Introduction to algebra with Sympy

In class today I gave an introduction to using Sympy to study algebra.

You can see a recording of the class here

In class I used Sympy to solve the following problem:

1. Rationalise the following expression: \(\frac{1}{\sqrt{3} + 1}\).

2. Consider the quadratic \(f(x) = -x ^ 2 + 8 x - 18\).

   1. Calculate the discriminant of the quadratic equation $f(x)=0$. What does this tell us about the graph of \(f(x)\).
   2. By completing the square, confirm that \((4, -2)\) is the maximum point of \(f(x)\).

This is similar to the tutorial in the python for mathematics chapter which is what your lab tutor will be taking you through in labs.

Here is the notebook I used in class: algebra.ipynb

Following along in class

A few students asked how to follow along in class when they are typing commands in to their computer at the same time (especially when a command doesn’t quite work: for example a student wrote sympy.symbol instead of sympy.Symbol which is easily done).

My advice is essentially to follow along in the same way you would any other mathematics class. Perhaps in a calculus lecture you attempt to carry out the same calculations at the same time but at some point you do not fully follow. In this case I’d suggest making a note to ask what went wrong there and continue to follow along as best is possible (even if it means no longer carrying out the calculations). The only difference in this example and with computing is that perhaps at some stage you do not get the expected output. If you can type the next command and carry on but if that’s not possible follow as best you can and make a note to come back to it and work through it.

BUT Just like many of you did yesterday: please do ask me questions as we go. If a quick scroll back to a specific point in the code fixes the problem then I will super happily do that, if it’s a more involved problem that might need me to take a look at it we will find some time to do that.