\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amstext,dsfont,fancyvrb,float,fontenc,graphicx,subfigure,theorem,hyperref}
\usepackage[utf8]{inputenc}

%Linenumbers

%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
% We are not using the lineno right now, it does not work properly unless a space is added before any math environment (e.g. \begin{equation}), and that leaves too much empty space.
%\usepackage[left]{lineno}
%\linenumbers
%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
\usepackage{tikz,everypage}
% file needs to be compiled twice for the numbers to appear correctly on the left (1 through 50 on each page)
\AtBeginDocument{%
  \AddEverypageHook{%
    \begin{tikzpicture}[remember picture,overlay]
      \path (current page.north west) --  (current page.south west) \foreach \i in {1,...,\fakelinenos} { node [pos={(\i-.5)/\fakelinenos}, xshift=\fakelinenoshift, line number style] {\i} }  ;
    \end{tikzpicture}%
  }%
}
\tikzset{%
  line numbers/.store in=\fakelinenos,
  line numbers=50,
  line number shift/.store in=\fakelinenoshift,
  line number shift=5mm,
%  line number style/.style={text=gray},
line number style/.style={text=black},
}
%end Linenumbers (to be commented out in copyediting)


%This is a tex template for the PUMP Journal of Undergraduate Research. Modified parts of the sty file for the Electronic Journal of Combinatorics were used with permission.

%%%%% MARGINS AND GENERAL GEOMETRY OF THE DOCUMENT
\usepackage[letterpaper]{geometry}
\setlength{\textwidth}{6.3in}
\setlength{\textheight}{8.7in}
\setlength{\topmargin}{0pt}
\setlength{\headsep}{0pt}
\setlength{\headheight}{0pt}
\setlength{\oddsidemargin}{0pt}
\setlength{\evensidemargin}{0pt}



%%%% BOTTOMLINE INFO AND POSITION
\def\specs#1#2#3{\def\papno{#1}\def\volno{#2}\def\volyear{#3}}
\ifx\volno\undefined\def\volno{0}\fi
\ifx\volyear\undefined\def\volyear{2017}\fi
\ifx\pagno\undefined\def\pagno{000--000}\fi
%\def\dateline#1#2{{\small Submitted: #1; Accepted: #2; Published: XX}}

\newfont{\footsc}{cmcsc10 at 8truept}
\newfont{\footbf}{cmbx10 at 8truept}
\newfont{\footrm}{cmr10 at 10truept}

\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhead{} % clear all header fields
\renewcommand{\headrulewidth}{0pt} % no line in header area
%%%%%DO NOT REMOVE OR CHANGE THE NEXT 4 LINES
\lfoot{\footsc  \includegraphics[width=5mm,scale=0.05]{pump1.jpeg}\protect\raisebox{5pt}{the pump journal of undergraduate research {\footbf\volno} (\volyear), \pagno}}
\cfoot{}
\rfoot{\footrm\protect\raisebox{5pt}{\thepage}}

%%%%% THE FOLLOWING COMMANDS CONTROL THE FONT SIZE FOR  SECTION AND SUBSECTION HEADINGS, AND ADJUST THE SPACE JUST BELOW EACH SUCH HEADING.
\usepackage{relsize}
\usepackage{sectsty}
\allsectionsfont{\larger[-1]} 

\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}
                                    {2ex \@plus.5ex \@minus.2ex}
                                    {-1em}
                                    {\normalfont\normalsize\bfseries}}

\renewcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}
                                       {2ex \@plus.5ex \@minus .2ex}
                                       {-1em}
                                      {\normalfont\normalsize\bfseries}}

%%%% THE FOLLOWING COMMANDS CHANGE THE SPACING IN THE BIBLIOGRAPHY
\newlength{\BiblioSpacing}
\setlength{\BiblioSpacing}{0.4ex plus 0.1ex minus 0.1ex}
\newcommand{\SquashBibFurther}{
\setlength{\BiblioSpacing}{0.2ex plus 0.1ex}}

\let\oldthebibliography=\thebibliography
\let\endoldthebibliography=\endthebibliography
\renewenvironment{thebibliography}[1]{
\begin{oldthebibliography}{#1}
\setlength{\parskip}{\BiblioSpacing}
\setlength{\itemsep}{\BiblioSpacing}
}
{
\end{oldthebibliography}
}

