documentclass[twoside]{book}
usepackage[english]{babel}
usepackage[utf8]{inputenc}
usepackage{amsmath, amssymb, amsfonts}
usepackage{amsthm}
usepackage[utf8]{inputenc}
usepackage[T1]{fontenc}
usepackage{mathtools}
pdfpagewidth=6in
pdfpageheight=9in
textheight=6in
textwidth=10.5cm
hoffset=-2.25cm
topmargin=0cm
newtheorem{definition}{Definition}[section]
pagestyle{headings}
newtheorem*{remark}{Remark}
newtheorem*{problem}{Problem}
newtheorem{example}{Example}
newtheorem{theorem}{Theorem}
newtheorem{lemma}{Lemma}
newtheorem*{s}{Statement}
newtheorem*{corollary}{Corollary}
begin{document}

title{----------}
author{-----------}
frontmatter
maketitle
tableofcontents
mainmatter
setcounter{tocdepth}{4}
setcounter{secnumdepth}{4}
chapter{Preliminaries}

bigskip
bigskip
bigskip

Hello!!

end{document}