course


May 2021 
He's one of the best professors I've ever had. He latex typed all the class notes for us, and his lectures are clear and organized. Homework was a bit hard but definitely helpful for exams. All exams were takehome; they were on the longer side but overall they were fair. Though the class was application focused, he did a great job both showing us how to solve those problems and why the methods work. He also responded on Piazza fairly quickly.
Dec 2020 
AOP is a relatively easy course that is a survey of multi, linear algebra, and ODE with control theory and dynamic programming theory tacked on at the end of the semester. Professor Matetski is one of those "not great not terrible" professors. His lectures were basically writing out notes and examples, which were very organized and helpful. He did answer questions, but I wish there was a little more student engagement because I would often fall asleep during the Zoom class. I have no complaints about Professor Matetski and think that with some small adjustments to make lectures more engaging he could definitely be on his way to silver nugget status!
Dec 2018 
Shotaro is a lovely professor. I have nothing but good things to say about this man. 1. His conduct. Yes, classes are lecturestyle. But his lectures are very clear and structured, and correspond very highly to the problem sets and exams. Most of the content is from the textbook, but I managed to finish the semester with a good grade without even buying the textbook, just because it is substantially easier to learn from his lectures than from the textbook. He is also very friendly and does not have a disruptive accent. He makes it much more clear, and tells you exactly what he expects you to know. Which brings me to my next point: 2. Exams. GO TO LECTURES! Because he drops hints about the exam questions in class. Nothing not covered will be tested. Barely any "tricks" are required to solve his exams, which are very formulaic; the difficulty is in mastering the extensive content and being able to solve the problems quick. There were 2 midterms, both of which averaged at around 5060%. If you have a bit of brainpower and can identify themes in the class, it makes exams that much easier. Shotaro will never expect you to pull random calculus/linalg/real analytic results out of your a**. He will make it known what exactly is expected, which makes things comparatively lower stress. 3. Take his class. You won't regret it. He is also very helpful and jovial in office hours.
May 2018 
tldr really clear and good Professor. But honestly, If you don't have to take this class just take analysis. Dr. Makisumi is a great professor. He spends a lot of time making sure that the students understand the material. He is very clear and I rarely got lost during lecture. He follows the textbook pretty closely (the textbook is all you need, but it's light on examples). The class moves pretty slowly, reviewing a lot of calculus III and linear algebra. If you did well in those courses then this class will be relatively easy. This course just makes you think about optimization problems more carefully. The most annoying part of this class was by far solving all the systems of equations. It's also a decently useful course. KKT conditions pop up everywhere in Machine learning and advanced economics. However, all the conceptual/theoretical material I learned in this class was covered in greater depth and interest in Modern Analysis next semester. We do cover pointset topology, but not very in depth. The home works were generally computational or conceptual. Very little proofs in this class.
May 2016 
Deopurkar is a very good teacher. It’s a pretty standard math class. Weekly problem sets, some were easy and some were hard. The 2 midterms were pretty straightforward, with problems that were similar to the homeworks and practice problems. The final was pretty hard for me it seems like he made the problems more tricky than the midterms, and some of the calculations just didn’t work out for me. Deopurkar’s class notes are very good. You can definitely learn the material just from his lectures and notes. He has an accent but he is perfectly understandable. He is a good lecturer and knows how to explains things. No complaints!
Sep 2015 
I took this class as an econ major with an OK but not great background in math. I'd recommend it if you have to take it (especially since all my friends died in "real" analysis) but be aware: PROS: (1) Professor Maulik is decent. I was afraid we were going to get an Indian dude with a heavy accent but he grew up here and speaks American English. He's helpful and responds quickly to emails and is often willing to give extensions on the homework (2) The curve is pretty generous; something in the 80s range will get you an A (3) Zhenrui was an awesome TA! He held review sessions before every midterm and final which were super helpful as far as getting a feel for the material goes. Sometimes it looks like he's sleeping in the back and then he'll raise his hand and point out an error on the board or ask exactly the right question to clarify a point when a lot of people look confused. I didn't really interact with the other TAs that much but my friends that did said they were pretty OK too. CONS: (1) There is a steep learning curve if you've never done proofs before (I hadn't). A large part of lectures as well as the homeworks and the exams will require you to do proofs and not baby "derivation" proofs where you just work backwards and manipulate down some equations until they look like what you want like in Calc III. Points are taken off for unjustified steps or logical errors. Memorizing definitions is a MUST (2) The class is pretty dull; even though it's pitched as a math class for econ/econometrics/finance it's pretty obvious that Prof Maulik is a pure mathematician and doesn't really do applications. He tries to bring them in sometimes but it's usually not the same as when you actually have to use them in an econ setting (3) Half the time everyone was asleep since we were just going over stuff from Calc III or linal and the other half of the time everyone was totally lost (which might have been why the curve was so generous) (4) Class interaction probably *negatively* impacts this class. I have no illusions about my mathematical abilities but it seemed like only really dumb questions got asked in class, and then Prof M would waste time rehashing very basic concepts like the dot product because he thinks we don't understand it. Fortunately in a lecture of ~100 it's not very interactive.