%%%% MACROS AND DEFINITIONS 
\usepackage[strict]{changepage}
\def\abstractname{Abstract -}   % <-----------------
\def\abstract{\begin{adjustwidth}{1cm}{1cm} \par    \footnotesize \noindent {\bf \abstractname} 
\def\endabstract{ \end{adjustwidth} \smallskip }}
\def\keywordsname{Keywords~:} %<------------------
\def\keywords{\begin{adjustwidth}{1cm}{1cm} \par\footnotesize \noindent{\bf \keywordsname}
\def\endkeywords{ \end{adjustwidth} \smallskip}}
\def\MSCname{Mathematics Subject Classification {\rm(2020)}~:} % <-----------------
\def\MSC{ \begin{adjustwidth}{1cm}{1cm} \par\footnotesize\noindent{\bf \MSCname\/}
\def\endMSC{ \end{adjustwidth}  }}

%%%%% COMMANDS FOR THEOREMS
{\theorembodyfont{\itshape}\newtheorem{theorem}{Theorem}[section]}
{\theorembodyfont{\itshape}\newtheorem{proposition}[theorem]{Proposition}}
{\theorembodyfont{\itshape}\newtheorem{definition}[theorem]{Definition}}
{\theorembodyfont{\itshape}\newtheorem{lemma}[theorem]{Lemma}}
{\theorembodyfont{\itshape}\newtheorem{corollary}[theorem]{Corollary}}
{\theorembodyfont{\rm}\newtheorem{notation}[theorem]{Notation}}
{\theorembodyfont{\rm}\newtheorem{remark}[theorem]{Remark}}
{\theorembodyfont{\rm}\newtheorem{conjecture}[theorem]{Conjecture}}
{\theorembodyfont{\rm }\newtheorem{example}[theorem]{Example}}
\def\proof{{\noindent \bf Proof.~}}
\def\endproof{\hspace{\fill}{\boldmath $\Box$}\par}

\def\dedicatory{\date}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%   PLEASE DO NOT MODIFY ANY OF THE DEFINITIONS/COMMANDS IN THE PREAMBLE ABOVE. THANKS.




%%%% PLEASE FILL THE TITLE AND THE NAMES OF THE AUTHORS NEXT
\title{\Large\bf Title of Paper}
  \vskip 1.5em
\author{\sc A. One, B. Two, and C.D. Three\thanks{This work was supported by a PUMP research grant (NSF grant No.)}}
\dedicatory{\normalsize\em To Marilyn who made me a shirt}

%%%% PLEASE DO NOT DELETE/MODIFY THE FOLLOWING THREE LINES
\begin{document}
\setcounter{page}{1}
%\date{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\maketitle
\thispagestyle{fancy}

\vskip 1.5em

\begin{abstract}
Please make the abstract self-contained, do not include references to theorems in the article like this: Theorem \ref{theorem1}, or incomplete citations like this: \cite{one}.
\end{abstract}
 
\begin{keywords}
Separate them by ;
\end{keywords}

\begin{MSC}
Separate them by ;
\end{MSC}

\section{Title of First Section} 

This section contains a definition, a figure with the PUMP logo, and a theorem with a proof.

\begin{definition} 
This is a definition. 
\end{definition}

%%This is how you add graphics, if you don't need figures, please delete the next 7 lines. If you do need figures, please experiment changing the width and the scale to see how LaTex reacts. With the htb option, LaTex will try to place your figure, in order, in the position you placed it, or, if there is not enough space, at the top of a page, and finally at the bottom of a page.
\begin{figure}[!htb]
\begin{center}
% use \includegraphics to import figures 
\includegraphics[width=20mm,scale=0.5]{pump1.jpeg}
\end{center}
\caption{\label{fig:PUMP logo} This is the PUMP logo.}
\end{figure}

The following subsection contains the aforementioned theorem and proof.

