https://github.com/mitmath/julia-mit
Tutorials and information on the Julia language for MIT numerical-computation courses.
https://github.com/mitmath/julia-mit
Last synced: 11 months ago
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Tutorials and information on the Julia language for MIT numerical-computation courses.
- Host: GitHub
- URL: https://github.com/mitmath/julia-mit
- Owner: mitmath
- Created: 2013-09-05T18:29:35.000Z (over 12 years ago)
- Default Branch: master
- Last Pushed: 2025-02-05T00:21:08.000Z (about 1 year ago)
- Last Synced: 2025-04-07T17:03:47.802Z (12 months ago)
- Language: Jupyter Notebook
- Size: 22.8 MB
- Stars: 758
- Watchers: 51
- Forks: 107
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
Julia for Numerical Computation in MIT Courses
==============================================
Several MIT courses involving numerical computation, including
[18.06](https://github.com/mitmath/1806) / [18.C06](http://people.csail.mit.edu/moitra/096.html), [18.065/18.0651](https://github.com/mitmath/18065),
[18.303](https://github.com/mitmath/18303),
[18.330](https://github.com/mitmath/18330),
[18.335/6.7310](https://github.com/mitmath/18335),
[18.337/6.7320](https://github.com/mitmath/18337),
and
[18.338](https://github.com/mitmath/18338),
are
beginning to use [Julia](http://julialang.org/), a fairly new language
for technical computing. This page is intended to supplement the
[Julia documentation](http://docs.julialang.org/en/latest/) with some
simple tutorials on installing and using Julia targeted at MIT
students. See also our [Julia
cheatsheet](Julia-cheatsheet.pdf) listing
a few basic commands, and [various Julia tutorials online](https://julialang.org/learning/).
In particular, we will be using Julia in the [Jupyter](https://jupyter.org/) browser-based
enviroment (via the [IJulia](https://github.com/JuliaLang/IJulia.jl)
plug-in), which leverages your web browser and
to provide a rich environment
combining code, graphics, formatted text, and even equations, with
sophisticated plots via [Matplotlib](http://matplotlib.org/).
You can also look at the Jupyter notebook from the [fall 2020 tutorial](Tutorial.ipynb), as well as the [tutorial video (MIT only)](https://mit.zoom.us/rec/share/FcA8_JB8vZ-3FmX6_x2qaeRMk0aCOkFl9cMrba1rhQYDDv8TNeatMqTh7eXabBHq.7AQu81CA0eiu2z7g?startTime=1599594382000).
## Why Julia?
Julia is relatively new
high-level free/open-source language for numerical computing in the
same spirit, with a rich set of built-in types and libraries for
working with linear algebra and other types of computations, with a
syntax that is superficially reminiscent of Matlab's.
Basically, we are using Julia because, unlike Matlab or Python or R, it
**scales better to real computational problems** — you can write performance-critical
"inner loops" in Julia, whereas similar tasks in other high-level languages
often require one to drop down to C or similar low-level languages. (See e.g. [this 6.172 lecture](https://bit.ly/2QUrgB4) on performance in Julia vs. Python.) Because of
this, we are using Julia more and more in our own research, and we want to **teach
using software tools that we really employ ourselves**.
## Running Julia in the cloud
The easiest way to get started with Julia is to run it in the cloud on [`mybinder.org`](https://mybinder.org/), which is as easy as clicking this link:
[](https://mybinder.org/v2/gh/mitmath/binder-env/main?urlpath=git-pull%3Frepo%3Dhttps%253A%252F%252Fgithub.com%252Fmitmath%252Fjulia-mit%26urlpath%3Dtree%252Fjulia-mit%252F%26branch%3Dmaster)
That link opens up a [default MIT-math Julia + Python environment](https://github.com/mitmath/binder-env) that we set up, but you can also [easily set up your own environments](https://mybinder.readthedocs.io/en/latest/index.html). Although the link above gives you access to [our tutorial notebook here](https://nbviewer.jupyter.org/github/mitmath/julia-mit/blob/master/Tutorial.ipynb), you can create alternate links (e.g. for particular MIT courses) using [nbgitpuller](https://jupyterhub.github.io/nbgitpuller/link).
There are two major drawbacks to using the free `mybinder.org` service:
* It's often slow (sometimes an order of magnitude slower than a typical laptop), especially to start up, although it's probably fast enough for simple problems in coursework.
* It has a very short timeout: if you go for a coffee break, your session will probably have stopped running by the time you get back. Fortunately, [there are save/download buttons](https://discourse.jupyter.org/t/getting-your-notebook-after-your-binder-has-stopped/3268) that still work in a timed-out session, so you can save your work and restore it after restarting the binder session.
