Film

Far be it from my intention to clutter the blog with film reviews, but maybe this is a good time, just to give all of you a bit of relief from studying. In any case, it will only be a short remark about`The Class (Entre les murs),’ describing a year’s work for a teacher at a school in northeastern Paris. I do try to keep up with films about education and this one has been highly acclaimed (Palme d’Or and all that), so I was glad to catch it on the plane last week. Reasonably pleasant to watch, sure enough, but the show left me with a question, which perhaps some of you can help me with if you’ve seen the film as well: Are such innocent and impressionable students as depicted there really supposed to be problematic in some way? Somehow, I couldn’t at all comprehend that the situation could be perceived as a difficult one. There were minor obstructions here and there, but everyone in class seemed quite communicative and engaged.

After asking around a bit, I thought to pose the question here for some feedback. So let me know.

 

Correction

To my tedious post on `Practical responsibility,’ I’ve added a few words just in case someone misunderstands the the intent of my anecdote on the manager at Eli Lilly. Furthermore, I hope no one interprets my remarks as a discouragement of input from students.

To be a bit theoretical (or mystical), there is a rather age-old tension in education between

1. the intellectual gains of dialectic (e.g., argumentation); and
2. the spiritual gains of acceptance.

This is well-known, but I wished to relate this tension somewhat to mundane matters, perhaps from the perspective of the side that gets less explicit attention (I think). Of course there is no way to decide on one or the other once and for all.

 

As motivation,

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

 

In fact

Let me use this occasion to pose a question that might even be serious research material. Can one come up with a good measure of similarity between successive exams? That is to say, suppose you wanted to show me with suitably convincing rigor that I was really deviating from previous years. How would you do it? Of course, this would require a good theory combining formal logic, linguistics, epistemology, and of course, mathematics, both in the form of the theory and in the specific construction of the models that the theory tries to work with. I’m sure that a truly satisfactory theory would be close to impossible at this point. But it still might be fun to start thinking about it.

Very roughly speaking, there should be

a space of linear algebra exams

possibly of very high dimension, endowed with a natural inner product, using which we can measure the distance between exams. In this space, you might attempt to show that the exams of previous years form a pretty tight cluster, while my exam is convincingly distant from that cluster.

If you’re interested in thinking about a problem of that sort, let me know. I’m not an applied mathematician, but I think we might be able to do something.

 

Education, in Singapore and elsewhere

On the mathematical physics web log `The n-category cafe,’ a number of people have been discussing the teaching of mathematics, prompted by an article in the Los Angeles times. I ended up contributing a few scattered comments. A link is included here for the possible amusement of my UCL students.

 

Southwest Center for Arithmetic Geometry

It’s something of a constant concern of mine to put students of every level in touch with mathematical culture. So I thought I’d call your attention to the Southwest Center for Arithmetic Geometry where I did most of my public service work from 1998 to 2005. If you browse through, you’ll find ten years’ worth of surveys, projects, videos, etc. covering virtually all aspects of arithmetic geometry. They host an annual

Arizona Winter School on Arithmetic Geometry

for post-graduate students. Students doing an MSc or above at UCL could benefit from attending sometime. It’s a really great educational event and a chance to interact with first-rate mathematicians as well as students from all over the world.

MK

 

Some personal letters

Over the years, I’ve received a number of general inquiries from students about the life of a mathematician. Obviously, just from sitting in lectures and so forth, it is rather hard to get a real sense of what daily life might be like engaged most of the time in intellectual inquiry. Most importantly, in these diverting times, it’s impossible to entirely avoid the question of why?

During one of the last tutorials of the previous term, Jamal Muse asked me if I enjoyed doing mathematics, and even for this it wasn’t possible to come up with an entirely straightforward answer. Recursively, even the question of why the answer can’t be straightforward, I feel rather uncertain about. Meanwhile, I do take seriously a certain obligation on my part to give an honest answer to such questions,  since they relate to fairly serious decisions that can really affect the rest of a student’s life.

So I’ve finally decided to present an indirect reply. It is rather long, consisting of a series of twenty letters I wrote to my son a few years ago while traveling over the summer on research visits. Much of it is personal, and quite likely boring. I would myself normally frown upon such public exhibition of private letters. However, since I did at the time think exactly about the issue of conveying to my children some feeling for the time I spent away from them, it occurred to me that the letters may serve this other purpose as well.

To impart the semblance of an informal book, I’ve put in a title page and created separate links for the letters according to the dates. If you do end up browsing here and there, try to gloss over the very emotional passages. I’ve left them in to avoid the effort of editing. In any case, let me know if the letters are at all useful to you. Indeed, if they end up of any more than passing interest I may put in a more serious effort at some point to continue the story with a broader readership explicitly in mind.

MK

title page
15 May, 2005
16 May, 2005
17 May, 2005
18 May, 2005
19 May, 2005
20 May, 2005
22 May, 2005
23 May, 2005
25 May, 2005
26 May, 2005
29 May, 2005
31 May, 2005
6 June, 2005
12 June, 2005
15 June, 2005
18 June, 2005
19 June, 2005
21 June, 2005
25 June, 2005
29 June, 2005

 

Mathematical vistas

My first term in the UK and some recent contact with issues in primary and secondary education prompted a brief reflection on the teaching of mathematics to children, written mostly with fellow parents in mind. But if you have the time to read it, I would very much welcome comments from maths students as well.

Here is a link to a book review by Roger Howe that summarizes rather well the discourse on education in the US from the viewpoint of a mathematician. I refer you also to the Wikipedia entry on Faltings and the article by Allyn Jackson, `Comme Appellé du Néant–as if summoned form the void: The life of Alexandre Grothendieck, Part I and Part II.’

MK