May 2014 
Pros: I actually ended up enjoying this class. You learn some neat theorems and basic analysis for optimization problems, and by the end I felt very knowledgeable on the topic. After all of the math and stats professors that I've had at Columbia, Hongler has definitely been the best  both personality/approachability wise, and teaching wise. I always sat in the front row so I could laugh at his jokes and ask questions when I was lost (which was rare, because he explained things well, drew graphs, used examples). Cons: The main con was the homeworks. They tended to be long with several proofs. He also sometimes introduces some new theories and techniques in them which he expects you to know for the exams. I just went every Friday to the TA's office hours (*they have the homework solutions*) and tried to work out the problems as a group. I definitely felt more comfortable with the material after doing them. Also, there are a lot of theorems, but they all kind of make sense / extension of derivative/tangent line stuff we did in calc. Also don't even bother using the online textbook he links to  its honestly useless. I never looked at it.
Jan 2014 
The material taught in this class is not very difficult, I thought. The difficulty of the class however comes from the lack of practice problems and examples. The textbook is a piece of shit in that it does not provide very many examples at all. Instead, it just provides theorems and definitions with a few sample problems. And on top of that, there aren't many practice problems in the book, with only odd solutions in the back. This made studying for exams and doing hw a bit challenging, I thought. The quiz in the class was retarded, in my opinion. It was straight regurgitation of definitions. I expected it to be solving problems, but it wasn't... The midterm and final were both a joke, with averages probably in the 70s for both. The problems were very straightforward, with no tricks or curveballs. This was actually frustrating because I expected the final to be difficult but it turned out to be a bunch of simple problems and definitions, though I didn't remember some of the definitions.
May 2013 
Make no mistake, Hongler takes no distinguishable joy in teaching and puts in very little effort. However, he is an above average teacher (deserving of his silver nugget IMO) and his classes are never entirely boring. Even if you half pay attention, you will learn in his class. Some lectures he comes across as extremely lucid and other classes you are left wondering how all the methods he taught fit the puzzle. He is nice, amiable, and willing to explain. Just don't expect him to go the extra mile. He covers difficult topics fairly quickly, and he uses homework as a teaching tool rather than a reinforcing mechanism. Naturally, problem sets spanned the gamut from very difficult to mind numbingly easy. He does teach everything that shows up on the exams, whether through the HW or through lecture. You'll need to think outside the box on the harder questions though, and bring together various theorems. The material is not difficult (nor is it a breeze), but if you're new to the subject it can seem overwhelming. Would I take him again? Personally, I would. Is he a good teacher? Not particularly excellent, but not at all bad. You could do a lot worse. He gave us the famous "the limit does not exist!" Mean Girls problem on one of the questions. Is he a lenient grader? Yes, he tends to give as much credit as he can on the exams, as long as you write something relevant. Does he curve well? Word on the street is that he curves generously.
