consider that if you showed serious initiative in working out a scholarly theory of the sort mentioned in the previous post, I would probably write you a reference letter that might well render poor performance on the exam completely irrelevant 
May 9, 2008
As motivation,
Posted by minhyong kim under admin, algebra, analysis, education, geometry, linear algebra, logic, number theory, topology[5] Comments
May 9, 2008 at 9:16 pm
Well, It is quite interesting; the kind of irrelevant topics I often think about (frivolously speaking).
However, I think it is fair to say that despite an interest in such a field you are probably looking for someone to do an in-depth study rather than simply propose a theory with a page or two of explanation?
(Believe it or not, that was a question. The implied (yet absence of tone) is a problem your sister will likely have studied).
May 9, 2008 at 11:04 pm
You would need to construct a mathematical model. The basic geometry of the space of exams should be a simplex in
, where the basis vectors represent very basic exam types and the general exam is a linear combination of the basic ones. It would be best to get some second year students that actually took the exam involved. If you could organize such a group and come consult with me, that would be great. If such a theory could be used to show, for example, that the 2008 exams for the basic courses were considerably different from the previous 4-5 years (as some people believe), that would be quite interesting, and publishable somewhere, I think.
May 10, 2008 at 3:27 pm
Would be quite amusing also.
i suspect definitions and ’seen’ proofs would constitute basis vectors. And ‘unseen’ parts would be made from the span of them.
I would think anyone who has the mental capacity to make such a model using algebra has the mental capacity to not notice a difference in the exam style, when he/she took it.
May 10, 2008 at 8:53 pm
One can make it quite sophisticated, depending upon what factors to take into account, but a very simplistic model of an exam might have basis vectors
for the topics
-Elementary number theory;
-Polynomial algebra;
-Jordan canonical forms;
-Quadratic forms;
-Inner product spaces;
-Self-adjoint maps and isometries.
Then the general exam would look like
where
is some reasonable measure of the weight of topic 
in the exam. For example, 
stands for an exam where all problems are concerned with Jordan canonical forms and nothing else.
You should be aware that I’m only describing a very superficial model here. The basis vectors might need to represent much more sophisticated facets of the subject. We also need to build in somehow information on the weight of `theory’ versus the weight of `applications.’
May 10, 2008 at 9:00 pm
To take into account `seen’ versus `unseen,’ if you think those characteristics to be significant, you could give each
superscripts like
making the whole space 12 dimensional. Thus, for example,
would be an exam where half the weight is on JCF’s and half on inner product spaces. The IPS problems are all from seen material, while the JCF problems come in seen and unseen types with the displayed distribution.