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- academics - The final two exams went by today, and I couldn't have asked for much more for either of them. Foundations in Algorithms came first, and it must be noted that algorithmic problems generally fall into one of two categories - those that one knows almost immediately how to go about solving, and those that one doesn't (uh oh). Problems in the second category may well be fun, but not in a two-hour examination. As our professor (modestly) said, he may not be much smarter than us, but he has probably seen a heck of a lot more questions (and methods to solve them). 此乃吃的盐比你吃的饭多? [N.B. A surprising number of the CS profs pepper their lectures with the occasional Chinese phrase， for example the use of 管中窺豹 to describe the aperture problem] Well, borrowing more programming terminology, as the past year paper contained a couple of questions from the recommended textbook, one technique would be to memoize the answers by just attempting questions from the textbook and bringing the solutions in (the less scrupulous might be tempted to [illegally] procure the instructor's version of the text). Hey, it's an open-book test - don't bring only a knife to a gunfight (unless it's in a friendly game of Counterstrike)... Very fortunately for me, a couple of the questions given had been covered in this way, which was especially lucky as I had solved the given exercises fully only up to Chapter Four of the material; for one of the questions, I was in the happy position of simply copying my prepared solution into the answer booklet, especially as it was the sort which I would be unlikely to comfortably produce from scratch on demand. For the other question, I had neglected to type out the solution, but the fact that I knew it admitted a greedy solution (since it was listed under that chapter in the textbook) was already a tremendous help. Thomas Edison famously tried a thousand ways before getting his lightbulb right, but in an examination, there are only so many avenues one can explore before running out of time. The problem [Question 13 on page 4 of the PDF here] involves minimizing the weighted sum of the completion time of a series of jobs. However, ordering the jobs either by the time taken, or by their importance, can quickly be shown not to yield a correct solution. Because of this, students who have not seen this problem before might reasonably suppose that the problem does not have a greedy solution, since such solutions usually involve some simple ordering of some criteria on the objects involved. As it happens, however, such an ordering exists - but it is neither time taken nor importance by itself, but the ratio of the two. Okay, this fact can also be deduced by considering the equation that arises from swapping any two consecutive jobs, so saying that it is impossible to derive it would be incorrect.  Swap you your Job Two for my Job One However, the intuition that the ratio matters does not come very naturally, and had I not encountered the problem before I would probably have moved on to dynamic programming or some other more complex approach (and inevitably failed). It has to be said that analysis by inversions had come out for one of our homework assignments, but it was but one of a huge number of possible methods to attack the problem. [N.B. After the examination, one of the other students soon noted on the module forum that the solution appears in the 1956 paper, Various optimizers for single-stage production by W.E. Smith (which does use the proof by inversion, and may go to show that today's 30-minute examination question is just yesterday's original research)] The Computer Vision examination was, I felt, rather easy, especially in comparism to previous years (almost no linear algebra involved, for starters). Whether this is beneficial to a student depends on how well he has done on the Continual Assessment (CA) portion of the course, since a very easy (or very tough) final that sees most students score about the same, would place extra importance on CA scores. Then, how well do these examinations measure my proficiency in either algorithms or computer vision/pattern recognition? Well, perhaps not extremely well, since for instance my grade on the algorithms paper might have been rather poorer had I not been fortunate enough to have come across the question. Employing another computing/statistical analogy, examinations might be viewed as a form of sampling. What one really wishes to measure is how many facts/problems in the field a student knows/can solve, but even in the unlikely case that the field can be well-defined, there are usually just too many of these entities to check for. An examination therefore chooses a tiny subset of facts/problems, and works on the assumption that, since these facts/assumptions are often closely related, it is a good approximation of the student's true ability. Coincidentally, Singapore's exam culture made its seasonal appearance as the topic of the day, at least on my Facebook social network, with the foreign system of choice this time being the Canadian one. One obvious question would be why performing "volunteer" duties is considered particularly voluntary if it is mandatory for graduation (and marks can be gained for it); moreover, local schools do participate in their fair share of community work too. The more damning accusation is that "...one's future and career is based solely on academic results". Is that true? Well... if one wants to enter a profession, such as being a doctor, lawyer, engineer or accountant, among other such jobs, one can't quite run from meeting certain academic standards, i.e. passing competency exams, whether in Singapore or Canada. Surprise, surprise. There seem to be a few main issues here. One is that Singapore focuses too much on rote memorization and mugging narrowly on examinable content (especially for youngsters), another is that they are pigeonholed into talent brackets too early, and a third is that one can't make a decent living in Singapore without academic credentials. On the first point, yes, there may be some degree of cramming, and on the second point yes, there is a grouping of students by assumed ability (assumed, since some abilities may not quite mesh). But in the sciences in particular, there is no getting around the fact that there are certain foundational facts that are not quite open to reinterpretation, so why not get them right early? Also, I would be astonished if there really were no such things as "better" schools or "more advanced" classes, in Canada or elsewhere. So it boils down to the third point, and indeed many desirable positions require a degree at minimum. But is this really that different in other countries either? The knock on Singapore having no Nobel winners also rankles - even China and India have but a mere handful, and if some lone Singaporean genius (or two) manages one in the coming decades, would it suddenly redeem the local educational system in a flash? For now, just pass the freaking tests already (clip courtesy of twc): That, or think like a hamster and live a stress-free life. Next: The End of Skill
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