Prerequisites and Resources

Prerequisites and Resources#

There are no formal prerequisites for the course, but I will expect you to be comfortable with the material discussed here, which contains links to additional resources should you need to refresh your knowledge. Please work with your classmates to try to share knowledge as needed. Generally, I will expect familiarity with the following:

Domain Specific Preparation:

The most important prerequisite is the ability to communicate about and formulate complex problems in your field of study that would benefit from the techniques covered in this course. Students will expected to actively engage with the techniques taught in this course, apply them to relevant problems in their domain of expertise, and to communicate about the efficacy to the class.

Linear Algebra

Properties of Linear Operators (Self-Adjoint, Hermitian, Unitary, etc.), Matrix Factorization including the Singular Value Decomposition, Bases and Orthogonalization via Gram-Schmidt.

Real and Complex Analysis

Topology (notions of continuity), Calculus, Banach spaces (e.g. conditions for the existence of extrema), Fourier Analysis, Contour Integration, Conformal Maps.

Differential Equations

Formulation of differential equations, existence of solutions and boundary value requirements, Sturm-Liouville Theory.

Programming Skills

There are some specific skills you will need for this course, including basic programming skills, distributed version control, how to connect remotely to computers etc. with SSH. We will use the CoCalc platform so you do not need to install any of the software on your computer.

Version Control#

You should know how to use a distributed version control system such as Git or Mercurial. This project assumes you can use Git, but I actually prefer Mercurial which I find has a much more intuitive interface. Git is much more popular due to GitHub and GitLab (but keep an eye on Heptapod – a fork of GitLab for Mercurial), and you are likely to find more resources about Git online. Also, Heptapod is not yet ready for prime time, so GitLab or GitHub are to be preferred.

Note

If you install the hg-git plugin, then you can use Mercurial to work with Git repos. This is what I generally do, but it adds some potential complications, so I do not recommend it unless you are comfortable with Mercurial:

hg clone https://gitlab.com/wsu-courses/physics-581-physics-inspired-computation.git

To enable Mercurial with a useful set of tools, you can do the following:

python3 -m pip install --upgrade --user pip mercurial hg-evolve hg-git jupytext black

This allows you to use the Heptapod workflow

If you are not familiar with a distributed version control system like Mercurial or Git, the Software Carpentry program has two relevant courses you should work through completely:

Python, SciPy, NumPy, etc.#

While not absolutely required, a good working knowledge of [Python] is needed. You will also need to develop an understanding of the SciPy ecosystem, especially NumPy, Matplotlib, and the SciPy library itself. The following are a good place to start learning about these:

CoCalc#

You should be familiar with CoCalc; specifically:

  • Creating an account.

  • Creating projects.

  • Using Jupyter Notebooks.

  • Adding SSH keys to your project so you can use SSH to connect.

References#

SSH#

You should know how to use SSH to connect to remote servers (in particular CoCalc) with password-less login using ssh-keygen to generate a key, ssh-agent to add this key, and the forwarding this key so you can use this to authenticate to GitLab etc.

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