* There are at most 100 simultaneous users for a given configuration repository. (Therefore, if your instructor wants to use mybinder for a course, encourage them to set up their own docker configuration, perhaps by forking [our repo](https://github.com/mitmath/binder-env).)
Eventually you'll probably want to install Julia on your own computer to eliminate these frustrations. Fortunately, this is usually relatively easy:
## Installing Julia and IJulia on your own computer
First, [download the latest release of Julia](https://julialang.org/downloads/) and run the installer.
Then run the Julia application (double-click on
it, or run `julia` in a terminal); a window with a `julia>` prompt will appear. At the `julia>` prompt,
type a `]` (close square bracket) to get a [Julia package prompt `pkg>`](https://docs.julialang.org/en/v1/stdlib/Pkg/),
where you can type
```jl
(v1.11) pkg> add IJulia
```
You may also want to install these packages, which we tend to
use in a lot of the lecture materials:
```jl
(v1.11) pkg> add Interact PyPlot Plots
```
(You can install other packages later as you need them using the same interface, of course. Thousands of other packages can be found on [JuliaHub](https://juliahub.com/).)
#### Running Julia through the JupyterLab app
Download the [jupyterlab-desktop](https://github.com/jupyterlab/jupyterlab-desktop) program, and launch it. Click the "Julia"
button (or choose "New > Notebook" from the file menu and select the "Julia" kernel):
You should now have an interactive Julia notebook, whose usage
we describe below.
If you have **problems printing** or **exporting PDF** from the JupyterLab Desktop (on some systems this fails if you don't have LaTeX installed), a workaround is to *export as HTML* (from *File > Save and Export Notebook As… > HTML*), open the resulting `.html` in your browser (double-click on it) and print to PDF from your browser.
#### Running Julia through Jupyter in your browser
You can alternatively use Julia itself to install the Jupyter software
and have it run its interface through your web browser.
Switch back to the `julia>` prompt by hitting backspace or ctrl-C, and then
you can launch the notebook by running
```jl
julia> using IJulia
julia> notebook()
```
and type "y" if you are asked to install Jupyter. A "dashboard" window like this should open in your web browser (at address `localhost:8888`, which you can return to at any time as long as the `notebook()` server is running; I usually keep it running all the time):
Now, click on the *New* button and select the *Julia* option to start a new "notebook".
(You will have to leave this Julia command-line window open in order
to keep the Jupyter process running. Alternatively, you can run `notebook(detached=true)` if you want to run the Jupyter server as a background process, at which point you can close the Julia command line, but then if you
ever want to restart the Jupyter server you will need to kill it manually.
### Troubleshooting:
* If you ran into a problem with the above steps, after fixing the problem you can type `build` at the `pkg>` prompt to try to rerun the install scripts.
* If you tried it a while ago, try running `update` at the `pkg>` prompt and try again:
this will fetch the latest versions of the Julia packages in case
the problem you saw was fixed. Run `build IJulia` at the `pkg>` prompt if your Julia version may have changed. If this doesn't work, try just deleting the whole `.julia` directory in your home directory (on Windows, it is called `AppData\Roaming\julia\packages` in your home directory) and re-adding the packages.
* On MacOS, you need MacOS 10.8 or later.
* If the notebook opens up, but doesn't respond (the input label is `In[*]` indefinitely), try creating a new Python notebook (not Julia) from the `New` button in the Jupyter dashboard, to see if `1+1` works in Python. If it is the same problem, then probably you have a [firewall running](https://github.com/ipython/ipython/issues/2499) on your machine (this is common on Windows) and you need to disable the firewall or at least to allow the IP address 127.0.0.1. (For the [Sophos](https://en.wikipedia.org/wiki/Sophos) endpoint security software, go to "Configure Anti-Virus and HIPS", select "Authorization" and then "Websites", and add 127.0.0.1 to "Authorized websites"; finally, restart your computer.)
## Other Julia environments
### Pluto.jl
A different interactive-computing environment for Julia is [Pluto.jl](https://github.com/fonsp/Pluto.jl), which runs in the browser like Jupyter but is **more oriented towards "live" interaction** where updating one piece of code *automatically re-runs anything affected* by that change. Running Julia is as easy as:
```jl
pkg> add Pluto
julia> using Pluto
julia> Pluto.run()
```
### VSCode
For writing larger programs, modules, and packages (as opposed to little interactive snippets), you'll want to start putting code into files and modules, and use a more full-featured code-editing environment. A popular choice is the free/cross-platform [Visual Studio Code (VSCode)](https://code.visualstudio.com/) editor, which has a [Julia VSCode plugin](https://www.julia-vscode.org/) to provide a full-featured integrated development environment (IDE).
