Ordinary Differential Equations

Jan 2021

Johne is a piece of work. The sole source of my stress for the majority of the semester. I'll start with the good. This class is conceptually challenging and will force you to learn a lot of ODEs at a very high level. You will cover a lot of proofs. You will become intimately familiar with modeling the harmonic oscillator using an ODE. You will definitely never be bored. Now the bad. Johne is incredibly incompetent. His problem sets are atrocious and sometimes took me upwards of 20 hours. He writes all of his own problems, and they tend to be of the form "prove xyz = abc", which is hellish. Additionally, in 2020, his exams were take home, which sounds kind and forgiving, but in reality, Johne formatted it so instead of a 2-hour exam it was a 48-hour exam. Exams had millions of parts, were convoluted, and were incredibly difficult. And on top of it all, harshly graded! Finally, Johne's lectures suck. He just does a bad job telling you what is important, what you should write down, and what is irrelevant. His lectures are basically a series of worked examples, with a little theory thrown in. So you always have to go back and decipher his work. In essence, Johne takes an already-difficult class and makes it so indecipherable that it doesn't feel real anymore. If this class wasn't required for my major, I would have dropped it.

Aug 2016

This class was not particularly hard or interesting. The Professor generally lectures straight from the textbook so you are welcome to just read the textbook if you don’t want to go to class. The problems in this class are fairly algorithmic; you usually just have to identify the type of differential equation and then use the provided technique to spit out the answer. The examples in class are usually useful to see how one should think about the problems, so I would recommend going to class over reading the textbook. The answers to all the homework problems are in the back of the book which makes the homework average very high. The issue is that Panagiota is not always aware of what she put on the homework, so there might be problems from a section that was not explicitly covered in class, in which case you simply have to learn another formula and apply it to the required problems. Her exams are not particularly difficult, though there was one question from left field on both her first midterm and the final. Overall, this is a fairly straightforward class with a decent textbook and an alright teacher, but don’t expect much from her in terms of email or office hours.

Jul 2014

I found Prof. Chen to be straightforward and reasonable. His office hours are generally pretty empty, so be sure to go to ask your questions (and keep reminding him of your name). His course had a pretty heavy curve, and I did not find it difficult to get a good grade. Just stay on top of the material, do the homework, and check your answers in the solutions manual. I'd also recommend studying from the book series' study guide.

Jun 2014

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.

Jan 2014

bohan fang is a nice guy, and he will always try to help if you approach him. also, the class is quite easy because he gives practice midterms that are exactly like the actual midterms, and if you know the practice midterms, midterms, and practice final very well, you'll have no problem on the final exam. that being said, professor fang is one of the worst teachers i've ever had. i say this with no exaggeration or spite, but rather to offer my honest advice: do not attend the lecture, it will certainly hurt your comprehension of the subject. read the book on your own, watch MIT opencourseware lectures, find tutors in the math help room, but whatever you do, DO NOT ATTEND THE LECTURES. you will not be able to understand a word he says, his notes are disorganized, his chalkboard handwriting is dismal, and he provides no narrative whatsoever (not even simple motivations). he also expects you to know certain things that you may or may not know, and if you don't know those things going into the lecture then the steps he takes in examples and proofs will make no sense. what's worse, he doesn't say what he's expecting you to know, or even allude to the blanks you're supposed to be filling in on your own, so if you don't recognize where it is that you're missing a critical step, then the notes will be depressingly confusing. just stay away from the lecture room until exam time, work hard on all the homeworks and practice tests, and you'll do well in the class,.

Jan 2014

Pretty boring course. It consists of being given a new way of solving a very specific type of ordinary differential equation each class. The good part is that you don't have to really understand the material to do decently in this class, you just have to remember what to do when you are confronted with a particular kind of problem. It's kind of like memorizing an instruction manual. Chen spends each class writing down examples of problems on the board and solving them. The bad part is that Chen does not give you an intuitive or proof based understanding of why the methods work. The textbook doesn't help much in this regard either as it presents concepts in an over-complicated way. Furthermore, there is no application of what you learn to even slightly realistic situations as there are no word problems, just equations to solve. Also beware that a significant part of this course requires linear algebra to understand. You need to understand eigenvectors to really grasp how to deal with systems of differential equations and how to represent solutions graphically. In the absence of this you are forced to again memorise graphs for each type of solution. Chen also for some reason skipped LaPlace Transforms which every other section of ODE seems to cover. All in all, a pretty frustrating class.

