ChapterZero

Walk a mile east, a mile north, a mile west, and a mile south. Where are you, relative to where you started?

Schoolchildren from Caversham have become the first to learn a brand new theory that dividing by zero is possible using a new number - ‘nullity’.
…

Dr James Anderson, from the University of Reading’s computer science department, says his new theorem solves an extremely important problem - the problem of nothing.

“Imagine you’re landing on an aeroplane and the automatic pilot’s working,” he suggests. “If it divides by zero and the computer stops working - you’re in big trouble. If your heart pacemaker divides by zero, you’re dead.”

Nope, this is not an excerpt from the Onion, it’s from a BBC article.

I feel no compunctions about downloading pdfs of scanned math books. For one, the price of a given math book is usually much more than is reasonable; for another, if the book is worth anything, I end up buying it anyhow, sooner or later.

It seems there is a better, and probably more used option, which is yet not as widely known as pdf: DejaVu, a free file format for storing raster documents that is tailored towards the efficient storage of scanned documents. In addition to being open, it outperforms PDF compression, and free viewers and browser plugins are available. Newsforge did a nice article on it a while back.

I’d appreciate any pointers on where to find books in DejaVu format.

I’ve gotten myself in a fine mess. Just a couple of nights ago in Barbados, I had the sudden thought that I didn’t check my email to see if my final project (which we turned in by email) got through ok. And of course, when I checked it just now, I saw an email from the TA saying that she didn’t receive any of the attachments; that email was about two days before I left to go to Barbados, but in the haze of the end of the term, I wasn’t diligent in checking my email. I was too busy contemplating the break. So now, when I get back to school, I have to see what horrible grade in the course awaits me, and what I can do to get it back to what it would/should be.

Update: Turns out she wasn’t able to open the attachments under Windows, but when she switched to a Linux machine, she had no problems. I suspect the problem is more with the software she used than the platforms.

I ‘finished’ my last final, in complex analysis, about an hour ago. I’m not very pleased with my answers, but apparently everyone that took the class is in the same boat. The overwhelming majority of the students in the course are Aero students (interesting bit of trivia: the ACM department actually evolved out of the Aero department, as evidenced by the residual dominance of PDEs in our research, and the fact that Aero students tend to take a lot of the 100 level ACM courses). This morning an Aero student who’s not taking it said that the 1st years expect the results will make them look bad compared to the (3) applied math students in there, since we’re mathematicians. Amusing, because I always thought the Aero students would do better than us, since they should be accustomed to doing more hands-on mathematical manipulations of the sort that dominate the coursework. I have trouble figuring out simplifying changes of variables, because I haven’t used basic calculus in what seems like ages. I imagine they are much more in tune with that stuff than we are.

But apparently for both populations in the course, that was a killer final– just about everyone expects to get less than a 50. See for instance, problem 3. What the hell? I assume you solve that by Frobenius’ method, which gives you only one solution as a series with nontrivial coefficients, and then use reduction of order to get another independent solution. The calculations to get those coefficients was an exercise in algebra and series manipulation, and an object lesson in why CASes exist. Unfortunately, we couldn’t use any mechanical aid. Also interesting was problem 5, which I didn’t get, unless the BS I put down turns out to be magically true.

Of course, part of the problem, at least for me, is that the homework is optional…

I’m currently taking an extended break from my applied real and functional analysis final, by visiting the library and picking up books I’d like to read over the break. Of course, I’ll probably not read them, but it’s a relaxing exercise. I’ve limited myself to physics, since I’m studing math, so I’d like to see something different:

• The Large scale structure of space-time. Hawkings and Ellis. This is the most ambitious of the books, but it looks like rewarding reading: it introduces GR rigorously and relatively quickly, then goes on to develop two of its important predictions. Namely, singularities that take the form of the beginning and end of the universe, and black holes.
• The Geometry of Physics: an introduction. Frankel. Differential geometry, exterior differential forms, algebraic and differential topology, Lie groups, vector bundles and Chern forms. All that good math for physics stuff, with pictures, and seemly well suited to self-study.
• Special Functions: An introduction to the Classical functions of mathematical physics. Temme. Kind of cheat on my part, because I’d be reading it to get into asymptotic expansions, special functions, and related topics from a different viewpoint than that offered in ACM 101, but still very physic-al, and looks like entertaining reading.