Initial push of previous course

example-document/doc/math.tex

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+\section{Math}
+
+\subsection{Equation}
+
+This is an equation
+
+\begin{equation}
+    % A lonesome ( will have a fixed size
+    % But a \left( will be scaled to contain whatever it has to
+    \langle f, g \rangle_{\left[a, b\right]} 
+    =
+    \int_a^b f(x)\overline{g(x)} dx
+    % \\  % The equation env ignores \\
+    % a^2 + b^2 = c^2
+    \label{eq:inner_product}  % You may label equations for referencing later
+\end{equation}
+
+\subsection{Gather}
+
+This is the gather environment
+
+\begin{gather*}
+    E = mc^2
+    \\
+    E^2 = 
+        \frac{                          % You
+            mc^2                        % May
+        }                               % Use
+        {                               % As
+            \sqrt{                      % Many
+                1                       % Lines
+                -                       % As
+                \frac{                  % You
+                    v^2                 % Want
+                }
+                {                       % Sometimes
+                    c^2                 % It makes
+                }                       % Things more
+            }                           % Structured
+        }                               % ...though not always...
+\end{gather*}
+
+\subsection{Align}
+
+This is an \emph{anonymous} align environment
+
+\begin{align*}
+    24 &= 8 \cdot 3 \\  % Allows aligning glyphs by using &
+    &= 4 \cdot 6 \\  % The glyph marked with & on each line
+    &= 2 \cdot 2 \cdot 2 \cdot 3  % Will be aligned
+\end{align*}
+
+\subsection{Inlined math}
+
+% Math can be inlined with \( ..my math.. \) or $..also my math..$
+% $_$ is the old TeX way and is not advisable to use
+% \(_\) is the more modern LaTeX way and is more robust
+A \(\sum_n^k\) sum! And a $\frac{1}{n}$.
+
+% The \[\] is a \displaystyle math environment
+% There is no real reason to use it over the \begin syntax, but it's there. This env is displayed on its own line and is not a part of the paragraph in the same way $_$ and \(\) are.
+You can also: \[\alpha\] do this. 
+
+\subsection{Some symbols}
+
+Greek
+
+\begin{gather*}
+    \psi,\ \Psi  % The "\ " thing forces the insert of a space, otherwise whitespace is ignored
+    \\
+    \alpha, \beta, \gamma, \delta  % Lower case with _small_ letters
+    \\
+    \Gamma, \Delta  % Upper case with _Capital_ letter
+    \\
+    \epsilon, \varepsilon  % Variants with _var_
+\end{gather*}
+
+Other things
+
+% If you want a glyph, but don't know what it's called
+% Either try something (most glyphs have sensible names)
+% Or just search it up online, after a while you'll remember
+\begin{gather*}
+    \nabla, \partial
+    \\
+    \int, \iint, \oint
+    \\
+    \sum_{i = 1}^{n}, \prod_{1 \leq i \leq n}
+    \\
+    \frac{a + ib}{c + id}, i = 1, \dots, n
+    \\
+    \bar{x}, \vec{x}, x^\circ
+\end{gather*}
+
+Matrices (and vectors)
+
+\begin{gather*}
+    \begin{pmatrix}  % Parantheses
+        1 & 2 & 3 \\  % Columns separated with &
+        4 & 5 & 6 \\  % Rows separated with \\
+        7 & 8 & 9
+    \end{pmatrix}
+    ,
+    \begin{bmatrix}  % Brackets
+        1 & 2 & 3 \\
+        4 & 5 & 6 \\
+        7 & 8 & 9
+    \end{bmatrix}
+    ,
+    \begin{Bmatrix}  % _Curly_ brackets
+        1 & 2 &  \\  % You can leave elements empty
+        4 & \displaystyle\int_0^1x^2 dx & 6 \\  % You can make the elements complicated (and force roomy display with \displaystyle
+        7 & 8 & 9
+    \end{Bmatrix}
+    ,
+    \begin{pmatrix}  % Essentially a vector
+        x_1 \\ x_2 \\ x_3  % Just because \\ causes linebreak, doesn't mean you need a new line in the source
+    \end{pmatrix}
+\end{gather*}
+
+% Defining a new command, don't do it here, do it in the preamble or something similar
+% newcommand takes a command name, a number of arguments and the "function body" of the command. The arguments to the new command being defined can be accessed by #<number>
+\newcommand{\myvec}[1]{
+\begin{pmatrix}
+    #1
+\end{pmatrix}
+}
+
+% Works like a charm
+\begin{gather*}
+    \myvec{x_1\\x_2\\x_3} \leftarrow \text{My vector command}
+\end{gather*}