Dec 2011 
This class was probably one of the most painful experiences I have had at Columbia. Honestly, I am that kind of student who really tries to pay attention etc but I just dreaded our morning sessions with Julien. The syllabus itself is quite interesting, with many topics relevant to higherlevel economics courses, so it's understandable this is a requirement for econmath majors. Though the first part of the course can be very abstract, the optimization part is very interesting (and easier). However, Julien, despite probably being nice outside the classroom, is incredibly dry, does not say anything that isn't directly related to the class  not even good morning or "the class is over". If only this meant he was very pedagogical... Not at all: his blackboard method is frustrating, he barely uses any examples, and more generally is INCREDIBLY BORING. 90% of the time I left class feeling I hadn't learnt anything substantial. Furthermore, the weekly problem sets are extremely confusing and the averages were regularly below 65. I suppose this is because Julien demanded notions that were not properly covered in class, or also that the TAs were incredibly harsh graders. I understand that math is about precision, but how can the TAs ask for precision on topics that were absolutely not covered in class? It was a clear case of then the TAs have no idea of what is going on in the classroom. The graduate TA, in particular, was incredibly helpless: he answered questions on the course using topics from higher math courses and his solutions to the HW were so arrogant. This class is a requirement for many majors so you probably won't have a choice anyway, but beware Julien, unless you are extremely motivated. I highly recommend that you reach out to other students for the HW because they are very hard.
May 2011 
This class was like a trip to the dentist  you hate going to it more than anything else, but you still have to go through it because you signed up for it. The problem with the subject matter is that there truly isn't enough emphasis on optimization. It's simply a diluted version of Modern Analysis 1, with lagrange multipliers and linear programming. That's it. Now, for CLEMENT: My chief complaint of Clement is his lack of commitment to teaching. In short, he is more focused on his research than to teaching the class. It's obvious he doesn't enjoy teaching the subject, and he's often very rude and condescending. He knew 5 kids' names, and if you try to schedule office hours with him he will simply tell you "it's impossible since I must do my research." He makes mistakes on the board all the time, mumbles, etc. All in all, just not a good professor. In Clement's defense, the TA's sucked too. Of the 12 HW sets we did, maybe 7 were actually handed back. 5 were graded in the last week of the semester, so we couldn't use our graded HW to prepare for the exam. Plenty of people dropped out after the first midterm. And, well, I don't blame them. The first midterm was REALLY tough  highest grade an 88, lowest grade I think was around a 10. At least there was a generous curve... 6% in the class got you a D. I ended up with an A, and should've had a C.
May 2011 
The material: The first half of the class focused on analysis. We started with set theory, went through sequence and series, and moved to linear algebra and finally convexities. The second half of the class focused on optimization and covered linear optimization, primal/dual, simplex, lagrange multiplier, and KKT conditions. Don't let the 2000level number fool you. This class is HARD. Half of the reason is because the prerequisites do not adequately prepare you for the level of sophistication the materials requires. Everything is broken down to theorems and proofs. If you have a weak background in proofbased math(like me), you will be so lost as to what you are doing in class. The other half of the issue is with the textbook. The classes was based on Pinkham's textbook, which is probably one of the worst textbooks I have ever seen. The book follows a pattern of theorem>proof>theorem with an occasional example thrown in once in a while to make it look like the theorems are actually useful for something. If you already understand the materials, then the book is great. It rigorously defines everything you ever known and prove why they work. But if you don't already know the materials (which is pretty much everyone in the class), you will be banging your head on the wall trying to understand what one theorem is saying in order to understand the next theorem and so on. If you get stuck on one theorem, you'll have trouble understanding the rest of the materials. But even if you do understand what the theorems are saying, you would still have no idea how to answer the questions because they requires numerical calculations and the book gives no example on how to do them whatsoever. The textbook also lacks pictures and graphs, which is vital to a class like this. 80% of the materials can be be clarified with some simple pictures, which the book desperately lacks. A simple picture would better help explain what a affine plane or what a polyhedra is than 2 pages of symbols and texts. The internet is your best friend here. Hongler: Hongler is a really nice guy. Hongler stated at the beginning that the class is difficult and doesn't expect you to understand all of the materials and only hope you have learned something useful in the class. He actually means it. As long as you understand the basic idea of what you are trying to do, he'll give you points for those on the quiz and on the midterm. Unfortunately his lectures comes mostly from the textbook, which is why its rather dull and confusing at times. He does work hard to try and explain it, but it doesn't help much. Most people resorted to teaching themselves instead. The lecture attendance dropped to 30% or so by the end of the semester. The homeworks are deceptively hard, usually taking 3 to 5 hours if you are lucky, and longer if you don't know what's going on. Go to his office hours if you want to be able to do them within a reasonable amount of time AND get full scores on them. He gives partial credits and lot of extra credit opportunities on the hw and the tests. In summary: The class is hell. Avoid taking it unless you have to (EconMath majors)... If you have to take it, take it with Hongler, you will have a much easier time, but still expect to learn a lot of the materials on your own though. Also, he gave a REALLY generous curve for the final grade, which helps a lot.
