Computational Linear Algebra

Apr 2021

Hands down one of the best CS profs I've had. He's very nice, his lectures are very straightforward, he answers piazza posts very quickly, and explains the concepts very well. If you're not a fan of theoretical math and enjoy more plug and chug kinda math, then yeah this class will be a bit more difficult but as someone who struggled my way through Multi, I was not expecting to take this class and get As on all the assignments. I also liked how tethered this class was to AI / ML, (especially the labs) and it felt like I was learning practical math that I'd actually use someday.

Apr 2021

I remember wondering if I should take this course because all of the old reviews, but I am very glad I chose to take it anyway! I don't know if he has changed things, but this course was my favorite all semester and was not a problem. I really like Dear's teaching style, and the hws were never to hard to finish and he gave us plenty of time to do them. Also, TAs had plenty of office hours, and they would literally walk you through the problem step by step if needed. Labs were a bit more difficult because they were pretty rushed, but prof adjusted and gave us the whole weekend to complete them which really helped out. On hw and labs, averages tended to be high, the midterm was a bit harder bc of the time crunch, but people did not flunk for sure. Overall, one of the better SEAS courses in my opinion.

Sep 2020

tl;dr don't take his class unless you're very very good at math and/or have a REALLY good support group of friends to help you with his insanely difficult problem/programming sets. This guy is the definition of "let's make this class harder than what it actually needs to be because this is Columbia and you're all in the Ivy League so you all need to be severely challenged". Don't get me wrong, he's a very nice, sweet, caring guy who is incredibly smart and always willing to help you during office hours, but his homework problem sets are absolutely insane. Most of the time, the TA's have no idea how he got the correct solution because he writes his homework questions in such a confusing, complex, convoluted way it will take you a full day just to understand what he's asking in the question, then another day just to solve the problem (if you can solve it in the first place). His programming labs are essentially the same way. They are brain crushingly hard and will leave you asking yourself, "What is this problem even asking me to do?" Problem sets are about 4 or 5 questions, but they have many, many, MANY sub-parts, making each assignment like 16 or so questions. The book and lectures help, but he mainly repeats the same material as in the book, with almost the same exact example problems. I get it, linear algebra is a very dry topic, and it's hard to make it enjoyable to learn, but I could have basically tried to read the book or watched youtube videos in place of his lectures, as they are just the same problems as in the book. After the whole coronavirus debacle, he uploaded short 10 minute videos for each topic, telling you exactly what you needed to know for that particular section. Those videos were incredibly helpful, honestly, it was a bit of an embarrassment to the university system as a whole because you could simply condense each class to a few minutes, (I wish they would have cut the classes short and paid me back my tuition money!). Exams are challenging, but doable. You REALLY have to understand the material inside and out to get anything higher than a C. I'm OK at math, and did OK on his exams, but I had such high problem set grades that I didn't quite care what I got on his final. Luckily, I had a really good team of "battle buddies" who helped me work through his brutal weekly problem sets. A few of them were VERY good at math, and his problem sets didn't intimidate them the same way it did to me. I hate to leave such a nasty review like this, as he's a very nice, caring guy who is very polite, but his class is sooo much more difficult than what it needs to be, but then again, that's like 99% of the classes at Columbia. This silly school would make "relaxation and stress relief" one of the hardest things you've ever done. go figure.

