\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage[round]{natbib}
\let\cite\citep




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}










\begin{document}

\title{USI Extra Credit Homework}



\author[1]{Sofiya Elyukin}%
\affil[1]{New York University (NYU)}%


\vspace{-1em}



  
  \date{May 07, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup








\sloppy


1. Create the following formulas in LaTeX:

\[ Q \le  Q^{\max} - \Sigma\ p\left(w\right) \]

\[Z=\frac{\Pi^n_{j=1} X_i}{\Sigma^n_{j=1} Y_i}\]

\[ \left\{ \begin{array}{ll}
a=b+c \\
b=a+c \\
c=a+b \end{array} \right. \] 

2. Create the following table in LaTex\selectlanguage{english}
\begin{table*}[htb]
\begin{center}
\begin{tabular}{| c | c c | c | c |}
\hline
\multirow{2}{*}{Network} & \multicolumn{2}{c|}{Modularity score} & \multirow{2}{*}{Deviation} & \multirow{2}{c|}{NMI} \\
 & Best & Alternative & & \\
\hline
 1000 & 0.4 & 0.3 & 0.000987 & 0.923345\\
 2000 & 0.3 & 0.2 & 0.007971 & 0.732029\\
 3000 & 0.6 & 0.6 & 0.001272 & 0.924726\\
 4000 & 0.6 & 0.6 & 0.028605 & 0.784013\\
 5000 & 0.6 & 0.6 & 0.019975 & 0.553769\\
 6000 & 0.6 & 0.6 & 0.003363 & 0.919872\\
 7000 & 0.6 & 0.5 & 0.014161 & 0.741351\\
 8000 & 0.6 & 0.6 & 0.000399 & 0.651622\\
 9000 & 0.6 & 0.6 & 0.000121 & 0.971705\\
10000 & 0.6 & 0.6 & 0.004788 & 0.816490\\
\hline
\end{tabular}
\end{center}
\end{table*}

\selectlanguage{english}
\FloatBarrier
\end{document}

