Don't take Savin's class unless you have no other option. He's very smart (as expected), but not good at teaching students who aren't at his level. He often seems exasperated when students ask him clarifying questions or make casual errors during demonstrations. The concepts/problems Savin covers in his lectures and homework (taken directly from the textbook) are also NOTHING compared to the exams he makes. On multiple occasions, many other students and I were simply unable to answer questions because we didn't know what the hell we're looking at. This is an example of Savin assuming students can do the same mental gymnastics that he does. The average grades on both midterms were in the 60s (I can't remember what the final was). I left Savin's class with a general understanding of differentiating multivariable functions and calculating gradient vectors, which I suppose means that Savin did his job. However, that doesn't mean the process wasn't unnecessarily obtuse and arduous.
Professor Savin is a genius, but he's one of those geniuses that doesn't understand how everyone else doesn't understand the super complex ideals that come so naturally to him. I can see how he'd be a great professor for higher-level maths, but Calc III this semester (Fall 2020, online) has just not been it, my dude. He assumes we basically know everything already or understand it all the first time. He tends to ramble on a bit and focuses on over elaborating easy concepts and saying "well, you should just understand this intuitively" when explaining difficult concepts. Don't get me wrong, he seems like a nice guy who really wants us to learn. However, I think his own incredible brilliance (he literally scored perfectly on the IMO) keeps him from being a good prof for basics like Calc III. Most of our class doesn't show up to lectures anymore:( take him for diff. eqs., but not for this.
Savin is OK, not that good but not awful either. He teaches poorly, spends huge amounts of time proving easy concepts and then rushing through examples. And he honestly shouldn't try to rush, because he has a hard time solving calc problems: he doesn't bother to work them out beforehand, so he tries to wing them in class and always gets lost somewhere, and then stands in front of the board trying to find the mistake until a) he gives up and says "well, the rest is easy, you should know it from Calc III", or b) a student finds the mistake and points it out for him. The majority of the class ended up just staying home and reading the book, which was much clearer and a more efficient way of learning the material. Beware though of the last third of the course, after the second midterm, when he starts teaching calculus of variations. It's not in the textbook, so you'll need to go to class to learn that. He assigns relatively straightforward homework problems, but gives extremely hard ones on his exams. The curve is decent (B/B+), so you can struggle through the exams and still come out fine, but if you really want to feel like you have a firm grasp on what you're doing, you won't get that here. Ultimately, if you really have to take his section, it won't kill you, but there are better sections out there for sure.
Tldr: Savin is a completely fair professor who does his job and nothing more. Long version: Savin is a solid professor to learn Calculus IV from. Although I didn't attend most of this lectures (I had him for the 8:40 section and he teaches right out of the books/notes), the few lectures I did listen to were completely clear and intuitive. He stresses geometric intuition over rigorous proofs and teaches you to visualize what's going on with the random integration techniques you learn. He's not very personable though. His tests can be kinda tricky in a "goddamnit I should have gotten that question kinda of way." The "hard" questions are tricky because they force you to integrate over an awkward region, require you to see some trick like symmetry or rely on some intuitive understanding of geometric calculus. They're just difficult to solve in a testing environment. Just a note: Savin doesn't follow the usual complex analysis shtick. He does calculus of variations which I think is easier if you actually try to understand it. Problem is most people are too lazy and just didn't try. Luckily it was barely tested on the final and the related questions were unbelievably easy.
