La pregunta se relaciona con la tabla de contenido

Question

Dado que su clase de documento amsbookno es una de las estándar, es mejor no usarla titlesec; El siguiente código contiene las redefiniciones necesarias para las unidades seccionales y también agregará el símbolo delante del número en el ToC:

\documentclass[11pt,a4paper]{amsbook}
 \usepackage{bbold,amscd,amsmath,amssymb,amsfonts,ifthen,amsthm}
 \usepackage[utf8]{vietnam}
 \usepackage[all]{xypic} 
 \usepackage{kpfonts}
 %%%%% FOR SEARCHING LABELS AND REFS %%%%%%%%%%%%%%%
 \usepackage{color}
 \usepackage[color,notref,notcite]{showkeys}
 \definecolor{refkey}{rgb}{0,0,0}
 \definecolor{labelkey}{rgb}{0,0,1}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \usepackage{newcent}   
 %\usepackage[unicode]{hyperref}
 \usepackage{cmap}

 %%%%%MARGIN %%%%%%%%%%%%%%%%%%%
 \oddsidemargin 2cm %0.3cm
 \evensidemargin 2cm % 3cm
 \topmargin2cm
 \textwidth12cm %15
 \textheight18.5cm %22
 \headheight3ex
 \headsep5ex
 \topskip3ex
 %% FOR TYPESETTING VIETNAMESE WITH AMSART %%%%%%
 \def\firstofone#1{#1}
 \let\uppercase\firstofone
 \let\MakeUppercase\firstofone
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  

 %STYLE%%%%%%%%%%%
 \def\thepart{\Roman{part}}
 \def\thechapter{\arabic{chapter}}
 \def\thesection{\arabic{section}}
 \def\labelenumi{\roman{enumi})}
 %\numberwithin{thm}{section}
 \numberwithin{equation}{section}

 %THEOREM%%%%%%%%%%%%%%%%
 \theoremstyle{plain}
 \newtheorem{thm}{Theorem}[section]
 \newtheorem{dl}[thm]{Định lý}
 \newtheorem{bd}[thm]{Bổ đề}
 \newtheorem{hq}[thm]{Hệ quả}
 \newtheorem{md}[thm]{Mệnh đề}
 \theoremstyle{definition}
 \newtheorem{nx}[thm]{Nhận xét} 
 \newtheorem{chuy}[thm]{Chú ý}
 \newtheorem{dn}[thm]{Định nghĩa}
 \newtheorem{vidu}[thm]{Ví dụ} 
 \newtheorem{bt}{}[section]
 % miscellaneous 

% Chapter and section headings
\makeatletter
\def\@makechapterhead#1{\global\topskip 5.5pc\relax
  \begingroup
  \fontsize{\@xivpt}{18}\bfseries\centering
    \ifnum\c@secnumdepth>\m@ne
      \leavevmode \hskip-\leftskip
      \rlap{\vbox to\z@{\vss
          \centerline{\normalsize\mdseries
              \@xp{\scshape{\chaptername}}\enspace\thechapter}
          \vskip 2pc}}\hskip\leftskip\fi
     \normalfont\scshape#1\par \endgroup
  \skip@34\p@ \advance\skip@-\normalbaselineskip
  \vskip\skip@ }
\def\@makeschapterhead#1{\global\topskip 7.5pc\relax
  \begingroup
  \fontsize{\@xivpt}{18}\normalfont\scshape\centering
  #1\par \endgroup
  \skip@34\p@ \advance\skip@-\normalbaselineskip
  \vskip\skip@ }
\def\@sect#1#2#3#4#5#6[#7]#8{%
  \edef\@toclevel{\ifnum#2=\@m 0\else\number#2\fi}%
  \ifnum #2>\c@secnumdepth \let\@secnumber\@empty
  \else \@xp\let\@xp\@secnumber\csname the#1\endcsname\fi
 \ifnum#2=1 \def\@secnumber{\S\thesection}\fi
 \ifnum #2>\c@secnumdepth
   \let\@svsec\@empty
 \else
    \refstepcounter{#1}%
    \edef\@svsec{\ifnum#2<\@m
       \@ifundefined{#1name}{}{%
         \ignorespaces\csname #1name\endcsname\space}\fi
       \@nx\textup{%
         \csname the#1\endcsname.}\enspace
    }%
  \fi
  \@tempskipa #5\relax
  \ifdim \@tempskipa>\z@ % then this is not a run-in section heading
    \begingroup\ifnum#2=1\relax\noindent\textbf{\S}\fi #6\relax% NEW
    \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty\@M #8\par}%
    \endgroup
  \csname #1mark\endcsname{#7}%
    \ifnum#2>\@m \else \@tocwrite{#1}{#8}\fi
  \else
  \def\@svsechd{#6\hskip #3\@svsec
    \@ifnotempty{#8}{\ignorespaces#8\unskip
       ñññ\@addpunct.}%
    \ifnum#2>\@m \else \@tocwrite{#1}{#8}\fi
  }%
  \fi
  \global\@nobreaktrue
  \@xsect{#5}}
\def\section{\@startsection{section}{1}%
  \z@{.7\linespacing\@plus\linespacing}{.5\linespacing}%
  {\normalfont\bfseries}}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\pagestyle{myheadings}
\begin{document}
\parskip4pt
\renewcommand{\baselinestretch}{1.1}

