French exams
Posted by Martin Orr on Saturday, 20 March 2010 at 22:45
In the past six weeks I have taken four exams: two on the courses from the first semester (October-January) and two on the courses I have taken January-February. The reason the latter came so soon after the former is because they are in different institutions - the first two were here in Orsay, the second two in other institutions in Paris with different timetables. These exams were hard, and very different from exams in Cambridge. (Note: this post discusses pure maths exams only.)
Examples: Orsay M2 Algebraic Geometry, Cambridge Part III Commutative Algebra, a Part II exam.
The biggest difference is that in the French exams, you are permitted to bring your notes with you into the exam. Cambridge exams are mostly bookwork, i.e. they ask you to write down definitions and proofs from the lectures or example sheets. Obviously such questions have limited value in an open book exam.
Instead French exams contain problem questions, asking you to prove some substantial result that you have (probably) not proved before. These are not olympiad exams so each problem is broken up into a series of steps; some of these are trivial but some require ingenuity. One thing I found difficult was not having any clues which steps are supposed to be hard.
The biggest shock I found with the French exams was how soon they come after the end of the lectures - two or three weeks. I am accustomed to lectures finishing in March, then having six weeks of Easter holiday and four weeks of Easter term to revise before the exams. I suppose that lots of revision time is more important if you have to commit precise statements of theorems to memory, but I always find that I learn a lot that I missed the first time through the course.
For the short time I did have to revise for the exams here, I didn't know (and still don't know) how I should revise, given that learning proofs is not useful. Also there tend to be fewer past papers available (and certainly no revision supervisions). I would like it if there was some sort of guidance on how one should revise (this is just one part of my general wish for guidance booklets or talks from the Department).
There are some specialised courses which develop a theory in a linear fashion and for which it might seem that it is hard to find problems which are non-standard but easy enough to set on an exam. I thought this was true of the course "Representations of GL(2, F) (F a p-adic field)" but the exam neatly solved the problem by asking you to develop the similar theory of SL(2, F) - quasi-bookwork but different enough to force you to understand your notes. Of course that is only one example and I don't know for sure if it generalises.
On the whole I think that the open book exams are a good thing. Problem solving ability is a more worthwhile thing to test than brute speed and recall. On the other hand, bookwork exams are probably easier to set (this is an advantage for the examiners). Another advantage of the exams here was that I learned things from them, which rarely happened in Cambridge exams.
I suppose figuring out for oneself which steps in a problem are hard and which are trivial is a useful skill to have.
True but usually (i.e. not in an exam) if you get it wrong you have time to revise your opinion.