Edit a default latex/beamer theme to show section numbers

Question

I am using beamer to create a presentation. The theme I chose is Singapore. It has a nice header with section names and bullets for subsections.

What is the easiest way to modify the header so that it will also display the section number, not just the title?

Bonus question: how can I make the section numbers also appear in the table of contents?

So instead of:

Introduction Concepts Realisation

it should be:

1. Introduction 2. Concepts 3. Realisation

Answer 1

You can redefine the section in head/foot and section in head/foot shaded templates to add \insertsectionheadnumber. For the bonus, you need to redefine section in toc to add \inserttocsectionnumber; an example illustrating these redefinitions:

\documentclass{beamer}
\usetheme{Singapore}

\setbeamertemplate{section in head/foot}{\hfill\insertsectionheadnumber.~\insertsectionhead}
\setbeamertemplate{section in head/foot shaded}{\color{structure!50}\hfill\insertsectionheadnumber.~\insertsectionhead}
\setbeamertemplate{section in toc}{\inserttocsectionnumber.~\inserttocsection}

\begin{document}

\section{Test Section One}
\begin{frame}
test
\end{frame}
\section{Test Section Two}
\begin{frame}
test
\end{frame}
\section{Test Section Three}
\begin{frame}
test
\end{frame}

\end{document}

An image of the resulting ToC showing the numbering both in the ToC entries and in the headline: