Related Posts

Share This

How not to get a good mathematics degree

Definition of Abelian

Definition of Abelian

I’ve been marking homework for Group Theory. (Another exciting Sunday afternoon for me, eh?) I was reminded of a question last year from a student. I was discussing mathematics with some students and one asked me about showing a group is abelian. Their homework question asked them to state whether a particular group was abelian or not. The student liked this question because, she said, it didn’t ask her to justify her answer. She had a 50/50 chance of getting it right and that was good — she knew that she would be unable to supply any reason if asked and so would stand no chance of getting marks

At first, I mistakenly thought she we wanted me to explain how to show a group is abelian. I was wrong. What she wanted was a shortcut, some rule of thumb say, that allowed her to tip the chances in her favour, maybe 60/40 or 70/30.

Now, I’m not sure if there is a decent rule of thumb (if you see Sn or Dn it’s not abelian maybe) but this is definitely the wrong way to go about getting a good degree. Trying to memorize all the short cuts without understanding is not a good recipe for success at university-level mathematics — even if that strategy worked reasonably well for A-Level!

The message for any student reading this is simple. If you have a weakness in your understanding — the student above certainly knew she did — then aim to remove it not by using some shortcut but by understanding the problem. Shortcuts will help only in the short run. In the long run they will do more damage than good.

Get the newsletter!

Fancy a newsletter keeping you up-to-date with maths news, articles, videos and events you might otherwise miss? Then sign up below. (No spam and I will never share your details with anyone else.)