\subsection{Title of First Subsection} 

\begin{theorem}\label{theorem1}
The first theorem.
\end{theorem}
 
\begin{proof} 
This is the proof of Theorem \ref{theorem1}
\end{proof}

\newpage

Next you may find examples of lists, arrays of equations, and matrices.
 
\begin{enumerate}
\item A
\item list
\item with
\item five
\item items
\end{enumerate}
  
\begin{example}
Some trig:
\begin{align*}  
\cos{2x} & =  \cos^2{x} - \sin^2{x}  \\
      & =  (1- \sin^2{x}) - \sin^2{x}  \\
      & =  1- 2\sin^2{x}  
\end{align*}
\end{example}

If you want to refer to these as formula (\ref{sometrig1}) or formula (\ref{sometrig2}) in Example \ref{example} you can do the following (notice the difference between the two commands):

\begin{example}\label{example}
Some trig:
\begin{eqnarray} \label{sometrig1}
\cos{2x} & = & \cos^2{x} - \sin^2{x}  \\
 \label{sometrig2}     & = & (1- \sin^2{x}) - \sin^2{x}  \\
      & = & 1- 2\sin^2{x}  
\end{eqnarray}
\end{example}

If you want to display an equation in the center of a line, do this:
$$\cos^2{\frac{x}{2}}=\frac{1+\cos{x}}{2},\;\forall x\in\mathbb{R}$$

If you want to refer to it as equation (\ref{halfangle}) do this:
\begin{equation}\label{halfangle}
\cos^2{\frac{x}{2}}=\frac{1+\cos{x}}{2},\;\forall x\in\mathbb{R}
\end{equation}

If you put this inside a line, it will look like this: $\cos^2{\frac{x}{2}}=\frac{1+\cos{x}}{2},\;\forall x\in\mathbb{R}$ in order to make it fit between two lines, so if you want it to look like in equation (\ref{halfangle}) but still put it inside a line, use this: $\displaystyle{\cos^2{\frac{x}{2}}=\frac{1+\cos{x}}{2},\;\forall x\in\mathbb{R}}$.

Finally, a matrix:
\[
M = \left[
\begin{array}{ccc}
1 & 2 & 3 \\
\pi & e & \phi \\
\sqrt{2} & \sqrt[3]{4} & \sqrt[4]{7}
\end{array}
\right]
\]

\section*{Acknowledgments} %%% ADD HERE YOUR THANKS AND ACKNOWLEDGMENTS; please do not change spelling
 
This is at the end of the paper, right before References.

\section*{Instructions for preparing the reference list}

The following should be observed when preparing the list:
\begin{itemize}
\item leave no space between strings of initials
\item all authors names appear, separated by commas (do not use et al.)
\item  there is a comma after the article title
\item the journal title is abbreviated (use the standard abbreviation, if you don't know it you can look it up on MathSciNet or zbMATH)
\item the journal title appears in italics
\item in the case of books, the book title appears in italics
\item the volume number appears in bold face, and the issue number is not listed
\item  the year appears in parentheses after the volume number, and is followed by a comma
\item  use a double dash between page numbers 
\end{itemize}

\newpage 

{\footnotesize
\begin{thebibliography}{00}
% USE THE FORMAT BELOW FOR JOURNAL REFERENCE(S)
\bibitem{one} A.B. Author, C. Author, D. Author, Title, {\it Journal abbreviated title}, {\bf vol} (year), 000--000.

% USE THE FORMAT BELOW FOR BOOK REFERENCE(S)
\bibitem{two} E. Author, {\it Title}, Publishing House, year.

% USE THE FORMAT BELOW FOR URL REFERENCE(S)
\bibitem{three} PUMP Journal, available online at the URL: \url{https://journals.calstate.edu/pump}
\end{thebibliography}}
 
%%%%%%%% AUTHORS' INFORMATION. DELETE/ADD AUTHORS AS NEEDED
{\footnotesize  
\medskip
\medskip
\vspace*{1mm} 
 
\noindent {\it Author One}\\  
Hogwarts University\\
123 Wizzard Lane\\
Someborough, Scotland\\
E-mail: {\tt aone@univ.edu}\\ \\  

\noindent {\it Bauthor Two}\\  
Faber College \\
456 National Lampoon's Dr\\
Hollywood, CA 90210 \\
E-mail: {\tt btwo@college.edu}\\ \\

\noindent {\it Cauthor D. Three}\\  
University of Los Angeles \\
789 Vin Scully Dr\\
Dodgertown, CA 99999 \\
E-mail: {\tt cthree@institute.edu} \\ \\   
%%%%%%%%%%%% Please do not remove or move the } sign below, do not remove blank line before it

}

%%%%% Please do not change or remove the lines below, they will be changed in copyediting
\vspace*{1mm}\noindent\footnotesize{\date{ {\bf Received}: April 31, 2017\;\;\;{\bf Accepted}: June 31, 2017}}\\
\vspace*{1mm}\noindent\footnotesize{\date{  {\bf Communicated by Some Editor}}}

\end{document}