Savin is a boss. Somehow he makes everything seem obvious. He never looked at the book or notes during his lectures, and always talks in a very matter-o-fact manner. It's important to not let this get to your head too much- review the notes and make sure it really is as obvious to you as it is to him. Savin holds the class to a high standard (or, if you ask him, a reasonable standard). He's sad when the average is always less than he thinks it should be. Here is an excerpt from the email he sent us after the class was over: "The average on the final exam was 52. The exam was difficult and also the material we tried to learn." I actually think this class is important for math majors to take, even if it's not as sexy as other subjects. I did most of the homeworks pretty honestly, and I feel as though I learned a lot about how to think about PDEs and how to prove basic stuff about them (uniqueness, maximum/minimum principles, etc.) The class has more in common with analysis than it did with ODEs. (BTW, having taken ODEs before I took this class, the material / approach of the class is completely different; it's not necessary but if you're not a strong student it'll help you out.) Keep in mind that most of your grade will be based on two tests where time pressure will be an important factor. DEFINITELY review the homeworks WELL, but don't stress out about knowing little facts. The tests will see if you understand the general philosophy of the proofs, which I'll outline here: 1. If you have to show the only solution to a PDE is 0, first try to prove that its minimum is >= 0 and its maximum is <= 0 by keeping in mind that if u is maximized then u' = 0, u'' <= 0, plugging those conditions into the PDE. If that doesn't work, analyze the solutions of its characteristic curves or use some maximum principle. 2. If you have to show uniqueness of a linear PDE with certain boundary conditions, show that if u and v satisfy those conditions then u - v = w (with 0 boundary conditions) must be identically 0 (see above). 3. If you have to show that some quantity is decreasing, show that its derivative with its respect to time is always negative. To do this use ALL INFORMATION GIVEN TO YOU IN THE QUESTION, remember mixed partials are equal, and for the love of god integrate by parts (or use the divergence thm) until your expression is a bunch of stuff that looks like the integral over -u^2 or -u'^2 or something. Savin won't tell you these general strategies, but if you're reflective you'll pick these strategies up from the homework and use them all the time on the tests. Also, never leave a test answer blank! Just write something, write down the wave equation or the maximum principle or something. He'll try and give you as much partial credit as his conscious will allow because he's so depressed at how badly his students do. There's no way to fake yourself to an A in this class, but if you take it seriously Savin will be less disappointed in you than he is in everyone else.
Ovid, as he told us we could call him on the first day of Calc III, is a pretty great professor. I believe this fall was his first time teaching Calculus (at least in many years?), but he didn't seem rusty at all, though perhaps a bit bored with the basic and stoic material we had to cover. Either way, he taught extremely clearly and was willing to answer any question that a student had for him. He is funny, every now and then, though his lectures can get a little dry. It is mostly because he is so clearly brilliant that the class remains exciting. And it was pretty full, too. Not sure how many students were registered, but I would say about 2/3 were always there. Overall, a great and clear way to learn math fundamentals!
As many reviewers have previously said, Savin truly is a brilliant man. Moving away from that, I personally enjoyed his very straight forward way of teaching. He would do his best to explain the concepts he had to go over. Often it was clear he knew the material very deeply (I think he referred to the textbook in class only two or three times). Savin loves it when people ask questions, and will do his best to answer. Often times he would joke with the class about how little we asked questions and how he would like that to change. The important thing is that you are very clear when you ask him your question, often times it would need to be repeated a couple of times before he got it and proceeded to answer it. The material is difficult if you've never had something like this before, but overall, most of the questions are very algorithmic. The hardest part of the "straight forward" questions would be recognizing which method you had to use. Also, often the questions would reference methods exclusively mentioned in the homework questions (and not talked about in the chapter reading or discussed by Savin in class). At the end of every midterm and final, he put an unofficial "challenge question." This question was often very difficult and was generally only answered by those who deeply understood the material as well as had a good grasp of generalizing math. I can't speak to his office hours, as I've never gone, but I heard he was pretty solid in them.
Well, I just survived a year of Honors Math, and now that I've gone home and thought about it, here's my review of the course. To begin, Prof. Savin is a savant (look him up online and be amazed at all his accomplishments, which includes a perfect score at the IMO) who can effortlessly teach without notes and solve most challenging proof problems on the spot. Really, the greatest impediment to the teaching is his wonderful but sometimes incomprehensible accent, but his notes on the board and his office hours more than make up for this minor shortcoming. If you truly enjoy the intricacies of math, I highly recommend you take this class, which serves at the alternative to the laughable Calc III sequence. (The class started with 90 but eventually whittled down to about 30 by the end of second semester.) It's sufficiently challenging enough to get you well-acquainted with the higher-level math courses in the department, and despite the incredibly low test averages (see below), there is a very generous curve that will save your grade at the end of the semester. Plus, the second semester of the course is much easier than the first; perhaps at that point, Savin has successfully conditioned his students to expect the worst on his exams and they react accordingly. Lastly, the only way to study for Savin's tests are to make sure your definitions and ability to do computations are solid, because you're going to get destroyed on the proofs he gives out regardless.