May 2011 
This course is required for Econ/Math majors, and from what I'm told it can replace Modern Analysis for Math Majors. Apparently also some engineers take it for some reason or another. It is a mix of some real analysis, with a chapter or two of topology, and linear programming of the sort that would be seen in an operationsresearch type class. There are a lot of beautiful, incredibly profound results that come out of this course but unfortunately, it is taught so poorly and the notes so worthless that only someone who is already very interested in math, or works very hard, will appreciate it. Everyone else will more likely hate this class for the amount of work it requires to understand, the uninterested teaching, and the frustratingly opaque and obscure book. Professor Dubedat is very smart, and was helpful during office hours before and after class, but clearly did not care at all about lecturing. His thick French accent, distracted mumbling, and uninterested approach to covering (or not covering) what was covered in the book meant that for the most part, the class was entirely selftaught. The notes used in class were almost entirely taken from the 'book' Pinkham's incomplete, unclear, and almost entirely useless (more so for optimization than analysis, but still) set of lecture notes that he is attempting to publish or something. They are useless because they are often garbled and unclear, referring to future sections before they are covered and referring to long past results by number rather than name (ie in chapter 12, something like "this follows from theorem 3.4.2." as if you could remember what that was without trying to find it), and provide "examples" along the lines of "example x.y.z work this out for yourself." Seriously, one of the most frustrating classes I have experienced. At the time I started, one of the chapters and one of the essential sections of another had been left unwritten, although a later edition was finally released. In a sense all math is selftaught, but this is much more so than it needs to be. If you do take this class, make sure to sample the different professors and get your hands on a copy of the book "Further Mathematics for Economic Analysis" and "Mathematics for Economists" for clearer examples and expositions of the second half. Perhaps you should find one for analysis too, although I don't know. For me the homework and material were all very hard (though with more time, some of them perhaps could have been medium), and if this is your first rigorous math course and you attempt to do this with the provided book and notes alone, I suspect they will be for you too. The grading is rather odd though. The problem sets seemed to be graded incredibly leniently, with only the most egregious mistakes resulting in lost points for the last problem set, I remember not even arriving at answers at 3 out of the 5 problems, and still receiving a perfect scores. I had a hundred on one of the quizzes, even with red writing and some crossed out sections. The average on the first mid term was a 34 out 54, and 38 was the border between A and B, while 25 was the border between B and C. After each exam and quiz, I consistently felt like I failed, even after long nights of attempted selfteaching every problem set and exam, and yet somehow I did well. I think the grading is almost designed to test how much you care ie a sketch of a proof with mistakes will get a lot of partial credit. This will work heavily in your favor, if you stick with the class and put effort into it.
Feb 2011 
I know what you applied math majors are thinking: math 2500 has to be better than math 4061. FALSE. if you plan on taking analysis and optimization with pinkham, well, i am very very sorry for you. this class is IMPOSSIBLE. pinkham cannot teach. the end. choose modern analysis. okay details. the analysis part of the class was terrible the textbook, which he is currently writing, makes no sense at all, and you will have to depend on google and yahoo answers (surprisingly helpful!) for any helpful hints to the ridiculous proofs that he wants you to spell out. each hw was like 5 proofs, taking maybe 5 hours per proof. the optimization part of the course wasn't too bad, since i could at least find other sources online to help with those problems, and they were generally simple calculations, using linear algebra at the most complex parts. midterm: incredibly incredible. but you can pass as long as you memorize the hundred definitions, theorems, and proofs that he has in his book. same with the final. the key to passing this class is to show up so he knows who you are. im pretty sure that bumped up my grade a little.
