Suppress chapter number but keep section number in section headings

Question

How do I format a book so that the chapters are sub-divided into numbered sections, where:

1. only the section number, but not the chapter number, appears in the section heading (i.e. the third section of chapter four should be headed by 3, rather than by 4.3);

2. the section number is centered in the page; and

3. the section number is preceded by a "section" symbol?

4. And is there a command that will produce the section numbers in lowercase roman numerals?

Answer 1

\documentclass{book}
\usepackage{sectsty}
\sectionfont{\centering}
\renewcommand{\thesection}{\S\,(\roman{section})}
\begin{document}
\chapter{Introduction}
\section{section 1}
\chapter{Topics in Claims Reserving}
\section{section 1}
\section{section2}
\chapter{Conclusion}
\end{document}