\frontmatter

\tableofcontents  
\normalsize
\chapter*{Lời nói đầu}
Thử xem thế nào.\\ 
Let's try it.\\
\chapter*{Các ký hiệu}
\markleft{\sc Các ký hiệu}
\markright{\sc Các ký hiệu}
Ta sẽ dùng các ký hiệu sau \\
We will use these following notations.\\
\mainmatter

\pagenumbering{arabic}


\markleft{\hfill \sc Nguyễn Minh Hà}
\chapter{Hướng của đoạn thẳng}

\markright{\sc Hướng của đoạn thẳng\hfill\ }
\section{Hình thang và hình bình hành}
We define the following figure.\\
\section{Đoạn thẳng}
We define the following arc.\\
\backmatter

\begin{thebibliography}{99}
\end{thebibliography}
\end{document}
\documentclass[11pt,a4paper]{amsbook}



\begin{document}

\chapter{Test Chapter}
\section{Test Numbered Section}
\section*{Test Unnumbered Section}

\end{document}

ingrese la descripción de la imagen aquí

También cambié la respuesta en la pregunta vinculada para no usar titlesec.

Una observación final: las clases de documentos de AMS fueron diseñadas para envíos a AMS, por lo que tienen configuraciones muy específicas que, como ha visto, pueden ser difíciles de anular.

Si no está obligado a utilizar una de las clases de AMS, le sugiero que cambie a otra clase de documento; hacerlo podría ser un buen intercambio, ya que los cambios en el formato ahora se pueden realizar fácilmente utilizando paquetes existentes (que son incompatibles con las clases AMS). Como ejemplo, tome el siguiente documento que produce su formato (tanto en el documento como en el ToC) con un mínimo esfuerzo y también incorpora algunas de las configuraciones de estilo de amsbook:

\documentclass{book}
\usepackage[compact]{titlesec}
\usepackage[titles]{tocloft}
\usepackage{chngcntr}

\counterwithout{section}{chapter}

\newlength\mylen
\renewcommand\cftchappresnum{\chaptername~}
\renewcommand\cftchapaftersnum{.}
\renewcommand\cftchapfont{\normalfont}
\renewcommand\cftchappagefont{\normalfont}
\settowidth\mylen{\cftchappresnum\cftchapaftersnum} % extra space
\addtolength\cftchapnumwidth{\mylen}
\renewcommand\cftsecdotsep{\cftnodots}
\renewcommand\cftsecpresnum{\S}
\renewcommand\cftsecaftersnum{.}

\titleformat{\chapter}[display]
  {\normalfont\LARGE\scshape\filcenter}{\chaptertitlename\ \thechapter}{15pt}{}
\titleformat{\section}
{\normalfont\Large\bfseries}{\S\thesection.}{0.5em}{}

\begin{document}

\tableofcontents

\frontmatter
\chapter{Test Chapter}
\chapter{Test Chapter}

\mainmatter
\chapter{Test Chapter}
\section{Test Section}
\section{Test Section}
\chapter{Test Chapter}
\section{Test Section}
\section{Test Section}

\end{document}

Answer 1