eon

Posted by tpc at April 17th, 2009

A classical and computational introduction is a new book by L.J.P. Kilford. New enough that it even has reference to the resolution of Serre’s conjecture. But this book is really an introduction to the classical aspects of the theory of modular forms and it does a great job. I took a few days to read through the book (of course, ignoring the details and proofs) and I would say it is very enjoyable. Kilford adds in lots of funny and quirky anecdotes, most of which I’ve read from different places but it’s nice to have everything collected in one book. For example, he mentioned Lang’s famous foreword:

“It is possible to write endlessly on elliptic curves. (This is not a threat.)”

I remembered being so tickled when I first saw this in Lang’s book.

Back to this book. Even with the subject of modular forms it is the same. He knows he can’t possibly explain everything and so is not afraid to be a little vague at times and cite the various references to where more in depth discussions can be found. Thus, he is able to accomplish much in this modest sized (200+ pages) book. My one small complaint is the title should not include “and computational”. I found the last chapter on computational aspects too brief. He highlighted some history, discussed MAGMA and SAGE, giving some examples of the codes used, but I believe that this is not enough for someone interested in computing modular forms to get started on. And the appendixes on MAGMA and SAGE codes are each one page long with two longish lines of commands.

Posted by tpc at April 11th, 2009

by Yoko Ogawa. I remember watching half a movie on a plane which was called “The Gift of Numbers” (Hakase No Aishita Sushiki) and was based on the 2004 Japanese novel by Ogawa. Since then, I place the book in my to read list and it so happened that two weeks ago, I read a review of the book on the Sunday times. Apparently, the english translation just appeared under this new title and it turned out fortuitously that the library carried this book.

The story of the book is about how the housekeeper was assigned to this number theory professor who had an accident, lost his short term memory and only retained 80 mins of memory. To remind himself, he pinned a note on his clothes that says “I have only 80 minutes of memory.” It’s an interesting proposition to say the least, but what is engaging is the relationship developed between the professor, the housekeeper and her son called Root because he has a flat head. There was only a very brief and subtle exploration into the anguish of the professor at his state.

There are quite some mathematics mentioned by the professor, for example, on amicable numbers, Ruth-Aaron numbers 714 and 715, as well as the perfect number 28 which happened to be the shirt number of the professor’s favourite baseball player Yutaka Enatsu.

For another review see Math fiction.

Posted by tpc at April 8th, 2009

I chanced upon this neat number puzzle devised by William Wallace, via wild about maths. It’s form is certainly recognizable, but still the effort deserves praise.

I remember a similar puzzle played with a deck of cards. You lay out the cards in rows and ask the participant to tell who which row his card is in. The trick is to collect the cards back horizontally, but deal out the next four rows vertically, this way after a few deals, you can tell which card is it.

This happen to tie in with a class I’m teaching tomorrow, maybe I’ll print out the cards and try it in class.