Markdown in Visual Studio Code

In this course we will mostly work with Jupyter notebooks in the VS Code editor. These notebooks are a mixture of text and code, and the text is written in a simple markup language called Markdown. For us, the main point will be that you can include LaTeX code for mathematics. Many example notebooks will be distributed throughout the course, and you can look at those to see how things are done, or you can find one of the many detailed guides to Markdown on the internet. Some basic points are as follows:

If you hover with your mouse between two cells of the notebook, or before the first cell or after the last cell, you should see two buttons appear, marked Code and Markdown. You can click on one of these to add a new cell to the notebook.
Each cell has a label at the bottom right saying whether it is a Python code cell or a Markdown cell. You can change the type of a cell by clicking on this label.
Markdown cells are often displayed in closed mode, where you see nicely formatted mathematics instead of LaTeX code, but you cannot edit anything. You can toggle between these modes by clicking on the cell and then pressing Enter or Esc.
Inline mathematics is enclosed in single dollar signs, like $ E=m c^2 $ . For displayed equations shown on a separate line, you can use
$$ \int_{-\infty}^{\infty} e^{-x^2} = \sqrt{\pi}. $$.
It does not work to use square brackets like \[a^2 + b^2 = c^2\]. However, you can (and should) use an align* environment for groups of equations, like this:
```
     \begin{align*}
      a &= 12345 \\
      b &= 67890 \\
      c &= a + b
     \end{align*}
    
```
You should use \tag{} to label equations that you want to refer to later, like this:
```
     $$ \frac{1}{\pi} = \frac{2 \sqrt 2}{99^2} \sum_{k=0}^\infty
      \frac{(4k)!}{k!^4} \frac{26390k+1103}{396^{4k}} \tag{A} $$
    
```
Then you can write "Equation (A) was proved by Ramanujan" in the text.
If you have a large expression and you need large brackets to enclose it, you should use \left( and \right), for example $ \left( \frac{a}{b} \right)\left(\sum_i c_i\right) $ .
Use a # symbol followed by a space to indicate a major heading, like
# My New Theory of Everything.
Use two or more # symbols for more minor headings.
Use a single - symbol followed by a space to indicate a bullet point. You can use 1. followed by a space to indicate a numbered list.
Use ** to indicate bold text, like **important**. Use * to indicate italic text, like *urgent*.
To embed links in markdown, use the following pattern, with the link text in square brackets and the URL in round brackets:
Python was developed by [Guido van Rossum](https://en.wikipedia.org/wiki/Guido_van_Rossum).
The best way to embed an image is as follows. Select the image in your file manager, copy it with CTRL-C, then paste it into a markdown cell with CTRL-V. When the markdown cell is open for editing, you will see text like this: ![cat.png](attachment:cat.png). When the cell is closed, you will see the image instead of the text. When the image is inserted this way, the image data is stored in the notebook file, so you can move the notebook to another computer and the image will still be there.
For more complicated things, you can include HTML code in Markdown and it will usually work.