Dec 2013

Exactly what you would expect, no more and no less. As straightforward as they get, this is a course where you can definitely get by without attending a single class. The book is clear, the solutions to the HW are in the back of the book (make sure to get or have access to the right edition!), tests are straightforward (with the exception of the second midterm which had a couple of odd questions). Chen's English is decent and understandable, and he is relatively approachable, answering homework questions in office hours and very willing to raise grades harshly given by the TA. Every lecture consists of the basic mechanics of some new technique and then examples. If you want a simple, easy, no-frills introduction to ODEs to satisfy a requirement or some such, this is the course for you. If you're interested in the theory, the higher math, the ideas- look somewhere else. But Chen does an excellent job of delivering on the course as it is.

Dec 2011

I really enjoyed having Ovidiu this past semester. Unlike most of the engineers in the class, I was one of the few students from Columbia College. I decided to take this class as an elective. At first, I was a little concerned because Ovidiu is a very quiet man with a somewhat thick Romanian accent and sticks strictly to the lecture and at first, some of the topics like integrating factor make no sense. After a couple weeks though, he becomes really endearing to the entire class and the material magically makes sense. He's like a giant teddy bear you want to hug. I took the 9:10 am lecture which most students don't attend; however, I would highly recommend attending lectures (he also offers an 11 am lecture). There is a lot of material he covers that is not strictly in the textbook that is on problem sets and exams. If necessary, I would advise attending his office hours especially if you are confused about Laplace Transforms (they are a nightmare!!!!). Ovidiu is extremely knowledgeable and willing to help any of his students. Overall, I would definitely recommend this class!

Nov 2011

Take this class with Ovidiu Munteanu if you get a chance, this class is extremely clear and surprisingly funny, considering Ovidiu's tone and facial expression. I don't think he was trying to be funny a lot of the time but, the amalgamation of his monotonic voice and straight face, some of the things he said were just hilarious. Once, he was talking about the Vandermonde Matrix and emphasized tot the students that he was not talking about Voldermort! The math in this class is pretty mechanical and computational, he will show you proofs in class (which is nice for those who are interested) and he will go over variable of examples that will pretty cover the range of things you need for the hw and exams. Overall, good experience and manageable workload.

Jun 2011

If you've taken the class elsewhere, and simply need to take it at Columbia since Columbia doesn't give you the credit from elsewhere, take this class. It'll be easy. You may choose to not go to class. I still went to all lectures. They weren't helpful, but if you can learn the stuff on your own, it doesn't matter. The homework was somewhat annoying, but since they comprise an insignificant portion of the grade, it doesn't really matter if you can't get through the long proof. The exams were easy. Compared the ODE class I took in high school, this was a joke. Sure they got harder, but they were very challenging in a doable way. Again, you'll only find it fun if you're really into math, and have some knowledge of ODE beforehand. He generously gives out A+, so definitely aim for that. If you have no knowledge of ODE and are not sure what it'll be like, good luck; I suggest you take the class with a different teacher.

May 2011

Do not take his class. I repeat: DO NOT TAKE HIS CLASS. I took this class because I thought it would be an easier way to learn ODE than taking the course in the math department. Boy, was I wrong. First off, you'll immediately notice the incapacity of Professor Fang to teach effectively. His lectures are fairly well structured, and would have some good information in them...if you could hear them. He lectures facing the chalkboard for the entire 75 minutes, turning around maybe twice to look for questions...but by that time, you'll be too confused scribbling down notes about concepts he hasn't fully explained to remember what you were gonna ask in the first place. His accent is thick enough that you will need to hear him say something a couple times before you actually figure out what it is. Trying to ask him for help after class is also useless...he'll just give you the same exact explanation he gave for that topic in class, so if you didn't get it then, you're definitely not gonna get it now. He also wears the same sweaters for months at a time. Lovely. And then came the tests. Each one that comes out gets progressively harder--he's not testing you on the course material so much as your ability to solve problems much harder than you've ever seen before in an unreasonably short time limit. The final was much, much harder than any of the homework problems--to the point where the actual answers were considerably more complex than anything I could have come up with. Isn't there an unwritten rule that answers on a math test should always come out somewhat neat? Not in Bohan's class. Despite all of this, I figured that since I did my homework, had done decently on the midterms, and only slightly worse on the final, I could still walk out of the class with a slightly disappointing, but acceptable final grade... ..and boy, was I wrong again. I don't think he curves this class at all...if anything, he probably curves against you. I got a full letter grade lower than I expected...and I really didn't think I was expecting much. And to believe he taught 2 out of the 3 sections of this course? Unbelievable. Columbia, I know you don't hire professors to teach, but this was absolutely absurd.

Apr 2011

Cagatay Kutluhan is an excellent professor. His lectures are crystal clear and so is his handwriting. I shopped around different professors before I settled on his class. Very fair grader. Straight-forward exams. His notes are much better than the text itself. I wish all math professors at Columbia were like him! I have not received my grade yet, but I don't care as the knowledge I gained from attending his class is priceless. The TAs he selected were perfect too. I would highly recommend taking any class under him.

