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When I was a physics major at UCI the abstract algebra course ended up being my favorite course. The prof was young, and a real hard ass. Apart from the usual,

When I was a physics major at UCI the abstract algebra course ended up being my favorite course. The prof was young, and a real hard ass. Apart from the usual, he forced us to memorize proofs and regurgitate them for tests, as well as come up with original proofs. That might sound draconian (it certainly did to me; none of my real analysis classes asked that of us) but it turned out to be really hard to do unless you understood the entire proof. And it also turns out that if you understand a proof, or a set of them, you can produce new ones. Of course, almost everyone failed the course. One guy got an A, a couple of us got C's (I was one) and the rest got F's. Never been prouder of a C in my life.

Smaug123 10y ago
Your analysis exams didn't require bookwork? For someone who has done four years of maths at Cambridge, this idea is dumbfounding: about a third of each exam was bookwork. (Except, in my year, Category Theory, in which there was no bookwork at all. Of course I don't hold a grudge about how much time I spent learning the proofs of the monadicity- and adjoint-functor theorems.)
- javajosh 10y ago
  Not sure what you mean by "bookwork". Is that what memorizing proofs is called in the UK? Most of the exams and homework were more typical math exercises, e.g. little proofs and calculations within the context of special cases. I mean, I remember getting tested on parts of the "epsilon delta" definition of a limit in analysis, for example, but I don't recall ever being asked to regurgitate the entire thing correctly. It's funny but I don't even associate important tools like Taylor series with "proofs", only applications. The lecturer would sometimes prove things, but we were never tested on the proof, only the ability to apply the result. Mind you, I was physics not math so perhaps that's the difference. In fairness there is a LOT of math tools to learn, and I'm not sure there's really time to get into proving everything as an undergrad, but perhaps that's a mistake.
  - Smaug123 10y ago
    Wiktionary's definition of "bookwork" is accurate: "The act of memorising information; used attributively to describe or denote questions that test information learned rather than requiring additional thought." It notes that the definition is "chiefly University of Cambridge", which I didn't realise. Perhaps it is indeed a physics/maths thing.
- rocqua 10y ago
  I'd be appalled if a third of an exam was "reproduce this proof of this theorem". However, if a third of the exam is "Produce a proof of this theorem" and people don't care about whether the proof is original or reproduced, that seems fine. Certainly, being able to proof any theorems your rely on is important. But being able to recall how any given theorem was proven in a book isn't important.
  - Smaug123 10y ago
    Sure, but there's usually a reason a particular proof is used in lectures: it's either much faster or much more comprehensible than the others :)

Smaug123 10y ago

Your analysis exams didn't require bookwork? For someone who has done four years of maths at Cambridge, this idea is dumbfounding: about a third of each exam was bookwork. (Except, in my year, Category Theory, in which there was no bookwork at all. Of course I don't hold a grudge about how much time I spent learning the proofs of the monadicity- and adjoint-functor theorems.)

javajosh 10y ago
Not sure what you mean by "bookwork". Is that what memorizing proofs is called in the UK? Most of the exams and homework were more typical math exercises, e.g. little proofs and calculations within the context of special cases. I mean, I remember getting tested on parts of the "epsilon delta" definition of a limit in analysis, for example, but I don't recall ever being asked to regurgitate the entire thing correctly. It's funny but I don't even associate important tools like Taylor series with "proofs", only applications. The lecturer would sometimes prove things, but we were never tested on the proof, only the ability to apply the result. Mind you, I was physics not math so perhaps that's the difference. In fairness there is a LOT of math tools to learn, and I'm not sure there's really time to get into proving everything as an undergrad, but perhaps that's a mistake.
- Smaug123 10y ago
  Wiktionary's definition of "bookwork" is accurate: "The act of memorising information; used attributively to describe or denote questions that test information learned rather than requiring additional thought." It notes that the definition is "chiefly University of Cambridge", which I didn't realise. Perhaps it is indeed a physics/maths thing.
rocqua 10y ago
I'd be appalled if a third of an exam was "reproduce this proof of this theorem". However, if a third of the exam is "Produce a proof of this theorem" and people don't care about whether the proof is original or reproduced, that seems fine. Certainly, being able to proof any theorems your rely on is important. But being able to recall how any given theorem was proven in a book isn't important.
- Smaug123 10y ago
  Sure, but there's usually a reason a particular proof is used in lectures: it's either much faster or much more comprehensible than the others :)