\documentclass[a4paper,12pt]{article}
\usepackage[centertags]{amsmath}
\usepackage{amsfonts,amssymb,amsthm}
%% Language and font encodings
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsfonts}
%% Sets page size and margins
\usepackage{upgreek}
%% Useful packages
\usepackage{graphicx}
\usepackage[authoryear,round]{natbib}

\theoremstyle{definition}
\newtheorem{defn}{Definition}[section]
\newtheorem{fig}{Figure}[section]
%
\theoremstyle{plain}
\newtheorem{res}[defn]{Result}
\newtheorem{thm}[defn]{Theorem}
\newtheorem{cor}[defn]{Corollary}
\newtheorem{prop}[defn]{Proposition}
\newtheorem{lem}[defn]{Lemma}
%
\theoremstyle{remark}
\newtheorem*{case}{Case}
\newtheorem{rem}[defn]{Remark}
\newtheorem{ex}[defn]{Example}
\newtheorem{exs}[defn]{Examples}

%\numberwithin{equation}{section}

\usepackage[colorinlistoftodos]{todonotes}
\usepackage[colorlinks=true, allcolors=blue]{hyperref}
\usepackage[margin=1in]{geometry}
\newcommand\me{\mathrm{e}}
\newcommand\mb{\mathbb}
\newcommand\mE{\mathbb{E}}
\newcommand\mP{\mathbb{P}}
\usepackage{hyperref}
\title{The title of your report}
\author{\textbf{Your name}\\\emph{\normalsize{Department of Mathematics, University of California, San Diego}}}
\date{}
     
     \begin{document}
     \maketitle
     \section{Font effect}
     \textit{words in italics}\\
     \textbf{words in bold}, more        \quad       spaces only count as one
     \section{Font size}
     \tiny{tiny word}\\
     \large{large word}\\
     {\huge huge word}
     \subsection{subsection one}
     \subsubsection{this is a subsubsection}
     \subsection{subsection two}
     \section{List}
     \begin{enumerate}
     \item First thing
     \item Second thing
     \begin{itemize}
     \item[(i)] A sub-thing
     \item[(ii)] Another sub-thing
     \end{itemize}
     \item Third thing
     \end{enumerate}
     \section{Special characters}
     \{.   \}, \$, \%
     \newpage
     \section{Equations}
     \begin{itemize}
     	\item Write equation without any environment: 1+1=2
     	\item Write in \$: $1+1=2$
     	\item Write in \$\$: $$1+1=2$$
     	\item Write in begin equation: 
     	\begin{equation}
     		1+1=2
     	\end{equation}
     	\begin{equation}
     		2+2=4
     	\end{equation}
     	\item Write in begin align:
     	\begin{align}
     	1+1&=2\\
     	8+10+20&=38 \notag \\
     	xy+yz+zx&=x^2+y^2+z^2	
     	\end{align}

     \end{itemize}
    \section{Sums and integral}
    $$\sum_{x=1}^5 y^x$$
    $$\int_1^3x^3\,dx$$
    \section{Greek letters}
    $\alpha, \beta, \delta, \Delta, \lambda, \Lambda$
    $$f(x)=\sum_{i=0}=0^\infty\frac{f^{(i)}(0)}{i!}x^i$$
     \end{document}

