Is it possible to tweak the amsbook-class such that the uppercase headings (e.g. Chapter 1) are changed to small caps?
Are there any "typographical objections" in doing so?
Is it possible to tweak the amsbook-class such that the uppercase headings (e.g. Chapter 1) are changed to small caps?
Are there any "typographical objections" in doing so?
An etoolbox patch of \@makechapterhead (the macro responsible for setting the (numbered) chapter heading) is sufficient:

\documentclass{amsbook}% http://ctan.org/pkg/AMS-LaTeX
\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
\makeatletter
% Change case of chapter title
\patchcmd{\@makechapterhead}% <cmd>
{\uppercase}% <search>
{\scshape}% <replace>
{}{}% <success><failure>
\makeatother
\begin{document}
\chapter{A chapter}
\end{document}
If you wish to change the chapter title (A chapter above) to small-caps from the default bold, use
\makeatletter
% Change formatting of chapter name
\patchcmd{\@makechapterhead}% <cmd>
{\bfseries}% <search>
{\scshape}% <replace>
{}{}% <success><failure>
\makeatother
Of course, you can do both if needed:

To set the chapter name in small-caps and bold, you need a font that can manage both. For this, see Small Caps and Bold Face. Using bold-extra provides this font, but at a very low quality:

Perhaps a fake-small-caps-bold approach might work with the aid of contour:

\documentclass{amsbook}% http://ctan.org/pkg/AMS-LaTeX
\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
\usepackage[auto]{contour}% http://ctan.org/pkg/contour
\contourlength{0.01em}
\makeatletter
% Change case of chapter title
\patchcmd{\@makechapterhead}% <cmd>
{\uppercase}% <search>
{\scshape}% <replace>
{}{}% <success><failure>
% Change formatting of chapter name
\patchcmd{\@makechapterhead}% <cmd>
{\bfseries}% <search>
{\scshape}% <replace>
{}{}% <success><failure>
% Fake-bold chapter name
\patchcmd{\@makechapterhead}% <cmd>
{#1}% <search>
{\contour[100]{black}{#1}}% <replace>
{}{}% <success><failure>
\begin{document}
\chapter{A chapter}
\section{A section}
\end{document}
See the contour package documentation for more options (I've used a 0.03em contour length, and 100 repetitions for a smooth finish).
There is no real typographical requirement here, just as long as the headings show some form of structure. Font shape/face/size all show this, and one shouldn't go too overboard. Also think about consistency across sectional units. If you're sticking to bold, say, just vary the size across the hierarchy.
My Question was concerning the chapter head. But now I'm also thinking about changing the chapter title to small caps.
Although when I use your second code snippet the chapter title is in small caps but not bold. In my opinion this is a little to thin, especially in comparison with the bold section headings.
Is it possible to change the chapter title to bold small caps?
Also consider the second part of my question (In my opinion the chapter heading in small caps does look for aesthetic.).
– CraigPr Jan 07 '14 at 21:25\patchcmd{\chapterrunhead}{\uppercasenonmath}{\scshape\@secondoftwo}{}{}. However, a quick fix is to call\chapter{\scshape A chapter}- this will also migrate to the ToC. – Werner Jan 07 '14 at 22:15I tried: \patchcmd{@makesectionhead}%
{\bfseries}%
{\scshape}%
{}{}%
\makeatother
But didn't work out.
– CraigPr Jan 11 '14 at 16:27\chapters are special. All other (lower) sectional units are formatting with a generic set of macros (which doesn't include\@makesectionhead). You would need\patchcmd{\@sect}{\@hangfrom}{\mdseries\scshape\@hangfrom}{}{}(which would change everything from\sectionto\subsectionto\subsubsectionto use\mdseries\scshape. – Werner Jan 11 '14 at 16:45\makeatletter...\makeatotherpair? – Werner Jan 11 '14 at 17:10