You think a month's vacation is a lot of time, but then by the time it comes to an end, it just doesn't feel like it was enough. That is especially the case when you spend the vast majority of it studying. I must say it felt quite weird to be "on vacation" while still being at school, let alone studying for exams, although that last part isn't too unfamiliar given that we generally have exams after vacations or breaks at MIT. Student life died down dramatically, and even my hallway was even eerily quiet at times. Sure, there were indeed delegates and conference attendees from time to time, but the noise they made pales in comparison to that of the hustle and bustle of everyday students.
As the weeks passed, I did come to appreciate the quiet, as that sort of environment is very amenable to studying for the Tripos. The days were almost a blur, as they largely consisted of getting up, eating food at buttery, going back to my room to study, eating food at buttery again, going back to my room to study, going to sleep, and then repeating the process all over again the next day. However, even with that constant studying, there were many moments when I was blown away not only by just how much material we had covered in a single term, but also by how we now had to remember all of it for just one 1.5 hour exam. I asked some of the Cambridge students, "how do you guys do it?". All I got were shrugs and laughs shrouded in weariness and relief that they had been able to "survive" the Tripos paper ordeal already for at least a year if not two or three. In the first two terms, I had not really appreciated their significance or difficulty, but as I began to settle into the studying and reviewing of past papers, the obstacles or difficulties began to emerge.
One thing about MIT courses is that if you do the problem sets and the past exams, you should in general be well-prepared for the exams. Somehow, that paradigm does not seem to hold at Cambridge. After reviewing the lecture notes and examples papers, I was surprised to see a somewhat noticeable lack of intersection between the examples papers and Tripos questions. Given the wealth of material covered in a single module, it seemed that the examples papers were perhaps not sufficient in covering all of the material in the lectures, and it was as if the Tripos papers were picking up the slack in some cases. I was also puzzled by the topic allocations at times, with entire questions sometimes centred on points that seemed to have been remotely covered during lecture.
Another stark contrast between MIT exams and Cambridge Tripos is the large focus on derivation and regurgitation of extensive proofs done during lectures. Whereas MIT exams are essentially applications of material taught during lecture with good alignment to the problem sets and past exams, parts of questions on the Tripos are devoted to seeing if you can remember all of the details of an expression's derivation. This part of the exam was both revealing but also disconcerting as well. I figure derivations will show up on my exams in the coming weeks, but which derivations exactly? Some of the lecture notes were littered with derivations, and to memorize all of them (some of them were largely centred on assumptions and mathematical tricks to obtain the final expressions) seemed like a momentous task, one that doesn't even target understanding from a teaching point of view. As a real-world engineer, we don't spend time deriving expressions. We spend our time applying the expressions and equations we learn to build and design cool and amazing things! So what was the rationale behind it?
I got a clue perhaps when I attended a supervision in the middle of the vacation (as a tangent, my supervisions during Lent term for reasons unbeknownst to me started EXTREMELY late and as a result, had to spill over into the vacation). My supervisor posed to me a past Tripos paper question that was supposed to be a derivation of a rule to which we were introduced in lecture. After some struggling, I managed to do it, and when I asked him why such a question was on a Tripos paper, he told me it was because that's how they can then differentiate between the "good" students and the "really good" students. I should first say that "really good" (a.k.a First) is much more elusive than an "A" is at MIT. In some ways, that's what makes MIT easier compared to Cambridge even though the day-to-day (or even week-to-week) work is much more stressful due to the constant problem sets and exams, but I digress. From the point of view of differentiating students, the organization of the Tripos paper makes a lot of sense in terms of testing derivations or even asking questions about seemingly remote topics. Chances are that many students will not remember them, but the few who do are then rewarded for their efforts (or their luck in having remembered it / learned it before, who knows?). Whatever the reason maybe, you can't really rail against the system too much when they've been utilizing it for about the past 800 years! So it does work! :)
Well, it's getting late, and my first exam is bright and early at 9:30 am! Tripos papers, here I come!