James Williams


I am currently studying for a PhD in Mathematics (Group Theory).




This semester I am a teaching assistant for Algebra 1B.

Below you will find rough explanations and answers to emails I have received. Usually if I think an email will be of interest to other students, I will upload the explanation here.

Algebra 1B *NEW*

For the first time, I am uploading some of my personal notes and lesson plans for tutorials that I am unable to deliver. Please remember that these notes are based on an older version of the course and so some material and question numbering may be different.

Tutorial 3 (23 Feb 2018)

Tutorial 4 (02 March 2018)

Tutorial 6 (16 March 2018)

Tutorial 9

Algebra 1A

How to show something is an equivalence relation

Sheet 6 Hints/Similar Examples

Some advice based on my experience of studying university Mathematics

How to write a proof that the composition of injective functions is injective, for people not used to proof writing.

Examples of equivalence relations and partitions and transversals

Examples of the equivalence relation ~n and remainders of division by n.

An explanation of some questions on sheet 3 and on equivalence relations.

Equivalence Classes and Multiplicative Inverses

A quick and dirty guide to Group Actions, Orbits and Stabilisers