LaTeX

$\text{LATEX}$ is the definitive typesetting system for any sort of mathematics or physics rendering.

Syntax

For a matrix:

\begin{bmatrix}
1 & 2 & 3 \\
a & b & c
\end{bmatrix}

For a determinant:

\begin{vmatrix}
1 & 2 & 3 \\
a & b & c
\end{vmatrix}

For a piecewise function:

\delta_a(t-t_0) = \begin{cases}
	0 & 0\le t < t_0 - a \\
	\frac 1{2a} & t_0 - a \le t < t_0 + a \\ 
	0 & t \ge t_0+a
\end{cases}

Development environment

An opinionated set-up:

• IDE — Visual Studio Code with LaTeX Workshop
• Distribution — MiKTeX

Overleaf is another good choice. It has some decent features, like a well-thought out interface that doesn’t need too much messing around with. This is probably where you’d want to start with a fully fleshed out environment. Notably many collaboration and version control tools are paywalled.