“I could tell you my adventures — beginning from this morning,” said Alice a little timidly: “but it’s no use going back to yesterday, because I was a different person then.”

“Explain all that,” said the Mock Turtle.

“No, no! The adventures first,” said the Gryphon in an impatient tone: “explanations take such a dreadful time.” (Alice’s Adventures in Wonderland, Chapter 10)

I write about puzzles that interest me. I hope you will be interested too 🙂

The emphasis is more on the puzzles than the rigor. Logicians might classify this as an attempt to use what Richard Borcherds calls High School Algebra as the basis of everything.

Warning: This is not a Bourbaki-esque type blog, where I rigorously reconstruct math from first-order logic and some flavour of ZFC. Instead, it is inspired more from Euler and focuses more on interesting problems.

Posts are constantly being revised, mostly adding more examples or explanations. NB many integrals are taken from math.StackExchange, and presumably these are taken from somewhere else; nevertheless, I always try to cite where problems are taken from (…if I remember…).

Right now the current plan is: discuss calculus, then linear algebra. I don’t know what I’ll do after that, probably differential equations a bit…perhaps mathematical physics or differential geometry?

I may discuss some programming stuff too, if it’s an interesting puzzle.

My biography:

I am very tough and have been known to break a Vienna roll with my bear hands. I am very handsome, having a powerful physique, and I change my shirt regularly every Monday morning. When resting between assignments I live in a French Provincial chateau on Mulholland Drive. It is a fairly small place of forty-eight rooms and fifty-nine baths. I dine off gold plate and prefer to be waited on by [beautiful] dancing girls. But of course there are times when I have to grow a beard and hole up in a Main Street flophouse, and there are other times when I am, although not by request, entertained in the drunk tank in the city jail.

…I am thirty-eight years old and have been for the past twenty years.

1. Amy Hurford says:

Hi Alex,
I like your blog. Based on some tests I just did, I don’t think I’ve figured out this latex in wordpress thing yet. Here goes: $\frac{\alpha}{\beta}$. No? there’s something I’m missing, isn’t there?

• Amy Hurford says:

Ah ha! I’ve got it now. $\tau \eta \alpha \nu \kappa \sigma$!

• Alex Nelson says:

Yes! There are a few tricks I should mention too.

The first is: use $latex {\displaystyle ...}$, which will make the equations look prettier.

The second, which may or may not help you, I sometimes write equations first “conceptually”, e.g.,

${\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}\begin{pmatrix}\mbox{quantity of}\\ \mbox{stuff in }\Omega\end{pmatrix} = \begin{pmatrix}\mbox{stuff created}\\ \mbox{in }\Omega\end{pmatrix} + \begin{pmatrix}\mbox{stuff flowing}\\ \mbox{into }\Omega\end{pmatrix} - \begin{pmatrix}\mbox{stuff flowing}\\ \mbox{out of }\Omega\end{pmatrix}}$

To write text like this, you need to put it in \mbox{your text here}.

The parentheses are given by the “environment” \begin{pmatrix} ... \end{pmatrix} (an “environment” in LaTeX is anything with these \begin{...}-\end{...} pairs).

The last trick I should mention, which may or may not help much, is using \begin{aligned}...\end{aligned}, which helps when you are doing a lot of algebraic manipulation. For example

{\displaystyle\begin{aligned} (1-2)+3 &=(-1) + 3\\ &=3-1\\ &=2\end{aligned} }

Good luck with your math! 🙂