# Scientific writing

I was cleaning out some old CDs the other day, when I happen to stumble over a copy of my master thesis. My thesis was about the mathematical properties of artificial neural networks and I would never have been able to do it without $\LaTeX$. Try to typeset something like

$f_j(x,\theta) = F\displaystyle{\left(\sum_{h=0}^lG(\bar x'\gamma_j)\beta_{jh}\right)},\ h=1,\ldots,l.$

Definition 2.2
For any (Borel) measurable function $G(\cdot)$ mapping $R$ to $R$ and $n\in N$ let $\sum^n(G)$ be the class of functions

$\displaystyle{\left\{f:\mathbb R^n\rightarrow \mathbb R | f(x)=\sum_{j=1}^l\beta_j G(A_j(x)),\ x\in\mathbb R^n,\ \beta_j\in\mathbb R, A_j\in\mathbf A ^n,\ l\in\mathbb N\right\}}$

The WordPress plugin I have found for typesetting $\LaTeX$ does not do a very good job, so please bear with the above.

I have recently installed MacTeX on my iMac. I have no idea of what I should use if for right now, but it feels good and maybe I should try to finish some of the stuff I’m writing on and try to get it published, even though it will be hard not being in the university community any more.

Let’s just take another few equations for the fun of it 🙂

$\displaystyle{\int_{\mathbb R^n}\int_{\mathbb R} a^\alpha D^{|\alpha} G(a'x - \theta)\frac{|b|^n \hat f(ba)e^{2\pi ib\theta}}{\hat G(b)}\mbox{d}a\ \mbox{d}\theta}$