Savin is a brilliant guy, but brilliance doesn't necessarily come from other brilliant people. This is not his first time teaching a freshman course, but he clearly did have much higher expectations at the beginning than we were capable of fulfilling. Much of this was due to the lack of transition from computational math to proofs. His proof-based homeworks were very insightful, or at least they would have been if anyone knew how to do them, and those who claim they did can't really be sure since the TA was clearly not thorough. It takes a lot to teach this class, and Savin did a great job. However, there is a stern line between teaching how to get from point A to point B and just telling a class it should be at point B by next Monday. This was particularly true once multivariate integration came back and the class had absolutely no clue how to handle parametrization let alone surface integrals, divergence theorem, etc. Savin had little time, and that's probably the Achille's heel of this class, so he has to send his students to the book for practice. Unfortunately, Apostol (our textbook) sucks at establishing a basic understanding of the subjects it teaches. It teaches from a proof-oriented perspective and then throws a bunch of poorly worded and arbitrary calculation based problems in the exercises, but I do have to admit the grueling differentiation exercises were good. All and all, the nature of this course is much like reviewers for other professors have stated, so I can't really blame him for the content. The curve is alright but nothing to keep your hopes up for. I think Savin curved the mean to a B+, and if you screwed up any of the actually do-able problems you were thrown back far. If you did the impossible, you were thrown ahead. Studying helps to a point, but intuition is where its at. Savin's personality is very unique. I don't think I could do it much more justice than has been done below, especially the amazon one. He's an impersonal but warm fellow who is always looking to help when he's teaching (he really does scan peoples expressions to see if they understand what's up), but he won't go out of his way to help you or show you a drop of mercy. The TA was good for the most part, but he quit giving homework solutions after they were turned in, which would have helped a lot for some problem sets. Overall I'm glad I took this course. It was a good introduction to higher mathematics and whats along the future. Would honors linear algebra and Calc 3 and 4 have been better? GPA-wise probably. Proof learning-wise probably. Stress-wise probably. Experience-wise who knows... probably. Savin's great (not that he'll even be teaching it again), but the course is too vast to give more than a wishy-washy understanding of all it entails and the grade distribution promises to hurt at least half the class.
This is Prof. Savin's first year teaching a freshman course, and it showed: he assumed that most freshman students actually knew what mathematics meant. But we didn't. We thought "oh we get to look at curves and surfaces and put them in our calculator, or write down their equations, and compute facts about them! After all, how could our high school give us the wrong idea about Math?" I think about 1/2 to 3/4 of the way through the year most people begin to come to the realization of what we should actually be aiming for in the homework sets (in Savin's words: "Think of the picture, then the proof is obvious, I don't need to write it"). Starting with single variable calculus, which in its standard form as required by every other science/engineering/econ major is horrendously mundane, Savin gave us "interesting" problems for the homework and tests, much to our naive horror. Looking back, those first few homework problem sets (well not the first one, which was rigorous proof in the real number system) were the most interesting, and difficult, part of the class. Unfortunately, by the time most of us had got our math bearings, other members of the Math department (or perhaps even Savin himself) had smelled the freshman blood in the water and the class became easier tenfold. Which is a shame, as all of the homework sets for Linear Algebra were directly from the book, which compared to Savin's sets are akin to a coloring book in difficulty (but a lot less fun). However, most of these obstacles aren't faults with his teaching, they are faults with the way Math is taught in the US all the way up through high school. It is not surprising that many of us did so poorly (and thus were saved by the curve) on Savin's first midterm: for most, this is the first real Math course ever taken. Math is an art, and Savin does try to help us starry-eyed first year students understand that (without directly stating it, of course). Go into this class with that clear in your mind, and 1) the homework and tests will be easier. Especially the tests: Savin will take an elegant idea-driven proof over an algebraic plug-and-chug any day, 2) his digressions into interesting subtopics and counter-examples of Calculus I/II and Linear Algebra (Fourier, anyone?) will be the highlight of the course, not the bane of your existence, and 3) when Savin says his now (in)famous "go home and think about it", you will actually look forward to it. Don't take this class just because you were told you were "good at math" in high school Calculus (unless you were lucky enough to have received a real Math education, and were saying "duh" throughout this whole review); take this class because you are curious and actually want to play and struggle with the implications of our notion of derivative, integral, and vector space. Also, Savin is a really nice guy: if you do take this class, don't make the mistake of skipping out on his office hours. He directly helps you with the homework and is always excited to help you gain a foothold on understanding the sometimes abstract solution process of his more difficult problems.
