# The Samovar

An equation
February 17, 2007, 3:08 pm
Filed under: Mathematics

WordPress has just included equations so here is the major result of my PhD thesis:

$\displaystyle \mathrm{Tr}_{A^nB}^\prime(\mu_{A^nB})=\frac{-i n^3\mathrm{Tr}_{A}^\prime(\mu_A)}{\pi^2}+O(n^2)$

Wow! 😯

Too bad it doesn’t work in comments. It’s awfully impressive though, whatever it means …

Comment by azahar

It now works in comments as well.

Behold: \$latex sin \Theta = \frac{\sqrt{2}}{2}

Comment by Darmok

In my excitement, I neglected in include the closing dollar sign.

So here’s another example to behold: $\phi = \frac{1+sqrt{5}}{2}$

Comment by Darmok

OK, let’s try it, another section from my thesis:

The Maskit slice, can be very simply embedded in $\mathbb{C}$ in the following way. Define

$\displaystyle g:\mathbb{C}\longrightarrow\mathrm{Hom}(\Gamma,\mathrm{SL}_2\mathbb{C})$ by

$\displaystyle g(\mu)(X)=-i\left(\begin{matrix}\mu&1\\1&0\end{matrix}\right),\quad\mbox{ and }\quad g(\mu)(Y)=\left(\begin{matrix}1&2\\ 0&1\end{matrix}\right).$

Let $\pm:\mathrm{SL}_2\mathbb{C}\rightarrow\mathrm{PSL}_2\mathbb{C}$ be the quotient map. The map $[g]:\mathbb{C}\rightarrow R_p(\Gamma)$ is defined by setting $[g](\mu)=[\pm g(\mu)]$, and the set $\overline{\mathcal{M}}=[g]^{-1}(\overline{\mathcal{QF}})\cap\mathbb{H}$ is the Maskit slice.

Comment by Dan Goodman

Hmmm, that’s not quite right, but it’s getting there. Probably made a slight mistake somewhere in there.

Comment by Dan Goodman

very sexy! 😉

Comment by azahar

Yeah, it would be nice to be able to preview comments before submitting them to see if there were any errors (I forgot the backslash in my second attempt). I suppose I can just use a draft post to preview the equations, then copy them into a comment if necessary.

Comment by Darmok

Yes, this could make your blog a lot more…interesting. 😉

Comment by Edward the Bonobo

There we go, fixed the comment above. Now you can enjoy the algebraic definition of the Maskit slice in all its glory!

Right – gratuitous equations end here. 😉

All subsequent equations will be very much necessary to what I’m saying, oh yes.

Comment by Dan Goodman

Have you seen this?

Mathematicians set Chinese test

Comment by azahar

Please check your spam file – I think my last comment is there. Thanks!

Comment by azahar

Yes it was – now rescued. Going into the spam file is a slightly disturbing experience isn’t it? I was amused by the idea of ‘nude yoga’ though.

Funnily enough, someone else also sent me that thing about that Chinese test. I think a similar story came out when I was still at school – they had side by side comparisons of English and Chinese school level geometry exam questions. The thing is – it’s not a very meaningful comparison. Complicated straight-line and compass geometry just doesn’t form part of modern mathematics (and I would guess that they haven’t from say 1700 onwards, give or take a hundred years). Some mathematicians do think that learning it is useful general training in problem solving, but those sorts of problems themselves just don’t come up in practice.

That’s not to say that Chinese maths teaching at school isn’t better than over here though. I don’t know enough to make a comment on that, but these particular comparisons don’t tell you much.

Comment by thesamovar

Been thinking of you whilst reading The Indian Clerk by David Leavitt as I think you would quite enjoy it (if you haven’t already read it). All about Ramanujan and GH Hardy and populated with such ‘secondary characters’ as Bertrand Russell, Wittgenstein and DH Lawrence.

Having never heard of either Ramanujan or Hardy before stumbling upon this book the other day I’m finding it quite a learning experience as well as well-written and entertaining.

Comment by azahar

Thanks az! I haven’t read this one, but I’ve read quite a few things about Ramanujan, Hardy, and that lot. If your appetite is whetted by it, you might also like reading Hardy’s book “A mathematician’s apology”. It’s very short.

Comment by Dan | thesamovar