\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[greek,english]{babel}
\usepackage{alphabeta}
\usepackage{amsmath}
\usepackage{amssymb}

\title{Μαθηματικά}
\author{Μαρία Σαμαρά}
\date{12/06/2021}

\begin{document}
\maketitle
\newpage
\section{Σύντομη αναφορά}
Γεια σου είμαι η Μαρία
\section{Μαθηματικές εξισώσεις}
\begin{equation}
      \sum_{n=0}^{\infty}n=-\frac{1}{12}
\end{equation}
\begin{equation}
         \pi(n)=\sum_{m=2}^{n}\left\lfloor
		                       { \left(\ \sum_{k=1}^{m-1}
		                                   \left\lfloor (\ m/k)\ /
		                                   \left\lceil{m/k} \right \rceil
		               	                   \right\rfloor
		                        \right)\ } ^{-1}
		              \right\rfloor         
\end{equation}	
\begin{equation}
	p_{1}(n)=\lim_{m\to\infty}\sum_{\nu=0}^{\infty}
					{\left (\ 1-\cos^{2m}
						{ (\ \nu!^{n}\pi/n )\ }\right )\ 
					}
\end{equation}
\begin{equation}
	\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+x}}}}}}}
\end{equation}
\begin{equation}
	\prod_{j\geqslant 0}\left (\ \sum_{k\geqslant 0}a_{jk}{z}^{k}\right )\ =
			\sum_{n\geqslant0}z^{n}\left (\ \sum_{\substack {k_0,k_1,...\geqslant 0 \\ k_0+k_1+...=n}}
					a_{0k_{0}}a_{1k_{1}}... \right )\
\end{equation}
\begin{equation}
\begin{vmatrix}
	a&\cdots&z\\
	\vdots&\ddots&\vdots\\
	\alpha&\cdots&\omega
\end{vmatrix}
\end{equation}
\begin{equation}
	f(n)= \begin{cases} \displaystyle\sum_{n=1}^{\infty}n, & n \in\mathbb{R}\setminus\mathbb{Q}  \\ 0, & n\in\mathbb{Q}  \end{cases}
\end{equation}
\begin{equation}
	\sqrt[3]{i}\sqrt[n+1]{4+5+6+7}
\end{equation}
\begin{equation}
	\iint_0^{a=n} xdx{\left (\ \frac{a+b}{c}\right )\ }^{2}
\end{equation}
\begin{equation}
\begin{pmatrix}
	a_{11}&a_{12}&\cdots&a_{1n}\\
	a_{21}&a_{22}&\cdots&a_{2n}\\
	\vdots&\vdots&\ddots&\vdots\\
	a_{m1}&a_{m2}&\cdots&a_{mn}
\end{pmatrix}
\end{equation}
\begin{equation}
\begin{Bmatrix}
	\alpha=f(z)\\
	\beta=f(z^{2})\\
	\gamma=f(z^{3})\\
\end{Bmatrix}
\end{equation}
\begin{equation}
\begin{Bmatrix}
	x&=\alpha^{2}-\beta\\
	y&=2\gamma\\
\end{Bmatrix}
\end{equation}
\end{document}
 