Sep 2020

I've had a different experience than the one presented in the review below. TL;DR: If you're looking to plug numbers into equations, get your miraculously easy A, feel like a math sorcerer for a second, and move on with your life - this is neither the class nor the professor for you. But, if you wish to develop a strong foundation of Linear Algebra -- especially in the context of ML -- I'd highly recommend taking this class with Tony. -Background: I took it during my sophomore year as a Data Science major, had zero prior knowledge of Linear Algebra. -Lectures: Tony's relatively fast pace kept the class very entertaining and engaging (even via Zoom), and his lectures were extraordinarily organized and clear, containing little-to-no extraneous BS. The shift to online modality halfway through the semester was seamless. Tony would upload concise (~10-min) prerecorded lectures conveying the gist of what was to be covered in class beforehand, as a convenient way for us to prepare or revisit the material. I found this combination of short, priming lectures and full, in-depth ones very comprehensive and rarely consulted the textbook. Also, Jupyter notebooks implementing what'd been covered in class were uploaded as a complementary resource. -HW: The written HW assignments were as proof-based and tricky as you'd expect from a math class. But what I loved most about the class was its more applicative facet. Beyond the essentials of Linear Algebra, which you can easily learn from Youtube, Tony introduced ML-related applications as PCA, regression, and Markov Chain, which were later incorporated into the HW assignments. The coding projects were, while challenging, extremely well-crafted. Our penultimate project was to implement data-fitting on and predict the spread of COVID-19 in different countries around the world. -Exams: Tony's exams were challenging; there's no denying it. However, if you make sure to understand the underlying logic of the material, you'll do just fine without spending a single overly-caffeinated night at Butler. The questions were straightforward and fair, nothing pulled from the dark holes of the appendix. I studied for the final by merely reviewing the short prerecorded lectures, and I ended up getting 87 on the exam and a final grade of A (the class was curved s.t. ~90 was an A). To incentivize, Tony offered official letters confirming the final grade to those who obtained a final grade of B+ and above. -TA: I didn't have much interaction with the TAs, but I remember them being welcoming and helpful. All in all, it's still one of the best CS classes I've taken (having completed 1004 thru 4701).

Jun 2020

On the surface, this class is great. Professor Dear is organized, nice, and offers a lot of office hours for his students. This will especially be evident during the first week, where the material is trivial. However, I do not recommend taking this class for several reasons. The first is the fact that the lectures just spit out different theorems in a convoluted way, where he is just regurgitating statements from the textbook. So you think you can just learn the material from the textbook or online because this is probably not your first time experiencing terrible lectures at Columbia. In fact, it might seem tenfold better, where you can skip class and do the problem sets and learning yourself. So you try the textbook, and realize it's just as convoluted as the lectures, because well, he was regurgitating those statements. And so you go online to learn the material yourself, which works fine for actually learning linear, until you receive the problem sets and realize it's just as convoluted. I can't emphasize enough that the problem is not the fact that you can linear on your own, but to do well in this class, you have to answer those convoluted questions that you won't find any source teaching you how to do. And so you got the TAs, but they themselves admit that they do not know how to solve the problems. Most people have large groups of friends to try to crack the problems together. If you do not know linear, you will be screwed, because well, you will actually be trying to learn linear and find practice problem sets on your own, before trying his problems. Again the problems are convoluted because of his style, not because of linear itself that will be added as a twist. The workload is a lot, one problem set a week and a lab every two weeks. You will really need a light workload to try his class without any knowledge of linear. The most frustrating part is the fact that you will think "This is great. I love to be challenged!" but then realize you will be slaving away only to solve his specific problems because Professor Dear likes to overcomplicate simple concepts. You will spend so much time but learn nothing new. Only take this course if you know linear and want to be challenged to solve those sets, and perhaps not learn anything new. Save yourself and take the regular linear if you can before the curriculum change. If you cannot because you have to follow the new curriculum, learn linear before taking this class and make sure you know a lot if people in this class to do well.

Apr 2014

Pretty bad class. Incredibly easy, but I walked out feeling like I wasted a semester. It's required for CS majors, so you'll probably take it anyways, but be warned: you will not learn as much linear algebra as you should. He repeats all the material at least three times, rather than moving forward. The homeworks are a waste of time. He's an incredibly kind man, and will explain anything you want to you, anytime. Definitely worth talking to outside of class and gong to office hours. He'll also help you on exams, if you ask.