Savin really knows his stuff, but sometimes it seems like he doesn't really teach so much as just illustrate proofs in class. Which is fine, especially since he's got this wonderful Romanian accent, but you're definitely left to struggle with the material yourself some moreâ€”his response to more basic questions is usually 'go home and think about it'. That said, the class will teach you more than any other math class you've taken, since you take things more or less from the ground up. Although it's proof-based math, there wasn't much of an introduction to proof, and at times it seemed like we were both learning something for the first time and reviewing it as though we'd been taught it ages ago. The lecture hall was full the first few days of class, but it thinned to about half by the end. On the plus side, nothing gives more camaraderie than knowing that all of you are struggling togetherâ€”the average on our first midterm was 30/100. The homework is hard, the tests are impossible, the grades are curved at the very end, but I'd definitely take this class knowing all that.
First of all, I took this class four years ago, so it's possible some things may have changed, but I doubt it. This review comments on the material in this class, its difficulty and what Savin is like as a teacher. As others have said, this class is much harder and requires a much higher commitment than calculus or linear algebra. To really learn the material and get a good grade you're going to have to know Rudin backwards and forwards. You will also have to do all the problems Savin assigns, even the ones he doesn't collect, and then some. Be prepared to spend more time studying and doing problems than in any other class you've taken. The students who succeed are the ones who love math, I mean really love it, and expect to use this material for the rest of their lives. If you're looking to challenge yourself or take an interesting math elective, don't take this one--at least not with Savin. To give you an idea, the kid sitting in front of me during the 4061 final handed in a blank exam. That said, as long as you have the necessary preparation and motivation you don't have to be some magic genius to do well here. In my case I had already taken Honors Math which was key since it covers a lot of the methods used in this class. The optimization course may also cover some analysis techniques, but I never took it. Although Savin is indeed a super nice guy, he is by no means an easy grader. He told me that he wanted 20% of the grades to be an A- or higher. I don't know if he was actually that harsh, but that was what he said. Despite that he was the best lecturer I've encountered--and I've had quite a few classes in math and the humanities--simply for the depth at which he understands the material and his willingness to show that understanding to students. I don't know if he is Russian, but he has a very dry, ironic, very Russian sense of humor. Think Vladimir Putin but nicer. Lectures were very clear and businesslike without extraneous non-mathematical information. This puts off some people but I kind of liked it. Also, 4062 is harder than 4061 partly because the material is just harder and partly because the quality of Rudin's exposition deteriorates significantly in the second half--particularly in the chapters on power series, Fourier series, the gamma function, and differential geometry. I found Munkres to be much easier for diff geometry. It's also worth noting that there seem to always be a few grad students taking this as a gut course--I think the entire first year class in the Statistics department was taking it when I did--and that this effects the grade distribution.