### Other Editors
Of course, there is also good support for editing Julia in many other programs, such as [Emacs](https://github.com/JuliaEditorSupport/julia-emacs), [Vim](https://github.com/JuliaEditorSupport/julia-vim), [Atom](https://github.com/JuliaEditorSupport/atom-language-julia), and [so forth](https://github.com/JuliaEditorSupport).
## Updating Julia and IJulia
Julia is improving rapidly, so it won't be long before you want to
update to a more recent version. The same is true of Julia add-on
packages like PyPlot. To update the packages only, keeping Julia itself
the same, just run:
```jl
(v1.11) pkg> update
```
at the Julia `pkg>` prompt after typing `]`; you can also run `] update` in IJulia.
If you download and install a new version of Julia from the Julia web
site, you will also probably want to update the packages with
`update` (in case newer versions of the packages are required
for the most recent Julia). In any case, if you install a new Julia
binary (or do anything that changes the location of Julia on your
computer), you *must* update the IJulia installation (to tell IPython
where to find the new Julia) by running `build` at the
Julia `pkg>` prompt line (not in IJulia).
## Running Julia in the Jupyter Notebook
Once you have followed the installation steps above, then you
will want to open the Jupyter notebook interface.
As explained above, you can either launch the standalone
JupyterLab Desktop app (which you download and install separately),
or you can install Jupyter via Julia and run it via your web browser.
Either way, a notebook will combine code, computed results, formatted text, and
images; for example, you might use one notebook for each problem set.
The notebook window that opens will look something like:
In the browser can click the "Untitled" at the top to change the name, e.g. to
"My first Julia notebook"; in JupyterLab you click the "Rename" option in the "File" menu. You can enter Julia code at the `In[ ]`
prompt, and hit **shift-return** to execute it and see the results.
If you hit **return** *without* the shift key, it will add additional
lines to a single input cell. For example, we can [define a variable](http://docs.julialang.org/en/latest/manual/variables/)
`x` (using the built-in constant `pi` and the built-in function
`sin`), and then evaluate a polynomial `3x^2 + 2x - 5` in terms of `x`
(note that, unlike Matlab or Python, we don't have to type `3*x^2` if
we don't want to: a number followed by a variable is automatically
interpreted as multiplication without having to type `*`):
The result that is printed (in `Out[1]`) is the *last* expression from
the input cell, i.e. the polynomial. If you want to see the value of
`x`, for example, you could simply type `x` at the second `In[ ]` prompt
and hit shift-return.
See, for example, the [mathematical operations in the Julia
manual](http://docs.julialang.org/en/latest/manual/mathematical-operations/)
for many more basic math functions.
## Plotting
There are several plotting packages available for Julia. If you
followed the installation instructions, above, you already have one
full-featured Matlab-like plotting package installed:
[PyPlot](https://github.com/stevengj/PyPlot.jl), which is simply a
wrapper around Python's amazing [Matplotlib](http://matplotlib.org/) library.
To start using PyPlot to make plots in Julia, first type `using
PyPlot` at an input prompt and hit shift-enter. `using` is the Julia
command to load an [external
module](http://docs.julialang.org/en/latest/manual/modules/) (which
must usually [be
installed](http://docs.julialang.org/en/latest/manual/packages/)
first, e.g. by the `] add PyPlot` command from the installation
instructions above). The *very first* time you do `using PyPlot`, it will
take some time: the module and its dependencies will be
"precompiled" so that in subsequent Julia sessions it will load quickly.
Then, you can type any of the [commands from
Matplotlib](http://matplotlib.org/api/pyplot_api.html), which includes
equivalents for most of the Matlab plotting functions. For example:
## Printing/exporting Notebooks
Currently, printing a notebook from the browser's *Print* command can be somewhat problematic. There are four solutions:
* At the top of the notebook, click on the *File* menu (in the
notebook, *not* the browser's global menu bar), and choose **Print
Preview**. This should open up a window/tab that you can print
normally.
* For turning in homework, a class may allow you to submit the notebook file
(`.ipynb` file) electronically (the graders will handle printing). You can save a notebook file in a different location by choosing **Download as** from the notebook's *File* menu.
* The highest-quality printed output is produced by IPython's
[nbconvert](http://ipython.org/ipython-doc/rel-1.0.0/interactive/nbconvert.html)
utility. For example, if you have a file `mynotebook.ipynb`, you
can run `ipython nbconvert mynotebook.ipynb` to convert it to an
HTML file that you can open and print in your web browser. This
requires you to install [IPython](http://ipython.org/install.html),
[Sphinx](http://sphinx-doc.org/latest/install.html) (which is
automatically installed with the Anaconda Python/IPython distribution), and
[Pandoc](http://johnmacfarlane.net/pandoc/installing.html) on your
computer.
* If you post your notebook in a Dropbox account or in some other
web-accessible location, you can paste the URL into the online [nbviewer](http://nbviewer.ipython.org/) to get a printable version.