Jan 2011

Cagatay's method of teaching is unorthodox, but nonetheless effective. He makes sure everyone is paying attention. Sometimes he'll write something incorrectly on the board to make sure everyone is awake, and he guides students through proofs in class rather than just spoon feeding every derivation. He works through many examples, always listens to questions, and will challenge each of his students. As long as you are fundamentally sound in Calculus I-III, taking ODE with Cagatay will not be problem (he does expect that you remember integration by parts, fundamental theorem of calculus). Also know that as long as you pay careful attention to detail on the exams and take your time, you can pull off a B+ no problem.

Dec 2010

Okay teacher as of right now, decent at best. Lectures are mostly useless, consisting of quotes and occasionally paraphrases from Boyce and Diprima’s Elementary Differential Equations book (the only reason to go to class is to turn in your homework for the week). My chief complaint of Cagatay, shared by many in the class I spoke to, was his inability to connect with the students during lecture. I would sometimes come out having understood much less than half of what he was talking about. His explanations, and responses to student questions, were limited to rewordings of Boyce (which itself is a difficult text from which to self-learn) and offered little to clarify problems or elucidate the material. The results of the ridiculous first midterm, where the average was 40, median 39, led him to reconsider the scope of the class material, and he ended up cutting Chapter 7 (systems of linear equations) from the syllabus—we focused most of our time on series solutions and Laplace transforms. After a while, Cagatay did get more accommodating to student needs, and our second midterm was much more straightforward, as were the homework problems. The average was a 72. The final wasn’t bad either, and the average was also a 72. I think the distribution of grades was about what an engineering (but not math) class is normally—the average was curved to about a B/B+ (although Cagatay frightened us initially by saying he’d curve to a C+/B-). On Cagatay’s good side: he’s quite responsive to email and enjoys interacting with the students (he learned all our names within a few class meetings), and seems open to talking during office hours. However, he doesn’t seem too interested in teaching the class—as it’s sort of run by the engineering school while he’s in the math department. Cagatay will get better soon, I think, as seems very willing to change his lesson plan and heed student opinions (e.g. he gave us mandatory evaluations during class). Overall, after speaking to friends from the other ODE classes, I would say take Cagatay’s class if you can’t get into Lauda—who’s awesome, I had him for Calc III. Cagatay is probably better than Virdol et al but I still wouldn’t call ODE with him an enjoyable experience, as of now. P.S. I have serious difficulty believing it was anyone but the professor (or the kid in the back who got the A+) who wrote the previous review.

Dec 2010

Professor Kutluhan is new to Columbia, but is an excellent professor who will likely soon be known as one of the better math professors we have at the school. Initially, the pace of the class was extremely fast, and that led to the first midterm's average of 40/100, but as he settled in, the class become much easier to understand and very instructive. He is good at explaining concepts and always makes sure to clarify things when somebody asks a question. He's also very helpful if you ever want to ask him something after class or go to his office hours, or even through e-mail. All in all, a great professor who seems to enjoy his job and cares about his students.

Jun 2010

Let's start off with the very first day... Right off the bat I should have known this guy was going to suck. He was 5 minutes late to HIS first class. He taught a few things that were helpful the first 4 or 5 classes. After that he started talking about things that were beyond the scope of the class and mostly not understandable because they required more advanced knowledge of mathematics, so the class very quickly became useless. I stopped going nearly completely after that, except at the end of class to turn homework in. The book sucks because it takes a LONG TIME to read and teach yourself, and it's particularly dry, but Boyce and DiPrima taught me way more than Tignor ever did. I would say stay away from this man at all costs. He showed up 20 minutes late apparently one day. I left after 15 because that's all students are required to wait for their lame ass professors.

May 2010

Oh Kenneth. You are one goofy guy. Deadlines? Class start/end times? Grading? Completely oblivious to all of the above. Into class 5 minutes late and out of class 10 minutes late, midterms handed back a month after being taken, 4 page homework assignments due the day of the final, Tignor quite literally does not care a whit about this class. Not to mention his lecturing. You will be lucky to be graced with Tignor’s face once or twice during the class as he lectures to himself and the blackboard, back turned to any semblance of adherence to social norms or any relevance to the course material. 45 minutes tangents into linear algebra are the norms, not the exceptions. If it weren’t for the generous curve and otherwise obscene alternative ODE courses, Tignor’s class is a stay-away. But believe me, Virdol et. al. are very probably worse. Pick your poison.