The man. The myth. The Romanian. On the first day of 4061, Savin told us of an important aspect of analysis - in every problem, there is never any more or any less information needed to solve it than what is given. I felt this was a theme of his teaching throughout the course; he presents no more and no less than exactly what we need to know about each concept and topic. A variety of people take analysis for various different reasons. As someone who is took it for a solid foundation in pure mathematics and for plain old intellectual growth, I could not have asked for a better instructor than Savin. The textbook, "Principals of Mathematical Analysis" by Walter Rudin has been the standard analysis textbook for over half a century and has not been revised since 1976. In the first semester I cursed the thing's existence, as did most of the class. Even the TA said it is really not a good book from which to learn analysis for the first time. Aside from the prose, the problems were a new form of hell to all of us. An illustrative example was one particular problem that the TA solved during office hours with a very clever use of concavity and inequalities. When we asked him how he knew to do that he replied, "Well, a few hundred years ago someone sat around for a really really long time and figured this out, then he told someone, and that person told someone else, then years later someone told it to me, and now I'm telling it to you." The point being that there were many problems where once you see the solution your only reaction is, "How on earth was I supposed to know how to do that?" The answer is either someone tells you, or you are the guy or girl who sits around for a really really long time and figures it. However, by the end of the year, some of us really began to appreciate Rudin, and today I think it's one of the best mathematics texts ever written. I sympathize with those who complain about the amount of memorization required for the exams, and I can say that the run up to each exam was never a pleasant experience - one that I'm glad to be done with. However, Savin never assigns irrelevant things for the sake of assigning them, nor does he put any of the long and obscure homework problems on the exam; in each proof there is something important that he thinks you must understand. Memorizing in this class is not like memorizing a bunch of chemical names from flash cards, it really forces you to condense and rewrite the proof in a way that you understand it, and make sure that you understand every key logical step. From my own experience, there were original exam questions that I was only able to answer because of my careful study of the proofs he forced us to know. So putting the effort into knowing those proofs can be a two for one deal. One unfortunate part of 4062 is that the first topic, Fourier Series, was so goddamned confusing that a lot of people dropped after the first midterm (hell, some dropped in the middle of the first lecture.) Part of the trouble may have been that it was a continuation of the last topic in 4061, and the winter break severed the continuity. But after that chapter, the course shifted to completely different topics which were much more comprehensible and I felt were the most enjoyable of the entire year. Having talked to people who have taken 4062 with other professors, and having seen the syllabi of others who have taught it, Savin is one of the only professors who thoroughly covers every chapter in Rudin. In particular, most either skip chapter 10 entirely (Integration of Differential Forms, the longest chapter in Rudin,) or give it a very weak treatment. This is unfortunate as I found it to be my favorite part of the course. Savin's personality is really hard to describe. He is never overenthusiastic and never bored; if I had to describe his personality in one word: non-quirky. His lecture persona is that of the foremost expert of avant-garde film who has been sent in to the Amazon rainforest to explain the plots of various David Lynch films to the indigenous tribes. He is extremely approachable and always willing to help, though he never makes small talk or ever talks about anything other than the task at hand. He's one of the only professors that I've had who has not once said so much as a sentence about his outside life during lecture. You'll never hear anything like, "This reminds me of a joke my thesis advisor told me when I was a graduate student.." If you didn't hear it from other people, you would never know that he is Romanian, that his wife is Daniela De Silva, that he has a daughter, or that he eats and sleeps just like every other human being on this planet. This made him all the more intriguing and added to the cult status he holds with some of us who stuck with him for the whole year. I would take absolutely any class he teaches without hesitation. One aside about the course itself: an interesting social phenomenon in Modern Analysis is a fear that permeates through the class of phantom "math geniuses" who somehow know everything, dwell in the back of the lecture hall, and ruin the curve for everyone. One of the main reasons that so few people from 4061 go on to 4062 is that they think that 4062 is going to have all the "geniuses" from 4061. I'm going to call bullshit on this. From my observation, the people who did really well in the class were not savants, but those who worked hard and had a good amount of time to dedicate to the class relative to other courses.