Dec 2013

Computational Linear Algebra with Papageorgiou is a pretty decent class. He's definitely one of the nicest professors you will meet at Columbia and is a lenient grader to boot. Apart from the actual teaching, this class is great. Linear algebra is a super interesting subject and has applications in every single field. Homework assignments are reasonable - not insanely hard or long. Tests are graded generously and he will tell you if you are right or wrong during an exam. The class is essentially Linear Algebra + algorithms for matrix operations. It follows the standard Linear Algebra book by Strang. Papageorgiou generally starts his class with a 20 minute recap of the previous lecture followed by whizzing through the current material. He has a strong Greek accent which can make class hard sometimes. He is an above average teacher, but his abilities are nothing to brag about. He wants you to understand the material and not monotonously apply formulae you don't understand. However, between his accent and bad handwriting, you can occasionally get lost and fall behind (I got lost twice this class - once during RREFs and another time during eigenvalues and eigenvectors). He sometimes doesn't really explain stuff properly and just says "Boom! Boom! You're done" which causes endless frustration. It's important that you go to his office hours and clear up doubts because all the material builds up (which makes studying for the final very interesting because you see how stuff you learned in the beginning of the semester all ties together). Papageorgiou makes tests low stress by acting as a check-guard during exams. At any point, you can go up to him and ask him to look over our solution and he will tell you if it's right or wrong. As long as you know the material, you can easily get high grades on tests by making him check the harder problems. He obviously won't tell you the answer, but you will at least know that you're missing something. It's very possible to get perfect scores on every single test in this class as a result of his checks. Programming assignments shouldn't take more than 2-4 hours. Problem sets consist of 5-6 questions from the textbook. If you know the material, they can be finished in 1-2 hours. More often than not, you will have to read the material to solve the problem sets which makes them take more time. He has 4 quizzes which consist of 2-3 problems which keep you up to speed. They count toward your midterm and final scores. The midterm was straight forward. 5 problems - he gave us one of the problems a week before the exam (but it was a hard one) and told us that another problem would be solving a general system of equations. Pay attention to his revision sessions - he reveals the tricks needed to solve some problems on the midterms then. Final was harder than the midterm and he didn't tell us any of the questions before hand. However, it was completely doable, especially since he helped students out during the exam. It also had some cool problems that made you think and appreciate the subject better. Overall, this was a good class and Papageorgiou makes it as easy as it can be. If you pay attention, do the work and take advantage of Papageorgiou's help, there is no reason you shouldn't get a great grade and learn a lot in the process.

Jan 2012

Greatest professor EVER!!! AP is the nicest guy you'll ever meet. He really wants to give good grades to everyone in the class. As long as you go to class, this course is incredibly easy. AP doesn't mess around with tricks; he focuses on the core concepts and tests you on these same things. If you understand them, you don't have to worry about messing up on the tests. Getting near 100% is very doable, however AP reserves A+'s for those who also do the extra credits. Either way, if you go to class and make an effort, you should have no trouble getting a good grade. TAKE THIS CLASS.

Dec 2011

Prof. Papageorgiou teaches simply. He'll review material covered in the previous class, then get on and whiz through the topics he planned for the current class. And that's about it. Especially since the material isn't the most exciting stuff, class can get pretty boring. However, he really tries to make computational linear algebra accessible to everybody, and he tries to give everybody good grades. If you ask him to stop and repeat something, he'll do it. If you're a little confused about something on a quiz or a test, go up and ask him about it. He's very liberal with hints. There are five homework sets, four quizzes, a midterm, and a final. The homework sets are part theory (questions from the textbook) and part programming (often to implement algorithms he discusses in class). None were particularly challenging, except for the one for finding the null space of a particular matrix, and only because there were so many places for hiding potential counting errors. The quizzes and tests are really, really easy (he called one a "morale booster") and are meant to help your midterm/final grades. The midterm and final are also ridiculously straightforward (he'll even give you two or three of the five questions beforehand). Oh, and it doesn't hurt that you can ask Prof. Papageorgiou to check your answers for you. He'll tell you if anything's wrong and the correct way to get the right answer. This course covers a lot of topics, and if you're not interested in linear algebra, you'll find it incredibly tedious. But at least Prof. Papageorgiou will be there to simplify everything and help you get a nice grade in return for sitting through class. There is one side-effect of getting so much help from the professor, though. If you want to get an A+ and not just an A, you have to do the four extra credit assignments. But that's not really much of a side-effect because they're also unbelievably easy. He even give hints for those, too.

