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Tex

General

Difference between Engine and Formats. The webpage here makes sense of the different levels of TeX

  • https://www.tug.org/levels.html

Miscellaneous

Spacing between itemize

\begin{itemize}
 \setlength\itemsep{-.5em}
 \item ...
 \item ...
\end{itemize}

Side by Side

\makebox[\textwidth][c]{%
    \begin{minipage}{.3\linewidth}
        \begin{align*}
            \frac{\mathrm{d} X}{\mathrm{d} t} & = \beta\frac{S}{n}X   \\
            \frac{\mathrm{d} S}{\mathrm{d} t} & = - \beta\frac{S}{n}X
        \end{align*}
    \end{minipage}%
    \begin{minipage}{.3\linewidth}
        \begin{align*}
            \frac{\mathrm{d} x}{\mathrm{d} t} & = \beta sx   \\
            \frac{\mathrm{d} s}{\mathrm{d} t} & = - \beta xs
        \end{align*}
    \end{minipage}
}

\begin{minipage}[tbp]{width_of_page} - A minipage is a smaller page inside the main page, can control how close things are displayed \makebox[\textwidth][c]{%} - centers the two pages next to each other, as long as it's less than the linewidth

Math environments

Title Page

\documentclass{article}
...
\begin{document}
\begin{titlepage}
    \centering
    {\scshape \Large Math 714 \par}
    \vspace{2cm}
    {\bfseries \huge Homework 1}

    \vfill
    {\Large\itshape Michael Liou\par}
    \vfill
    {\large \today\par}
\end{titlepage}
\end{document}

Biblatex

Seems to be the new standard over Bibtex. Here's a couple helpful references for the package options:

Bibtex

How bibtex generally works. You have a .bib file that is the "database" of all the entries.

In the .tex file, this would be a minimal file

\documentclass{article}
\title{Example of bibtex}
\bibliographystyle{plain}
\begin{document}
This example is from \cite{Kant}.
\bibliography{master}
\end{document}

The .bib file should look like this 

@book{durrett2019probability,
  place={Cambridge},
  edition={5},
  series={Cambridge Series in Statistical and Probabilistic Mathematics},
  title={Probability: Theory and Examples},
  DOI={10.1017/9781108591034},
  publisher={Cambridge University Press},
  author={Durrett,
      Rick},
  year={2019},
  collection={Cambridge Series in Statistical and Probabilistic Mathematics}
}

The document looks for master.bib in the directory of the tex file. You may need to run pdflatex -> bibtex -> pdflatex -> pdflatex. I have no idea what's going on in this sequence, but it seems necessary to generate the references correctly.

bibtex from the command line looks at the generated .aux file for proper references. There, it will look for a \bibitem for the database of references, and use that file to make sure all the references are found. If not the error messages/log will tell you which references in the original .tex document are not found.

I'd also recommend using the package natbib.

tlmgr

This is the Tex Live Package Manager

Fixing the error "bbm.sty" not found, we can find the package that it's in.

tlmgr search --file bbm.sty --global
sudo tlmgr install NAME_OF_PACKAGE

Installation of additional Packages

Texmf tree, is tex and metafonts. The data file structure is TDS, tex directory structure.

  • https://en.wikibooks.org/wiki/LaTeX/Installing_Extra_Packages

Tables (Booktabs)

This is the package you should be using if you create a table. Here's a helpful reference Tables

     \begin{table*}[!ht]
         \centering
         \begin{tabular}{llllllll}
             \toprule
             \phantom{abc} & \multicolumn{7}{c}{Round}\\
                 & 1  & 2 & 3 & 4 & 5 & 6  & 7 \\
             \midrule
             Arm 1 & 10 &   & 0 & 0 & 0 &        \\
             Arm 2 &    & 0 &   &   &   & 10 & 0    \\
             \bottomrule
         \end{tabular}
     \end{table*}

Algorithms

Just use Algorithmicx. The syntax is easier than Algorithm2e, and it's fine.

Mathematical images

  • http://ctan.mirrors.hoobly.com/info/lshort/english/lshort.pdf
  • http://www.texample.net/tikz/
  • http://www.texample.net/tikz/resources/#tools-that-generate-pgftikz-code

Tikz

Axes

\draw [{Latex[length=2mm]}-{Latex[length=2mm]}] (1,0) node [below] {$P$} -- (0,0) -- (0,1) node [left] {$\beta (P)$};

Curves

\draw plot [smooth, tension=1] coordinates{(0, .7) (.5, .05) (1, .7)};
\draw [] (0, .7) to[in=180, out=0] (.5, .05) to[in=180, out=0] (1, .7)

Dots 

\node [circle, fill, inner sep=1pt] at (0,1) {};

Shapes

\draw [red, dashed] (0, 0) circle (5);

Graphs

\usetikzlibrary{graphs, graphdrawing} % graphdrawing makes the graph layout automatic
\usegdlibrary{layered, force} % provides "force" and "layered" layouts
\usetikzlibrary{positioning} % right = of a

\begin{tikzpicture}
    \graph[spring layout, nodes={circle, draw, .5pt}, edges={line width=1pt}] {
        1 -- 2 -- 3 -- 4 -- 1; };

Latex Specific

To comment on proofs, just use the \tag macro. \notag removes numbering of equations in align environments. \tag*{} comments without the parentheses.

\begin{align*}
1 + (2 * 4) &= 1 + 8    \tag{multiply}
            &= 9        \tag*{addition}
\end{align*}