YT Lee's simple notes

Example:

\documentclass[a4paper]{article}

%% Language and font encodings
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage[T1]{fontenc}

%% Sets page size and margins
\usepackage[a4paper,top=1.8cm,bottom=1.8cm,left=1.3cm,right=1.3cm,marginparwidth=0.5cm]{geometry}

%% Useful packages
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage[colorinlistoftodos]{todonotes}
\usepackage[colorlinks=true, allcolors=blue]{hyperref}

\title{Phonon dispersion with LO-TO splitting and acoustic sum rules}
\author{Y. T. Lee$^{1,2}$}
\date{%
    $^1$Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan\\%
    $^2$Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea\\%
    \today
}

\begin{document}
\maketitle

\begin{abstract}
Your abstract xxx xxx xxxxx xxxxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxx xxxxx xxxxxx xxxx xxxxx xxxx xx xxxxxx xxxxxxxx xxxxx xxx xxxx xxx xxxxx xxxxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxx xxxxx xxxxxx xxxx xxxxx xxxx xx xxxxxx xxxxxxxx xxxxx xxx xxxx.
\end{abstract}

\section{Introduction}

Your introduction xxx xxx xxxxx xxxxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxx xxxxx xxxxxx xxxx xxxxx xxxx xx xxxxxx xxxxxxxx xxxxx xxx xxxx xxx xxxxx xxxxxxx xxxxx xxxxx xxxxx xxxxx xxxxx xxxx xxxxx xxxxxx xxxx xxxxx xxxx xx xxxxxx xxxxxxxx xxxxx xxx xxxx. 

\section{Some examples to get started}

\subsection{Writing Mathematical equation}

Let $X_1, X_2, \ldots, X_n$ be a sequence of independent and identically distributed random variables with $\text{E}[X_i] = \mu$ and $\text{Var}[X_i] = \sigma^2 < \infty$, and let
\[S_n = \frac{X_1 + X_2 + \cdots + X_n}{n}
      = \frac{1}{n}\sum_{i}^{n} X_i\]
denote their mean. Then as $n$ approaches infinity, the random variables $\sqrt{n}(S_n - \mu)$ converge in distribution to a normal $\mathcal{N}(0, \sigma^2)$.

\subsection{Lists}

There are two types of lists with automatic numbering as below.

\begin{enumerate}
\item xxx,
\item and xxx.\cite{latexcompanion}
\end{enumerate}
\dots or dot points \dots
\begin{itemize}
\item yyy,\cite{einstein}
\item and yyy.\cite{knuthwebsite}
\end{itemize}

\begin{thebibliography}{3}
\bibitem{latexcompanion} 
Michel Goossens, Frank Mittelbach, and Alexander Samarin. 
\textit{The \LaTeX\ Companion}. 
Addison-Wesley, Reading, Massachusetts, 1993.
 
\bibitem{einstein} 
Albert Einstein. 
\textit{Zur Elektrodynamik bewegter K{\"o}rper}. (German) 
[\textit{On the electrodynamics of moving bodies}]. 
Annalen der Physik, 322(10):891–921, 1905.
 
\bibitem{knuthwebsite} 
Knuth: Computers and Typesetting,
\\\texttt{http://www-cs-faculty.stanford.edu/\~{}uno/abcde.html}
\end{thebibliography}

\end{document}

Result:

References:

[1] https://www.sharelatex.com/learn/Bibliography_management_with_bibtex

[2] https://www.overleaf.com/

[3] https://www.sharelatex.com/