Template I used for doing my Math and CS homework in LaTeX

homework_template.tex

\documentclass[10pt,twoside]{article}
\usepackage{multicol}
\usepackage{calc}
\usepackage{ifthen}
\usepackage{geometry}
\usepackage{amsmath,amsthm,amsfonts,amssymb}
\usepackage{color,graphicx,overpic}
\usepackage{hyperref}
\usepackage{polynom}
\usepackage[export]{adjustbox}

\polyset{
  style=C,
  delims={\big(}{\big)},
  div=:
}

\pdfinfo{
  /Title (Horrendous_Template)
% /Creator (TeX)
% /Producer (pdfTeX 1.40.0)
  /Author (Christopher E Goes)
  /Subject (My_First_Template(TM))
  /Keywords (pdflatex,latex,pdftex,tex)}

% --------------------------------------------------------------------------

% This sets page margins to .5 inch if using letter paper, and to 1cm
% if using A4 paper. (This probably isn't strictly necessary.)
% If using another size paper, use default 1cm margins.
\ifthenelse{\lengthtest { \paperwidth = 11in}}
    { \geometry{top=.5in,left=.5in,right=.5in,bottom=.5in} }
    {\ifthenelse{ \lengthtest{ \paperwidth = 297mm}}
        {\geometry{top=1cm,left=1cm,right=1cm,bottom=1cm} }
        {\geometry{top=1cm,left=1cm,right=1cm,bottom=1cm} }
    }

% Turn off header and footer
\pagestyle{empty}

% Redefine section commands to use less space
\makeatletter
\renewcommand{\section}{\@startsection{section}{1}{0mm}%
                                {-1ex plus -.5ex minus -.2ex}%
                                {0.5ex plus .2ex}%x
                                {\normalfont\large\bfseries}}
\renewcommand{\subsection}{\@startsection{subsection}{2}{0mm}%
                                {-1explus -.5ex minus -.2ex}%
                                {0.5ex plus .2ex}%
                                {\normalfont\normalsize\bfseries}}
\renewcommand{\subsubsection}{\@startsection{subsubsection}{3}{0mm}%
                                {-1ex plus -.5ex minus -.2ex}%
                                {1ex plus .2ex}%
                                {\normalfont\small\bfseries}}
\makeatother

% Define BibTeX command
\def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
    T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}

% Don't print section numbers
\setcounter{secnumdepth}{0}

\setlength{\parindent}{0pt}
\setlength{\parskip}{0pt plus 0.5ex}

% My Environments
\newtheorem{example}[section]{Example}

% --------------------------------------------------------------------------

\begin{document}
\raggedright
\footnotesize
% Creates N columns (N in this case being 3), content written left to right
\begin{multicols}{3}

% Multicol parameters
% These lengths are set only within the two main columns
%\setlength{\columnseprule}{0.25pt}
\setlength{\premulticols}{1pt}
\setlength{\postmulticols}{1pt}
\setlength{\multicolsep}{1pt}
\setlength{\columnsep}{2pt}

% Stuff above is not mine, it is an unknown source. Whoever it is, they're awesome!
%---------------------------------------------------------------------------
% --------------------------------------------------------------------------

\section{\textbf{Derivative of : Result}}
$c = 0$, $x = 1$, $x^n = nx^{n-1}$\\
$e^x = e^x$, $b^x = b^x\ln(b)$, $\ln(x) = 1/x$\\[0.1in]

$\sin(x)= \cos(x)$\\
$\csc(x) = -\csc(x)\cot(x)$\\
$\cos(x) = -\sin(x)$\\
$\sec(x) = \sec(x)\tan(x)$\\
$\tan(x) = \sec^2(x)$\\
$\cot(x) = -\csc^2(x)$\\[0.1in]

$\sin^{-1}(x) = \frac{1}{\sqrt{1-x^2}}$\\
$\cos^{-1}(x) = \frac{-1}{\sqrt{1-x^2}}$\\
$\tan^{-1}(x) = \frac{1}{1 + x^2}$\\[0.1in]

Product Rule: $d/dx f(x)g(x) = f'(x)g(x) + f(x)g'(x)$\\
Quotient Rule: $d/dx (f(x)/g(x)) = \frac{g(x)f'(x) - f(x)g'(x)}{g(x)^2}$\\
Chain Rule: $d/dx f(g(x)) = f'(g(x)) * g'(x)$\\