Jan 2011 
If the previous reviews were not enough to dissuade you from taking this class with Pinkham, then you clearly do not care about your GPA. You need this class to graduate you say? Forget about it. Graduate a semester late. Do NOT, i repeat, do NOT take this class with Pinkham. Saying he is a harsh grader is an understatement. You will have a quiz the second day of class that counts for 5% of your grade  according to Pinkham, this is to 'weed' out people. He will say he gives partial credit but he doesn't really  I got one part of a three part question wrong and he gave me a 0 on the whole thing. Appealing won't help. His lectures are abysmal and have nothing to do with the problem sets which are IMPOSSIBLE. You will be working 30+ hours on each problem set and if you are smart, you will be able to do perhaps half of it. He also didn't assign a TA for the first few weeks so that wasn't very helpful. Neither was the Math Help Room  after multiple unsuccessful trips, I realised that no one there knows any Analysis and even the ones who do will not be able to help you with the problem sets. He also wrote his own (unpublished) book for the course and is pretty proud of it. This book might as well be in greek  he uses lots of complex abstract methods to illustrate what could actually be simple concepts. There are also no examples of concepts in his book which he leaves as an exercise. Expect to learn everything you will need in this course from google (and fail at it). If you are lucky, you will get a C in this course. There were plenty of people who failed the first midterm. Pinkham is the best argument you will ever get against tenure  avoid him like the plague.
May 2010 
The first review was pretty much spot on, so I can't add much, but I feel compelled to write a review anyway since Lipyanskiy definitely deserves a shiny nugget next to his name. I was fearing the worst when I saw that this unreviewed professor straight out of MIT with an EasternEuropean name was teaching this class. But as soon as he walked in on the first day with his track jacket and sweet pompadour, all of my fears were instantly allayed. The man is as clear as glass and funny as hell, and not in a not corny math geek way; he's a naturally witty guy who would frequently crack the class up. Overall, a fantastic professor in every respect. The course itself consists of a lot more optimization than analysis: 80% plug and chug optimization techniques, 15% geometric intuition, 5% really basic topological concepts. However the plug and chug optimization techniques learned are extremely useful  the kind of stuff professors in science and econ classes will give you a 15minute primer on and expect you to whip out on problem sets and exams. So knowing this stuff is really useful. And yeah, you don't really need to buy the book, though it's a decent reference to have if you're an econ major. I should also note that quality of the student population of the class was pretty low; really dumb questions were asked during lecture and people consistently got homework problems wrong for which there were answers in the back of the book.
May 2010 
Let me get this out of the way first: I'm an applied math major and I was taking the course to avoid the W4061 Modern Analysis requirement. Having said that, I found this course incredibly easy. I was worried about this course because of past reviews of Pinkham's "debauchery" of the material, and there weren't any reviews of the new prof . Fortunately, Max was awesome. He explained things really clearly and tried to keep things simple. He gave us the definitions and theorems that we needed to know along with numerous computational examples. Heck, you didn't really need the textbook, which was quite technical and economically oriented. Your notes from class covered everything you needed to know for the hws and exams. No proofs were required in this class, which was pretty sweet. For the first half of the semester we covered Linear Algebra, basic topology, optimization of functions of several variables, Lagrange Multipliers, and KuhnTucker theory. Post midterm, we did some ODEs which was a joke if you've taken a class for that already, and Calculus of Variations which could be lengthy. I highly recommend taking a course with Max. Dunno how he'll teach Honors Linear Algebra in the fall, but based on my experiences it's probably not going to be too painful.
Dec 2009 
don't take this class with pinkham. it will be the worst experience of your college career. you'll come out having learned nothing. from the lectures, you'll wonder if pinkham even knows the math he's teaching. he has a phd, but it sure doesn't seem that way. the lecture notes are long, have unworked examples, and are riddled with typos. in office hours, pinkham doesn't even work out the homework problems...probably because he has no idea how to do them. on that note, neither does the TA. and the homework is long and difficult and graded harshly. finally, the book is a waste of 80 bucks. we used it once all semester and it's horribly written so you can't even learn anything from it. unfortunately, you're going to have to teach yourself all the material (and fail horribly). and you'll probably have a C to go along with it. the grading is ridiculously unfair. pinkham should have never been allowed to teach a mathematics course (or any course, in general). avoid at all costs.
