Posted by tpc at November 30th, 2005
My first paper was accepted! It’s a joint paper with my official advisor and a collaborator (who can be counted as my unofficial advisor.) Just did a check and found that both of them have Erdös number of 3 (via multiple paths) which means mine is 4.
Find out more from the project page.
Posted by tpc at November 12th, 2005
If you go to the zoo, the chimpanzee will wave to you. I do not understand their psyche, but I presume they do not understand what they are doing, except when they wave, they get food. I still remember seeing a tourist throw an ice-cream into the enclosure to the adorable chimp.
It’s sad when students are taught monkey tricks, i.e. techniques to solve problems without understanding. One example is at A level when they are required to diagonalize a 3×3 matrix (with distinct eigenvalues.) Some schools actually teach a method to find eigenvectors by using cross products. I know this because a few students asked me whether they can use that method in our course. I’m not sure how it goes, but I guess it’s this:
To find the basis for the nullspace of 
, take two rows and compute the cross product. This works because the rowspace is the orthogonal complement of the nullspace and nullity=1.
The problem with this method is that it only works when A is 3×3 and the eigenspace is one dimensional, but I have a good feeling the students don’t know this. I recall a friend (JC teacher) who tested his students by asking them to diagonalize a 2×2 matrix and some of them who knew how to do it for 3×3 matrices couldn’t do it in this simpler case!
Posted by tpc at November 12th, 2005
Back when I was an undergrad, the maths classes I attended could be broadly classified into two types - general and small classes. The latter are mainly algebra and topology classes which attract an enrolment of less than 15. The former are large classes, usually essential modules or courses that are thought to be easy. I never had much problem with those large classes. The reason being I was among the top end of the cohort and the lecturer needed to “dumb down” in order to cater to everybody. Even Lebesgue integration was never too intimidating. On the other hand, I had a lot of trouble with the group theory and topology and I often wondered during those days why I signed up.
In those big classes, there was one particular lecturer who was very well liked in general and always won awards. I didn’t like him because I felt he was “playing” to the audience, dumbing down too much, oversimplifying and very hand-holding.
Fast forward to the present. As a lecturer, I have this dilemma. The class is huge and the ability of the students diverse. As much as I want to teach rigourously, I find myself guilty of “dumbing down”, to the extent that one particular student commented that I should be replaced. Retribution, I guess. I’m still not sure how to find the right balance, considering that only 10% of the cohort may eventually end up graduating as math majors. How do you teach rigour without at the same time putting off the rest of the 90%, or worse still, extending the bad impression that they may have about mathematics.
Posted by tpc at November 8th, 2005
This is the TV series that’s already into its second season in the states. Here in Singapore it’s been showing for a month on cable and I have to say the show is quite good. Hey, even for non-math geeks, it’s still a good crime show with fairly interesting twists. Although you would probably fail to recognise the 
that appeared yesterday and the drawings of the complex plane near the critical line. I guess it is inevitable that the Riemann hypothesis makes an appearance somewhere, since people seems to have the idea that a proof would lead to a general meltdown of all encryption services.
Posted by tpc at November 2nd, 2005
By Denis Guedj. I read it (the English version of course) years ago, and picked it up again recently when I ran out of light reading. It has a wonderful plot although the ending fizzled out. Read Simon Singh’s review here.
The book can really be thought of as a walk through the history of mathematics, and despite knowing most of the stories already, it’s still fun to re-read them again. Actually, if it was up to me to decide, I really wouldn’t mind using this book to teach a course on the history of mathematics at my faculty. Murder, mayhem, pistol duels, crazy genius, there are enough stuff to whet the appetites of undergraduates, no matter what their mathematical inclination. I can even throw in Fibonacci and the Da Vinci connection.
A more scholarly textbook could be The Adventure of Numbers by Gilles Godefroy. It’s interesting that both books are all originally French.