Jan 2011

A.P. IS THE BEST PROF EVER. He is so nice and really clear with lectures, and flexible if you need an extension (although he looked really sad when I asked for one, so don't do it too much). He obviously cares a lot about students, and is really enthusiastic about Linear Algebra. There were a few 15-minute quizzes at the end of class, these were open-book and open-notes. He'd announce the topics the class beforehand. What's more, HE CAME AROUND AND HELPED after about 10 minutes. They weren't very hard, but due to his help I ended up getting 100 on all of them. Midterm and Final were similar, although not AS easy. One tiny, tiny complaint: I got over 100% on the class, but I didn't get an A+. Maybe he doesn't give them, or maybe it was because of the curve. Whatever, it was still one of my most stress-free and worthwhile classes. Bless him.

Dec 2010

GREATEST. PROF. EVER. Take this class with this man. I don't care what conflicts you have. I don't care if you aren't required to take this class. Just do it. It will change your view on professors forever. Imagine if you will a prof who cares about his students. Who makes every attempt to give them good grades AND have them understand the material. Who before every tricky concept, takes the time to explain why the material isn't tricky at all. A prof who doesn't need office hours but takes the time to explain concepts to you any time you show up at his door. A prof who knows how to create the perfect balance of practical and theory without overworking the class. A prof who doesn't try to trick you on exams but rather tests the fundamental concepts that you will take out of the class. The prof I'm describing is Papageorgiou. His lectures are clear and cover exactly what you need to know. His homeworks were fair (and even fun on some of the programming ones). He tests were incredibly straightforward. His review session goes over EXACTLY what you need to know.

Dec 2009

This class is billed as "practical methods in linear algebra for computer science". It is, without question, the least practical course I have ever taken. We've all taken Calc III, so we've all seen a class without content before (and let's be honest -- unless you plan to pursue a graduate degree in vision or graphics, all the linear algebra you need for a CS degree fits on the front and back of a sheet of paper). So Prof. Wozniakowski does what any reasonable theoretical mathematician would do, and turns this into a class about theory instead. This is not the problem. The problem is that his "theoretical" approach to linear algebra essentially consists of stumbling into class, drawing an arbitrary matrix on the board, and proving its special properties. Do not expect any discussion of the usefulness, significance or relationship of any of the topics you cover. Everything turns out to have very important practical implications, but Wozniakowski will not teach you about them. Unfortunately, you also wind up without the tools to do theory yourself. So when his exams ask you to prove new, different things about special matrices, you, and the rest of the class, will fail. The average on the midterm was below 50%. You will come out of this class knowing more things than you ever cared to know about Householder matrices and eigenvalues and the infinity norm and the spectral radius, but you will be able to do exactly nothing with that knowledge. Advice: -- Don't buy the book. Gilbert Strang's canonical linear algebra textbook is generally not very good, and it is absolutely useless for this course (every time you go to look up something we discussed in class, Strang simply says "we won't bother proving this right now"). One of my classmates remarked that his still has that new-textbook smell because he hasn't opened it. -- The TAs were atrocious. Whoever it is next semester, make sure to interrogate them about every homework assignment (this will entail 10 visits to office hours) or your grade will suffer. Over the course of the semester, I was deducted points for such offenses as writing my answer in the middle of the page where the TA couldn't see it, providing a python script that ran normally under CUNIX but not with the TA's fucked-up $PATH, and having the same first name as another student in the class. Be vigilant. At the end of the day, I don't feel like my time was completely wasted, simply because the material we're actually supposed to cover doesn't merit its own class. I feel like things make more sense now that I'm connecting the dots on my own (protip: your enjoyment will be greatly increased if you wiki every word that comes out of his mouth), but I can think of many less painful ways of learning this material, and in the end I'm not sure I really needed it in the first place.

