would require your reading the textbook or lecture notes on your own. He is generous in terms of grades.

Feb 2017

I know what you are thinking: "what the hell is going on in this class? Are these people around me understanding anything? Should I drop this class? But it is a requirement for my major." Don't worry, I am here to save you. What I can say about this class is that it is absolutely impossible to follow Mark Brown's slides during lecture. I used to take an average of 4 hours per slides presentation in order to have a good intuition about what was being taught (fully understand the slides is out of reach, at least for the mortals like me). It is no surprise that after the first two weeks only ten students were showing up to class. What I mean is that his slides are dense, and it takes time and patience in order to move through the material. Although there is a lot of proofs on them, you will not be asked to do any on the exams or homeworks. Your goal when reading the slides is to get the essentials about the material (ie the main formulas, underlying concepts, etc), not to fully understand each passage. Try to summarize the main points of each lecture after reading it. You will need that summary in order to study for the midterm and final. From my experience, I could understand reasonably well what was going on from lectures 1 to 8 (by studying the slides by myself, obviously. As I said, going to lectures is a waste of time). Those are the lectures that will be on the midterm. I did not read lectures 9 and 10 (they were dense examples above the material on lectures 1 to 8, kind of useless for the midterm, since the midterm exercises were a lot easier). I poorly understood lectures slides 11 to 20 (but still could get the main concepts and formulas) and I did even touch lecture slides 21 to 25. Regarding homework, there will be 4. They will be a lot easier when compared to understanding the slides. You will basically need to know the main concepts and try to apply it. Still, the homeworks are a lot harder than midterm and final. If you can understand the homework problems, that's a good sign. It means you understand the key concepts of the class. Now, the key to do well on the midterm and final is to have a good summary of the main concepts and formulas of the class. What you need to do in order to come up with a good summary is to understand the homework problems, understand the main ideas of lectures 1 to 8 and 11 to 20 and fully understand how to solve the practice midterm and final. The practice midterm and final probably taught me more than anything else in this class. Finally, I got an A in this class, even without touching 7/25 lectures slides. I am not telling you to do the same, I am just saying that you do not need to freak out if you do not fully understand the lectures or if the material gets impenetrable after lecture 21.

Nov 2016

This class will seem deceptively easy at first, but as the semester goes along the difficulty of the material increases drastically. Do not underestimate the materials! The lectures are dry but he presents plenty of examples to help you understand them. He also hosts help sessions where he shows you how to get the answers to the homework, if not show you the entire solution. Highly recommend you know your linear algebra, probability and calculus (absolute must). Grading will be separated between the undergrads and MS students so there will be two curves in the class based on this distinction. If only this had happened earlier...

Jan 2012

Most reviewers give an accurate sense of this course. I just wanted to add some advice on taking the course-- For the problem sets, Brown will often have "help sessions." Go to these. He basically goes through the entire problem set and does them. I missed the first two, and then was kind of shocked to see him seemingly give away all the answers in the later two. Immensely useful in bringing down the work in the course. Final and midterm were of the "pick and choose" format. For the midterm, something like 7 questions are given and you pick 4. Don't remember exact numbers, and he may change this. So if you don't have a ton of time to study, you can cram for just a few sections. For the midterm, I just learned all of the Markov chains questions really well and ended up with an okay grade. To reiterate what others have said: Brown is a very dry lecturer. The main things to know in the course are Markov chains and Exponential Variables / Poisson processes. Everything is built off of one of these two concepts, so just understand these and you'll be fine.

May 2008

This was an interesting class. What you get out of it is entirely a function of what you put in. Lecture is incredibly dry, granted, but the real gold is the posted notes and practice problems. Stochastic processes are incredibly wonderful things. I've never though so coherently before about series of random processes, but this communicates the subject well. What's really required here: You need to sit down with the book and the lecture notes and the problem sets and think about Markov chains and Poisson processes on a gut level. Everything else in the course is just an extension or generalization of this. Become familiar with limit theorems, with the expected values of many distributions and how they relate (for example, the sum of exponentials is just a gamma-- the quotient of two gammas is a beta. etc). There's more than enough practice material to fully ace the exams, there are no tricks on them. Dr. Brown is a wonderful man, but he injects a formalism into the course that's not needed for the problem sets (that you can do from the book) and is only tangentially needed for the exams (order statistics aren't mentioned in the book, but if you're smart enough, you'll be able to figure out the conditional expectations for the ordering of exponential distributions).

May 2006

Not a very impressive professor, as he is usually completely oblivious to his students. You can be in the first row with your hand raised, and he would just stare right past you and never call on you. Lectures are quite dry and quasi-mathematically rigorous, so it may be easy to fall behind occasionally. Otherwise, the subject matter is interesting and rewarding. I don't know how it is different from 4106 or 3106 though. It doesn't seem to be much higher in level. I think the previous reviewer did a good job scaring off most people, but it's not that bad.

May 2005

Holy freakin bejeezus. . . . . . . Be not fooled by the word "Elementary" in this course's title. This is THE hardest class in Columbia, without qualification. Ever. I can't believe I made it out alive. Unfortunately for Mark, the subject material is perhaps the hardest branch of statistics, in terms of intuition and concepts. He tries very very hard to make sense of it to us, but hopelessly so. No mistake, I think Mark would have been a decent teacher in another class. But in general, I think he's on a totally different level than the rest of the class. Problems seem easy when he solves them, but come homework, there is no way students would be able to complete them without his hints. I don't want to scare any potential stat majors, but the mean on the midterm was around 30 or 40. If you can't handle the heat of this course (which is actually graduate level) then take the much easier undergraduate engineering version. However, if you have the mathematical maturity and persistence to learn everything that is taught, then the world is yours -- just kidding, but it's still very interesting stuff.

May 2002

Here's the review for Intro to OR: Stochastic Models, which should be relevant because Sigman is teaching Elementary Stichastic Processes in the fall, which should be pretty similar. Excellent teacher! great class. Definitely the most interesting lecturer I've had for a math related class, and he makes difficult probability concepts fairly straightforward and understandable. You get the feeling that he enjoys teaching and really tries hard to get everyone to understand everything. Highly recommended.