May 2010

Don't be fooled. Professor Tignor explains things in the beginning of the course well, if a bit awkwardly. This will come to a screeching halt later on as he goes on tangents about linear algebra and complex analysis and how they can be used to prove things in alternate ways in the class. In the first month or so of the class, Tignor actually explained how to solve the problems; this made the homework easier. After that, all of class was spent deriving theoretical results, most of which were not relevant on the homework or on exams. Maybe one sample problem would be solved every two sections of the class.

May 2010

Virdol is hilarious. He's such a terrible teacher, it's entertaining. He comes in late, and he goes ridiculously fast through the material. In the latter half of the semester, he often dismisses class within 30 minutes. If you're going to class, bring an iPod to keep you entertained. The HW load is really good; 6-8 problems. He gives practice tests, which are usually the exams he gave the year before. They look exactly like the actually exam. Don't go to class. Learn and memorize the practice stuff. "Shamelessly grovel for points." (as a previous reviewer said)

May 2010

Professor Virdol is far by one of the worst teachers I've had at Columbia. So bad, it was actually kind of entertaining. Professor Virdol clearly abhors teaching. He often came in late (he did squeeze his office hour in between classes), burned through explanations and examples with little more than "So you've got dis guy... and den you get dis guy... And den you get dis guy." He once went through two book sections in 30 seconds. He's got horrible handwriting, e.g. a "t" looks like a "+", which both look like a "ψ". I found his lectures marginally helpful in doing the work. He never looks around to see if there are questions while he's lecturing, and has no intention of answering any even if he does see a hand go up. And at the end of class, he tries to burn out the door without staying to answer questions. HOWEVER, the workload isn't too bad. He assigns problems sets of about 6-8 problems a week, 2 from each section he covers. The homework problems he assigns are fairly representative of what you can expect on a test. Additionally, he gives practice exams that are very representative of what you will see on his exams. He goes through them in class (in my opinion, the most entertaining classes are the exam reviews: he burns through problems, skipping a lot of steps, and finishes the exam in about 45 minutes). Bottom line: Virdol's a horrible lecturer, but the class could be worse. You can skip lectures and be fine.

May 2010

Prof. Virdol was a horrible teacher. Perhaps it was the pacing of the class, but I cannot say that I learned anything due to what I was taught in class. Prof. Virdol would come in, quickly rush through the material for the day, and then give up and leave class after half an hour, saying that the textbook was too short for us. During exams, he would hand out the tests and then sit down, put his iPhone headphones in his ears, and then watch a movie and giggle to himself noticeably. Prof. Virdol would rarely finish solving an equation; he would instead go halfway through and then tell us that we could solve the rest ourselves. His examples did no elucidate the material, he could communicate the material to us effectively, and he could not answer questions satisfactorily. Midway through a lecture or question, he would stare at the board with his hand on his chin, thinking of how to solve the problem or what to say. This indicated that he had not prepared satisfactorily for the lecture, even if he did have notes. The grading process in this class was also impossible to understand. His exams were far harder than the material he attempted to teach in class, and his practice exams were nowhere near similar to the real exams. Homeworks were originally graded on a 100 point scale, but after the second midterm, were graded on a 10-point scale at most, with the value of the homeworks decreasing until they reached 6 points or less each. The homework was somewhat helpful in practicing the material, but the large amounts of graphing that we were made to do were never asked of us on the exams. The textbook, Elementary Differential Equations and Boundary Value Problems by William E. Boyce and Richard C. DiPrima, is a decent book. It helped in learning the material, but even then, it seems to teach by examples and does not give straightforward explanations of how to tackle the different methods for approaching differential equations. However, the textbook was far better in teaching the material than Prof. Virdol ever was. I would never recommend Prof. Virdol as a professor, not in a hundred years. No one deserves that sort of misery.

Jan 2010

This was a painless, if quite dull, class and a good section. Mu-Tao was a nice professor who tried to make the tedium of regular singular point series solutions at least bearable. He had his work cut out for him, and sometimes I'd catch myself falling asleep. His accent was not terrible after a few classes, once you got used to it. The material is very applications heavy, as you'd expect from an "engineering" ODEs class. You'd learn how to recognize many different types of ODEs and how to solve them, rather than spending time learning why the methods you choose work. I'd say take that into account while picking classes, but since this class is a requirement for many majors, I'm not sure there's much of a point in doing that (although there is the 3027 ODEs class). I honestly don't feel like I learned that much after the class, but I'm not sure if that's a function of the professor or of the class. I suspect the class, and so I'd recommend Mu-Tao as a good professor with whom to finish this requirement.

May 2009

Good professor, but will make you feel dumb if you ask a question during class. Overall a good professor for a course which was medium difficulty.