CS 4210 / MATH 4250 - Numerical Analysis and Differential Equations

General Information

Prerequisites

Linear Algebra (Math 2940, you don’t know how to multiply matrices, you’ll definite need to take 2940) and some Matlab experience (don’t worry if you don’t though)

Topics Covered

• Matlab Syntax
• Floating point representation (IEEE double precision typically) and ways of combating loss-of-significance prone computations. (Also interval arithmetic)
• Polynomial Interpolation (Vandermonde matrices, Langrange, Newton, chebyshev points and minimizing inf-norm error of the interpolation, “preconditioning” the vandermonde matrix) and also spline interpolation

Workload

It depends, the average homework solution is about 15-20 pages per problem set, but about 50% of that is taken up by graphs generated in Matlab. The homeworks are very reminiscent of lab reports, but without having to do lab.

Severe. Possibly the most work in a class I’ve encountered thus far because the average problem set is comparable to the average CS 3110 problem set, except these are WEEKLY.

I strongly agree with the severe remark. Each weekly problem set after about the third or fourth (the first few are very easy) could easily take upwards of 10 hours, and then there’s the final. It’s manageable if you follow in class very well and stay on top of textbook readings, however if you do not there’s a slim chance you will understand a large amount of the problem set.

This class should be on the EPA’s hot list for killing trees, since the weekly homework assignments will each average 15-20 pages and take up several hours to do. The take-home final will be significantly longer still. While most of the homework will consist of MATLAB-generated plots, it’s less trivial than I had thought to write the code and, more importantly, analyze the plots. Be prepared to print out mountains of homeworks for this class.

General Advice

Be slow and studious when approaching the problem sets. The problems aren’t generally very hard if you’ve had an easy time with diff-eq, multivar, or linear algebra; but if you get stuck, you can always turn in 50 page problem sets that the TA will never in her right mind look over and get an automatic 100.

^I strongly disagree with the above. The problems mostly have very little to do with diff-eq, multivar, or linear algebra; the linear algebra and diff-eq parts are trivial and you can usually just use WolframAlpha to solve it. Almost all of the math in this course is new if you’ve only taken multi+linear+diffeq, and you will need to pick up MATLAB quick (definitely don’t take this class if you have no programming experience). The problem sets are extremely time consuming and the TA is very picky; if you have one tiny error she will find it so it’s often better to write as little as possible.

I also strongly disagree with the first remark. I received an A in diff-eq, multi, and linear and also found these problem sets to be incredibly hard and time-consuming. Also the TA is indeed very picky and will take off 1 point out of 20 for a ridiculously minute error. I took this class knowing zero Matlab in the beginning, I would say that’s okay and I did fine, however if you have little programming experience stay away until you’re comfortable with basic imperative programming (you will program a lot for each assignment).

If you can, take CS 4220 before taking this class - even though the course number is higher, it introduces a lot of the concepts at a more relaxed pace, and can help a ton with building some of the “numerical intuition” that comes in handy for this course.

Testimonials

Good class, but it starts out very easy and at the end is almost impossibly difficult. Should definitely be structured better. Vladimirsky is a genius but I didn’t learn too much after the first half or two-thirds of the course, because it was over my head (and not for lack of a proper math preparation) and the homeworks got almost comically tedious.

It’s possible to get a lot out of the class (I know I learned a lot) but the class is incredibly demanding and there should definitely be a restructuring of the course. Make sure you’re interested in the material from the beginning, because it does not get any easier after the first problem set. The topics consistently build off of each other (which is really cool), but if you’re lost on one thing it’ll carry over and amplify through the rest of the topics. Also the homeworks were laughably tedious and the pace of the class is very strange.

As people said, make sure you understood the materials from previous sections. The math is fairly simple to understand, but somehow the homework still turns out to be 8-10 hours long. Go to office hours.

Vladmirsky can be intimidating at times, but when you go to his office hours, he is the nicest guy you will meet and he will do anything and everything possible to make sure you understand the material. Often he’ll catch onto small misunderstandings you might have and by the end of his office hours, you’ll be a pro at the material. With that said, the homeworks are still laughably tedious, in the sense that you will look at the assignment and cry about how many hours you’re going to be putting in.

Past Offerings

Resources

• http://www.math.cornell.edu/~vlad/math4250/
• http://www.mathworks.com/moler/chapters.html