Professor Savin is a great lecturer. He has a simple style that makes it easy to understand the material. I found the class interesting and fun to attend. Questions were always welcome and he was constantly asking questions for students to jump in and answer which made coming to class a little more exciting. The course was at a reasonable pace and followed the book quite well. I highly recommend taking the analysis sequence with Prof. Savin if he teaches it again --or anything else that he teaches. You will learn a lot. The workload was lighter than expected (~1 hour for each homework and several hours for the test preparation) and I think it wasn't hard to do well on the tests and homework.
His teaching style was ok (perhaps he could refer to intuition more to build relatively abstract concepts), but the course emphasized too much memorization. Besides that, there were three problems per homework and all were very difficult. In other words there was no foundation or nothing to build upon. It was sink or swim-- unless you are gifted at memorization, as many people in that class seemed to be. However, while the textbook is cold, dry, concise, and littered with circular logic and fallacy, Savin himself is a good person who would be willing to help if sought after. I think he could have surveyed notions such as that of continuity at a more philosophical level and attempted to show through emperical tests why they may hold true and aren't arbitrarily defined to create an abstract universe which is nothing like the physical universe. Also, he could have tried to build understanding more intuitively, as the basic ideas don't come from some arbitrary abstract universe (although that is where they may eventually lead to), they come from the physical universe, so something like, you can take a piece of wood and cut it into two pieces, three pieces, and thereby always find a piece of wood to cut into more pieces-- the set of natural numbers tends to infinity not in any abstract universe only, it also happens in the physical universe. The point is, these ideas have foundation, more or less, in emperical knowledge, and if he could supplement his lectures with more emperical intuition, that would make it probably much more accessible and interesting. Too much memorization killed it for me anyway, I had lost all hope and interest in class.
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 one-on-one. Highly Recommended.
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.
Prof. Savin has matured as a professor in a very short time. My roommate took his course in Spring 2008 and had the impression that he did not explain results well in class, and that he sprung surprises on exams. She did note that he was very able to field questions and respond to them effectively. The best professors are quick learners. I took 4061 with Prof. Savin in Fall 2008 and was struck this morning while sitting in on 4062 (in Spring 2009) that he had been to scanning the room between definitions and proofs to see if students understood the progression of concepts. I've never seen another math professor with that kind of self awareness or ability for self correction. Don't get the proof? Alright â€“ we'll tear it apart and put it together again. Definition not sticking? Let's take a look at another diagram. For this, I enjoyed Analysis I more than Calculus I. It's not an easy course by any stretch of the imagination, and the only way to do well is to work like a dog. It's a lot to learn, but in the end you'll know you have earned your understanding and you'll have built something beautiful in your mind. Either that, or you will drop out. The survivors learned to lean on each other, and for what it's worth, the TAs are unbelievably good at what they do.
The previous review which calls this class "miserable" was extremely unfair. Savin's expositions of the material were very good: slow, thorough, clear, with good examples and illustrations of the theory, and certainly no unfathomable logical leaps. Rudin's Principles of Mathematical Analysis, the textbook for the course, is very dense and Savin's good at helping you through it. The thing to take away from my review is this: math majors rarely seem to write reviews on CULPA. If you want to take analysis to look good for business school, don't. If you want to learn some great stuff, please take the class. I know of some econ kids who talked to Savin at the end of the semester and said they'll consider taking Analysis II iff Savin is teaching the second semester.
This was by far the hardest, most miserable class I've ever taken. Savin is brilliant and is quite good at explaining things if you ask, but without being prompted he will gloss over important details, assuming that the class is as brilliant as he is. I am good at math, but not that good at math. The material is interesting, and after the course you'll be an exceptionally logical person. But don't take it without a backup plan. It's hard as hell, the homework takes forever, and if you're not a natural it's a lot of memorizing infinite proofs and proof methods. It's definitely not for everyone, and it's terrible to get stuck in it if you're not sure you want to be there.
Super nice guy, ultra well informed, great one on one, not very clear in class and tends to say "and the rest is obvious..." when discussing non-obvious results.