\section{Integrals}
\subsection{Improper Integrals}
Always check the domain for f(x)!\\
a is where domain has gap eg x!=0\\
$\int_{\infty}^{-\infty} f(x)dx = \int_{-\infty}^{a} f(x)dx + \int_a^{\infty} f(x)dx $\\
$= \lim_{t_1 \to \infty} \int_{t_1}^{a} f(x)dx + lim_{t_2 \to \infty} \int_a^{t_2} f(x)dx $\\

\subsection{Basics/Essentials}
(Remember: + C if indefinite!!!)\\
Integration by parts: $\int u dv = uv - \int v du$\\
LATE(Choosing u): Log, Algebra, Trig, Exp\\
\begin{equation*}\int \sin^n(x)\cos^m(x)dx\end{equation*}
If n and/or m are odd, use $\sin^2(x) + \cos^2(x) = 1$\\
If n AND m are both even, use half-angle formulas/double-angle formulas\\
\begin{equation*}\int \tan^n(x)\sec^m(x)dx\end{equation*}\\
n even, split off $\sec^2(x)$ and let $u = \tan(x)$, m is odd split off $\sec(x)\tan(x)$ and let $u=\sec(x)$\\

\begin{equation*}
\int dx = x + C
\end{equation*}

\begin{equation*}
\int x^n dx = \frac{1}{n+1}x^{n+1},\hspace{1ex}n\neq -1
\end{equation*}

\subsection{Integrals with Logarithms}
\subsection{Integrals with Exponentials}
\subsection*{Integrals with Roots/Division}
\subsection{Integrals with Trigonometric Functions}
\subsection*{Integrals of Hyperbolic Functions}
\section{Trig Identities}

$\tan(x) = \sin(x)/\cos(x)$
, $\cot(x) = \cos(x)/\sin(x)$
, $\sin^2(x)+\cos^2(x) = 1$
, $\tan^2(x)+1=\sec^2(x)$\\

, $\sec^2 x = \frac{1}{ \cos^2 x} = \tan x + 1$
, $\csc^2 x = \frac{1}{ \sin^2 x} = 1 + \cot^2(x)$\\

\begin{tabular*}{\linewidth}[b]{*{6}{|c @{\extracolsep\fill}}|}
\hline &0$^\circ$& $\frac{30^\circ}{ \pi/6}$ & $\frac{45^\circ}{ \pi/4}$ & $\frac{60^\circ}{ \pi/3}$ & $\frac{ 90^\circ}{ \pi/2}$
\\
\hline $\sin \theta$ & 0 & $\dfrac{1}{2}$ &$\dfrac{1}{\sqrt{2}}$ & $\dfrac{\sqrt{3}}{2}$& 1\\[15pt]
\hline $\cos \theta$ & 1 & $\dfrac{\sqrt{3}}{2}$ &$\dfrac{1}{\sqrt{2}}$ & $\dfrac{1}{2}$& 0\\ 
\hline $\tan \theta$ & 0 & $\dfrac{{1}}{\sqrt{3}}$ &1  & $\sqrt{3}$ & ND\\ 
\hline $\csc\theta$ & ND & 2 &$\sqrt{2}$  & $\dfrac{{2}}{\sqrt{3}}$ & 1 
\\ \hline
 sec $\theta$ & 1 & $\dfrac{{2}}{\sqrt{3}}$ &$\sqrt{2}$  & 2 & ND 
\\ \hline
cot $\theta$ & ND & $\sqrt{3}$ &1 & $\dfrac{{1}}{\sqrt{3}}$ & 0 \\ \hline
\end{tabular*}

\section{Formulas}
\section{Series}
\subsection{aSubsection}
\subsection{Telescoping Series}
% $\sum a_n$ which can be written as $\sum( b_n - b_{n+c})$\\
% Use partial fraction decomp\\
% ex: $\sum_{n=1}^{\infty} \frac{1}{n(n+1)} = \sum_{n=1}^{\infty} \frac{1}{n} - \frac{1}{n+1}$\\
% $\lim_{k \to \infty} \sum_{n=1}^{k}(\frac{1}{n} - \frac{1}{n+1}) = \lim_{k \to \infty} 1 - \frac{1}{k+1} = 1 - 0 = 1$, therefore converges\\
\end{multicols}
%\begin{multicols}{2}
%\includegraphics[width=0.6\textwidth,left]{scan0001.pdf}
%\includegraphics[width=0.4\textwidth,right]{table105.png}
%\end{multicols}

%------------------------------------------------------------------------
% You can even have references
%\rule{0.3\linewidth}{0.25pt}
%\scriptsize
%\bibliographystyle{abstract}
%\bibliography{refFile}
%\end{multicols}
\end{document}