I thought I should write a note on this course offered by the Ross Business School of the University of Michigan on the Coursera platform that also ended last week. It’s a ten-week course that I enrolled in out of a slight interest I have in the subject, due to my passing knowledge in accounting and economics.

As with Algorithms 1, I learned a great deal but the quality of this course is markedly lower. Most notably, there was a complete lack of instructor presence and oversight on the official forums. This lack of feedback left many students frustrated and encouraged students to freely discuss and share solutions to assignments with each other. With no moderators to rein in behavior, this left the forums a chaotic mess.

The problem was also exacerbated by the limited pool of questions available in the exercises. For these reasons despite that the fact that this course offers a certificate and Algorithms 1 doesn’t, I’d put more stock in the integrity of the grades in the latter. And yes, this even takes into account the fact that the final exam for the Finance course is timed while the one for Algorithms isn’t.

One excuse is that the enrollment for the Finance class was much, much higher than that for Algorithms, so much so that Professor Gautam Kaul might have been discouraged from the start from being able to intervene in any meaningful fashion in the forums. I believe that there were over 50k students in the class. But I also suspect that quality of the forums was also degraded by the fact that many students were motivated primarily by the offer of a certificate rather than the love of learning. I found the many posts in the forums begging the professor to let them have the certificate despite failing the final to be ridiculous and in extremely poor taste.

Finally, while finance is in many ways more practical than algorithms, after all I hold significant investments but don’t make any money from writing programs, I can’t help but feel that it is less relevant. Despite all that I’ve learned, I still can’t see how the models apply to the real world, given that the models are supposed to work only in an ideal environment (perfect market, frictionless transactions, no taxes etc.) It’s all very interesting in a theoretical sense, but I can’t help feeling that it’s all a bit bunk and that academic finance, at least at this introductory level, is pretty much useless in a real world context. I think I’ll stick to the computer courses from here on out.

So the Algorithms 1 class by Professors Robert Sedgewick and Kevin Wayne of Princeton on the Coursera platform just ended. I just made my second of three attempts on the final exam, scoring 18.31 / 20.00. I may yet make another attempt next week as everything officially closes only on 30 September 2012. It’s been an amazing experience and I learned way more than I expected. Some thoughts:

• I found that I’m pretty strong on practical programming. I could complete all of the programming assignments with not much trouble, and ended up spending a fair amount of time on the forums helping others out with their programs too. I only struggled somewhat when implementing the optional extra optimizations that the professors suggested which are not graded. This mostly involved doing the same thing with half the memory or less, or cutting running time down drastically. For example, the toughest timing trial of the collinear points assignment gave you a maximum of 10 seconds to solve the problem. My first attempt came in at just under 7 seconds, and after much agonizing I got it down to just under 3 seconds. The very best students were able to get it down to just under 2 seconds.
• However I am terrible on the theory. I blame that on a lack of solid grounding in mathematics. I really suck at calculating things like the order of growth of running time for different algorithms or the minimum and maximum heights of different tree-like data structures. This calls for a good grasp of discrete mathematics. I’m also bad at internalizing geometrical principles, so assignments like collinear points gave me more trouble than the supposedly more sophisticated A* algorithm we used to solve the 15-puzzle. I’m currently signed up for Sedgewick’s Analytic Combinatorics class which runs next year but I’ll probably flunk that one.
• This class really thought me how beautiful some algorithms are and how you can achieve so much in just a few lines of code. At heart, they’re all about pure logic so it’s possible to even describe them to people with no programming knowledge whatsoever. I also think I finally managed to get the hang of recursive functions while doing the Kd-Tree assignment. I’ve always had trouble visualizing them before.
• I also learned how very limited even the powerful computers we have available to us today are. As a science-fiction fan, I’ve always taken it for granted that one day, perhaps sooner than we expect, we’ll be able to simulate sentient minds and even whole worlds inside computers. Unfortunately, even the lowly 15-puzzle is enough to make modern computers struggle. It’s pretty humbling. As Sedgewick likes to emphasize, while we can always look forward to ever faster computers in the future, it is even more certain that the size of the problems we need to solve in the future will grow faster than our computers will become more powerful. As we can’t rely on ever more powerful computers to do the work, we must instead design ever more clever algorithms.

Anyway, Algorithms II starts up in November so I’ll be back at it pretty soon. In the meantime, I should have a little extra free time.