Dec 2009 
analysis and optimization has the potential of being a very useful and applicable subject but you will get none of this from pinkham. the first half of the course was pure analysis for which there was no book and the only study notes we had were the ones that he typed up. these were not clear at all and the important parts were left as exercises for us to do. in class he only talked about the idea behind the proofs and then expected us to know how to do them with the rigor expected from the 4000 level class. the second half of the course is optimization and we used the pedregal book which is one of the worst and most useless books i have ever had for a class. you're basically wasting $80. again he typed up his notes but these were useless. by the end of the semester the whole class had no idea what was going on and no one could do the homework ... not even the TA! his grading at least for the midterm was also pretty bad. he didn't curve according to how the class did but according to how he thought we should do. i'm pretty sure that this man won't hesitate to fail half the class or at least give out loads of Cs. after all, he's a dean. don't take a class with him.
Dec 2009 
Pinkham is hands down THE WORST professor I have ever had in my 3 plus years at Columbia. Not only is he rude and pompous (because hes the Dean) but he can't teach. He stumbles around class posing questions that he doesn't give answers too and going off on unrelated tangents, and then expecting us to learn 60% of the material on our own. We had weekly problem sets that were long and harshly graded often he couldn't even find answers to them or explain the questions, yet we were expected to be able to do them. I spent at least 20 hours a week on this class and still struggled through. The material shouldnt be difficult but he makes it hard he never uses concrete examples, instead theorizing without explaining where any of it comes from. All in all, do not take this class with Pinkham. He cant teach and is a super hard grader who curves around a B/C+. Not worth the anxiety in any form.
Nov 2009 
Professor Savin is a good professor, but he requires a lot of knowledge from his students, particularly on a theoretical/intuitive level. You cannot get by in the class simply by doing the homework; you have to gain some intuition (which he tries to teach in class). He's a very nice guy, though, and curves very well; on the whole, I would highly recommend him, as you'll both learn something and do well. He's very approachable and will teach you oneonone. Highly Recommended.
Oct 2009 
Below par, even for a professor in the math department. Course and textbook are interesting, lecture is utterly useless. Savin would always be unprepared, spend the entire class going over a single proof, get stuck, and then have to spend the next class fixing up his mistakes. Class dwindled by more than 50% after the first midterm.
May 2009 
Professor Hou is a great math teacher. After having taken classes with him over the course of 3 years, he is one teacher that I can rely on. His lecturing style may be quick but each lecture is very clear. He breaks things down and explains concepts thoroughly, plus he draws really awesome pictures/graphs to go with almost everything. He seems very conscious of his English skills, but he speaks clearly albeit with a slight accent. On the board he is not only legible (which, in the math department is hard to find) but he writes nice and big and always steps away for you to copy down the notes. Although he may make a few mistakes during class, he doesn't make many (always double check with the textbook). His courses are the few math classes where I studied more often from my notes than from the textbook. For all of the courses, he has a different strategy for grade breakdown, but it never strays too far from a standard h/wmidtermmassive final mold. His course website always is uptodate with assignments, assignment solutions, and dates of tests/exams. He usually posts practice midterm(s) and final with solutions and gives a little review of topics before each. He may seem kinda awkward, that is because he is. Thus, he may seem unapproachable, but do not fear, you can usually find him napping/wearing awesome slippers in his office during office hours because nobody goes. He has office hours twice a week (for A+O an additional problem session on fridays) and he is always happy to explain things if you just ask! The bottom line: he covers material in a timely fashion, and he is organized. If you want to actually learn some math and not just stumble through a course, Hou is the man. It is totally possible to get a good grade in the course if you put the necessary effort in, and I would say the grading in the courses is consistently fair (curved to a B/B+ avg). If you have the opportunity, take Hou. (his vast collection of sweatervests is also a plus)
Jan 2007 
Like what others said below about Analysis and Optimization, Sean Paul is simply the most confusing and disorganized Math teacher I have ever seen. Though attendance was almost always full, I believe that 90% of the class did NOT understand what he was teaching, and he himself got lost from time to time when he was trying to do the neverending proof problems in class. If you're good at selfstudying and don't go to any class or rely on any notes and can still get an A, it's okay. Otherwise: avoid him!
May 2006 
Sean Paul is one of the nicest men I've encountered at Columbia and one of the most accessible proffessors that I have ever had. That being said, and despite the fact that I love the guy personally, he is an incredibly confusing lecturer who can be near impossible to follow. However, the topics covered in the class are interesting and the workload is not very difficult. Before each exam you'll feel like you have no idea what's going on, but that's okay because everyone is in the same state you are. The problem sets and exams are easier than the lectures will lead you to believe and the book is actually pretty good. Often Prof. Paul will tell you in class exactly what the difficult problems on the exams and then if you go to him for help he will solve them for you. Though I had to take the class, I though it was pretty good and I would definitely recommend it as an elective.
