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Following Astrinus's advice, you can add the two lines of code between \makeatletter and \makeatother, given in egreg's answer, to modify the entry in the table of contents. Here is how you can do this: \documentclass[12pt, a4paper]{article} \makeatletter \let\latexl@section\l@section ...

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You can easily do that with the titlesec/titlestoc package. It has commands that allow for a different formatting of numbered and unnumbered sections (if you want to add unnumbered sections) in the table of contents: \documentclass[a4paper]{article} \usepackage{titletoc} \begin {document} \titlecontents{section}[0em] {\vskip 0.5ex}% {\scshape}% numbered ...

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This happens because the bemaer column system uses the LaTeX minipage behind the scenes: a vertical box. As these are not set with a fixed height they don't stretch, in contrast to setting a frame where beamer does some resizing (so the stretch is important). For a one-off application I'd be tempted to use a raw minipage and adjust as require. For example ...

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To start the appendices section, you use the command \appendix, not an environment. Change \begin{appendices} to \appendix and remove \end{appendices} If you need more flexibility, load Will Robert­son and Peter Wilson’s appendix-package. Here is an ‘MWE’ something that at least compile: \documentclass[ 11pt, a4paper, draft, ...

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