\documentclass[11pt]{article}
%\usepackage[greek]{babel}
%\usepackage[iso-8859-7]{inputenc}

\begin{document}

\centerline{\LARGE $\mathcal{UNIVERSITY\ OF\ THE\ AEGEAN}$}



\bigskip

\begin{center}
\mathversion{bold}
Compare $\sqrt{x^2 + y^2}=0$ \mathversion{normal} with  $\sqrt{x^2 + y^2}=0$.
\begin{verbatim}
\mathversion{bold}
Compare $\sqrt{x^2 + y^2}=0$ 
\mathversion{normal} with  $\sqrt{x^2 + y^2}=0$.
\end{verbatim}
\end{center}

\bigskip

\centerline{Binary relations}
$\cap$ \verb+\cap+ \quad $\cup$ \verb+\cup+ \quad $\times$ \verb+\times+

$\pm\ \mp\ \otimes\ \oplus\ \uplus\ \wr\ \ast\ \star$ et.c.


\medskip

\centerline{Common symbols}
$\leq$ \verb+\leq+ \quad $\geq$ \verb+\geq+ \quad $\in$ \verb+\in+ \quad $\subset$
\verb+\subset+ \quad $\supset$ \verb+\supset+

$\equiv\ \subseteq\ \supseteq\ \Vert\ \neq\ \sim \ni$ et.c.

\medskip

\centerline{Arrows}

$\leftarrow$ \verb+\leftarrow+ \quad $\rightarrow$ \verb+\rightarrow+
$\mapsto$ \verb+\mapsto+ \quad $\Leftrightarrow$ \verb+\Leftrightarrow+

$\hookrightarrow\ \uparrow\ \downarrow\ \rightharpoonup\ \searrow$ et.c.

\medskip

\centerline{Other symbols}

$\ldots$ \verb+\ldots+ \quad $\cdots$ \verb+\cdots+ \quad $\vdots$ \verb+\vdots+ \quad
 $\ddots$ \verb+\ddots+

$\partial$ \verb+\partial+\quad $\nabla$ \verb+\nabla+\quad $\forall$ \verb+\forall+
\quad $\emptyset$ \verb+\emptyset+ $\exists$ \verb+\exists+ \quad $\infty$ \verb+\infty+
et.c.

\medskip

\centerline{Variable size symbols}

$\sum$ \verb+\sum+ \quad $\prod$ \verb+\prod+ \quad $\int$ \verb+\int+
\quad $\oint$ \verb+\oint+ \quad $\bigcup$ \verb+\bigcup+\quad $\bigcap$ \verb+\bigcap+

$\coprod\ \bigwedge\ \bigoplus$ et.c.

\medskip

\centerline{Functions}

$\lim, \cos, \sin, \log, \sup, \inf, \min, \max$ et.c.

\medskip

\centerline{Math spacing}

\begin{center}
\begin{tabular}{cc}
$x \qquad x$ & \verb+$x \qquad x$+\\
$x \quad x$  & \verb+$x \quad x$ +\\
$x \; x$     & \verb+$x \; x$    +\\
$x \: x$     & \verb+$x \: x$    +\\
$x \, x$     & \verb+$x \, x$    +\\
$x x$        & \verb+$x x$       +\\
$x \! x$     & \verb+$x \! x$    +\\
\end{tabular}
\end{center}

\medskip

\centerline{Variable size symbols No2}

$\{$ \verb+\{+ \quad $\}$ \verb+\}+\quad  $\langle$ \verb=\langle=\quad
$\rangle$ \verb=\rangle=\quad  $(\ ) [\ ]$ \quad  $\Vert$ \verb=\Vert=  et.c.

\medskip

{\it Forcing other sizes}

$\Biggl( \biggl( \Bigl( \bigl(  \bigr) \Bigr) \biggr) \Biggr)$ was created with

\verb=$\Biggl( \biggl( \Bigl( \bigl(  \bigr) \Bigr) \biggr) \Biggr)$=

\smallskip

$3 \Biggm/4 \biggm/ 5 \Bigm/ 6 \bigm/ 7 $ was created with

\verb=$3 \Biggm/4 \biggm/ 5 \Bigm/ 6 \bigm/ 7 $=


\bigskip
\bigskip




\centerline{\Large Exercises}

\medskip

$$\nabla^2 =\frac{\partial^2}{\partial x^2} +
                \frac{\partial^2}{\partial y^2} +
                \frac{\partial^2}{\partial z^2} $$


$${\frac{a}{b} \above1pt \frac{c}{d}}$$


$$\sqrt{abc}\qquad \sqrt[n]{abc}$$


$$f(x)\stackrel{def}{=} \int_0^\pi \sin (xt) dt$$


$$\sum_{{n\in A \atop m\in B} \atop k\in C} a_{nmk}$$


$$\overline{{\overline{x}}^2} \qquad \underline{\underline{x}+\underline{y}}$$


$$\overbrace{a,\ldots,z}^\mathrm{26\ letters} \qquad \underbrace{a,\ldots,z}_\mathrm{26\ letters}$$


$$\left( {p \atop 2}\right) x^2 y^{p-2} -\frac1{1-x}\frac1{1-x^2}$$
$$\sqrt[3]{ 1+\sqrt[4]{ 1+\sqrt[5]{ 1+\sqrt[6]{1+\sqrt[7]{1+x}}}}}$$


$$S\subseteq \Sigma \Rightarrow S\in S^\prime$$

$$(T\mathbf{y}, \mathbf{z}) \langle\sum_{i=1}^n y_i \sum_{k=1}^n \mathbf{t}_{i,k}
\mathbf{x}_k , \sum_{j=1}^n z_j \mathbf{x}_j \rangle   $$

$$\int_a^b K(x,y)p(y)dy =\sum_{i,j=1}^n c_{i,j} \int_a^b h_j (y) p(y) dy h_i (x)$$

$$G_3 (x) =\frac{F_3 (x)}{\Vert F_3 (x)\Vert} =\frac1{\sqrt{2\pi}}$$

$$\int_{-T}^T \int_0^{T-|u|} \Bigl\{ p_N \delta (u) + q_{NN} (u) \Bigr\} e^{-i\lambda u} dudv$$

$$\left[ \left(\frac{\int_1^\infty f(x) dx}{\int_1^\infty g(y)dy} \right)^2 +1 \right]^2 +1$$


$$\lim_{n\rightarrow\infty} \left\{ \int_D \left[ \langle G(P,Q)\rangle
-\left| \biggl\lfloor \sum_{n=1}^m \frac{u_n(P)}{\lambda_n} \biggr\rfloor
\right|^2 \right] dr_q =0\right\}+1=0$$

$$\left[
\begin{array}{cccc}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{n1} & a_{n2} & \cdots & a_{nn} 
\end{array} \right]
$$








\end{document}