Dec 2009

The professors does not speak english and was therefore very difficult to understand in class. Because the professor does not follow the book there was no real way to figure out what was going on if you did not understand what was happening in class. Good luck going to office hours - he doesnt even post his office number! The TA's were not much help either. The midterm was similar to the review questions but nonetheless impossible - he seemed upset at our low performances, but maybe he should have taught us something understandable in class. The homeworks were not impossible, but required extensive wikepediaing as they were neither in the notes or in the book. Worthless class.

Jul 2009

Hands down the best comp sci teacher I have had so far. He is an excellent professor who actually cares for his students and their understanding of the material. Professor Papageorgiou comes well prepared to class and actually teaches. He goes step by step to make sure everyone logically understands the progression of the lecture. If you go to the lectures and pay attention, the class will be enjoyable and rewarding. Everything on the midterms and quizzes was covered in depth, there were no surprise questions, and the extra credit is usually manageable. He emphasizes understanding not out-of-the-book memorization, so his tests are designed that way. Also, he will gladly take the time to help you out after class with any type of doubt or question on the homeworks. Going in, I thought this course was going to be a pain and was pleasantly surprised by everything I had learned towards the end. The comp sci deptartment needs more people like him.

Feb 2008

AP is the best professor I've had at Columbia. His lectures are the only ones I've ever bothered to go to, as he actually teaches instead of preaches. He goes over what is important, tells you implicitly what is going to be on tests, and goes step by step so it's almost impossible to get lost. If you do, he'll stop and explain. He doesn't believe in pointlessly long questions or tests. He's focused on the principles, the tricks, that are necessary, and on how these things are useful in applications; specifically finance, which is excellent for CS as many job opportunities will be finance related.

Dec 2005

Computer Science majors at Columbia tend to dread the Scientific Computation and Computation Linear Algebra courses, and as few as ten (out of thirtysome) people have shown up to class. I feel kind of bad that attendance was so bad, as the professor's a nice guy, but I'm not one to comment on why you should go to class, since I for the most part didn't. There are 5 Homework Assignments. In the first 4, there is a programming component that is worth 40%. The amount of programming involved varies widely, and the most difficult programming assignment is actually nontrivial, which was a shock to the class. The theory questions given are pretty easy, and it seems like we would learn so much more if we had less programming and more problems (For example, I don't think there was a question where we actually had to solve for the eigenvalue). The professor doesn't assign a homework until all of the material on it is covered, and then you get two weeks to do it, which is generous. You are not given as much time for extra credit (like a week), but extra credit problems are fairly easy proofs, so it is not too difficult to get all 10% of the extra credit, if you are not too afraid of proofs. The midterm was very easy, and the final was significantly harder. He is a pretty lenient grader, and doesn't plan to fail anyone. The textbook is followed pretty closely, and packets are made covering a few algorithms not covered in the book. While nobody's crazy about his teaching abilities, he is a very nice guy who will help you out if you ask him.

Oct 2003

Whether coincidentally or not, Sci Comp II bears a strong resemblance to Sci Comp I with Traub. This is basically a linear algebra class, except Wozniakowski teaches the material completely differently from how the book (which he doesn't order himself, he just says to get it at the bookstore since its the same book that linear algebra uses) shows the material. His classes are hit and miss. Sometimes he'll teach all new material, provide interesting history behind certain things, and generally make the material engaging. Other classes, however, are boring and drawn out reviews of previous classes. Beware that to do some homeworks, you need the book to understand what is going on. Otherwise, they are pretty easy.