Gauss-Jordan Assistant (gja)

Enabling live demonstration of the Gauss-Jordan algorithm in a terminal/console.

Installation

pip install gja

Description

The idea of this project is to enable live demonstration of using the Gauss-Jordan algorithm to solve systems of linear equations, using a simple console. This project is developed on Windows but should work using other operating systems.

Why?

I teach an introductory course in Linear Algebra by videoconference to students who are not math majors; the focus is on calculations, not proofs. As I teach remotely, I share the content of my screen. Many of the examples require, at one stage or another, that Gaussian elimination on a matrix be performed.

In my experience, using slides with all the content written up in advance (which is what I have mostly done until recently) is not a good way to maintain student engagement. My hand writing (either using a mouse or a tablet) on a computer screen is absolutely atrocious, which makes it difficult to do "live" examples.

I have also found that a small fraction of students do not seem to understand the basic step of Gaussian elimination, even when I attempt to provide additional explanations via email.

This tool, which I named the Gauss-Jordan Assistant (or GJA), allows me to do live computations on my screen in a legible way. I have tried to design it so that each computation includes some visual clues reinforcing some aspects of Gaussian elimination.

Using the GJA, I can ask students to suggest what should be the next step in the computation, just as easily as I could do it in a traditional classroom with a blackboard. If they suggest something that is incorrect, rather than telling them up front, I can type in their suggestion, observe the result, and follow with relevant explanations go wrong.

Bonus

It is possible to save the result of all the steps using LaTeX format, for easy inclusion (without typos!) in any LaTeX document.

Requirements

• Python 3.8+
• Rich (https://pypi.org/project/rich/). Rich is a fantastic project.

To work properly on Windows (which is what I use), you need the following:

• Windows Terminal (https://github.com/Microsoft/Terminal), which you can get from the Microsoft Store.