May 2006 
If you were to miss the first few classes and only look at the book, you would think this is one of the easiest math courses you have ever taken. But sit in one class with Sean Paul, and you will be lost. He is teaching relatively easy material (in terms of the material covered in the book) at a PhD level. I don't want a doctorate in math, so spare me the lectures even your neighborhood Columbia math genius can't understand, and just let me pass. If you can't remember everything you learned in Calc 3, Linear Algebra, and *gasp* even some ODE at the snap of your fingers, then forget about it. As far as the homework assignments go, they are few and far between, some are pretty long, but if you read the book, they are generally easy. Sean Paul likes to throw you off whack apparently, because after an average to slightly more difficult than average first midterm, easy second midterm, he throws in a whammy of a final. And that's where the general problem of Sean Paul come to light, the material he is teaching is not the material you are learning in the book. So the material you learn in class (which is way above the level it should be), you never actually utilize or practice, and at the same time, you wind up teaching the material for the problem sets to yourself. Tests fall somewhere in between. As far as the final went, I count only one question that actually had to do with "Analysis and Optimization." If you like class notes that are full of symbols and formulas that look cool but at the same time you are bound to forget 5 minutes later or not understand at all, then this is the class for you. If you want an actual 2000level math class (I'd say SP's A and O is harder than some of the 3000's I've taken), look elsewhere. And if you happen to get stuck in this, keep your Calc book handy and cross your fingers. Just make sure you are prepared and remember: WHAT YOU DID IN YOUR HOMEWORK AND STUDIED IN THE BOOK WILL PROBABLY NOT BE ON THE TEST.
May 2005 
First of all, I'm going to refer to Sean as St Paul. Because I guess he just doesn't want to be associated with the rapper in his emails. Anyways, in life you win some you lose some. St Paul's a funny guy with a quirky sense of humor and real enthusiasm: plus. St Paul expects that you actually remember Stoke's Theorem and the Laplacian in polar coordinates from Calc III, and he lied about not rehashing KhunTucker stuff on the final: minus x 3. Kudos to those who did not sell their Stewart's calc textbook. The real problem with the class is his constant insistence that results in class can be derived with only elementary concepts from calc, lin al, and common sense. What he doesn't understand is that his use of elementary concepts are strung together by very convoluted logic. For example, he claims that one need not have taken ODE to understand that the solution to the equation y'' + c*y = 0 is a harmonic function. I invite you to solve that one without ODE (no characteristic equations). Good luck. No. Not cool St Paul, not cool. But look, the entire course can be condensed into three equations: Jensen's Inequality, the Lagrange mult eq w/ Khun Tucker conditions and the EulerLagrange equation. That's bascially it. BTW, you will not learn about numerical approximations in this class.
May 2003 
this guy seems to have lost all interest in teaching. during lectures he completely ignores the class and goes into long proofs which are not particularly relevant to hw or tests. not very nice about questions. i went to see him becasue i had missed a minus signs ina problem on an exam and he took off 20 of the 30 pts. he was nasty to me and wouldn't even look at the problem. boring lecture. bad hand writing. hard to understand sometimes.
May 2002 
A decent, but not amazing professor. His lectures are very straight forward and well organized. He can be a bit hard to understand because of his accent and the fact that it can be difficult to distinguish various letters he writes on the board (as alluded to by an earlier reviewer). Also, if you have trouble understanding something in the beginning of class, it can be hard to catch up, since he doesn't repeat things very often. The problem is, the material for this class is just not that interesting (and I find math interesting in general) and Herve doesn't do much to make it more so. Perhaps he was discouraged from his occasional attempts at humor (which were sometimes quite funny), by the fact that this was the most humorless group of students I've ever had a class with; they never ever laughed. He was very accessible and was happy to talk to me during office hours. He clearly knows what he is doing, he was always able to competently answer the rare question that someone in class asked (although he did sometimes seem frustrated at how brain dead a lot of these questions were). I suspect he would be a better professor if he were teaching a more interesting class.