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5

Improved version Here is a possibility using the xkeyval package and a key-value approach: The code (explanations below): \documentclass{article} \usepackage[explicit]{titlesec} \usepackage{xkeyval} \usepackage{tikz} \usetikzlibrary{tikzmark,calc} \usepackage{lipsum} \newlength\LeftSep \newlength\RightSep \newlength\TitleWd \newlength\VertLineWd ...

3

The problem here is that the section title is included inside a TikZ \node with no provisions for text spanning several lines. The problem can be easily solved in a number of ways, perhaps the simpler one is adding a text width=<length> option to the node, as the following simple example demonstrates: \documentclass[10pt, compress]{beamer} ...

1

4

The \subsection command for standard classes could be defined as \titleformat{\subsection} {\normalfont\large\bfseries}{\thesubsection}{1em}{} You can just remove \bfseries like \titleformat{\subsection} {\normalfont\large}{\thesubsection}{1em}{} To make them un bold. Another way is to use the short form: \documentclass{article} \usepackage{titlesec} ...

2

Your document has \renewcommand{\thesection}{\thelecnum.\arabic{section}} so the section counter will be prepended by the counter lecnum which is stepped with the \lecture command. If you want your sections to increase, you have two options: Use a new \lecture command (the section counter will increase, but it will still have as prefix the lecture ...

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