Introduction to university mathematics: Coding Theory

Last year I visited a selection of schools in Cheshire in the lead up to my PGCE course so as to gain some experience in schools following the completion of my degree. One of the schools I visited was where I had been taught and the department were incredibly supportive in me venturing into the teaching profession. They offered me the opportunity to teach a lesson to the A Level Further Maths class and said I could do anything I wanted. As I have mentioned I had just completed my degree (in mathematics), and it struck me as an ideal opportunity to try and present them with some university level mathematics.

Within the time frames I had to both plan and deliver the lesson I needed to ensure the content I presented was accessible to the students. I chose to arrange a lesson based on one of my third year pure mathematics courses, coding theory, which required some prerequisite knowledge of very basic set theory notation and also modular arithmetic before introducing the core material. One of the most interesting aspects (for me) are the questions based on the ISBN-10 code which was used for book identification until the introduction of the ISBN-13 code.

The content which I delivered to the class was well received both by students and their teacher and I have recently reformatted the content into a PowerPoint presentation with an accompanying student worksheet and ‘Take it home…’ sheet. Due to time being tight at A Level anyway, this type of lesson would be most effectively used in some sort of after school session or as a one-off lesson when year 12 students return from exams in June (or when ahead of schedule). The links to these documents follow:

Coding Theory lesson – PowerPoint (notes for each slide are included)

Coding Theory lesson – Student Worksheet

Coding Theory lesson – Student Take it home… sheet

Please feel free to provide me with any feedback regarding the materials and I shall update them accordingly if there are any problems – I hope that they can be of use!

In time I hope to make further use of the notes and materials I have from my mathematics degree in order to create more ‘one-off’ lessons like this which provide accessible university material to (sixth form) students. I hope that they might spark interest in pupils to take mathematics to higher levels, or at the very least provide an enjoyable ‘alternative’ lesson.

Credit: Y. Bazlov, lecturer of MATH32031 Coding Theory at The University of Manchester 2013-2014.