Remember the third assignment on representation:
- due 2024-02-16 [problem set 03] [pdf] [solutions] [solutions pdf]
I was originally planning to give a lecture on usage of the
computer-algebra package/language GAP to solve group-theoretic
problems, but I second-guessed this decision because I anyhow plan to
use sage-math in the discussion of error-correcting codes, and it
seems redundant to introduce both. But: if you are interested, here
are some notes that I made for a lecture a couple of years ago about
GAP usage (the notes in particular contain links for installation etc…).
I finished up the discussion of representation theory on Monday; see below for the notes. In this lecture, I completed the remaining “unfinished business” by giving the proof that the number if irreducible (complex) representations of a finite group \(G\) is equal to the number of conjugacy classes in \(G\). I also tried to give some discussion of “applications of group representations to related parts of mathematics” – the notes probably don’t give all details of that discussion (ask if you want a reference!).
On Wednesday, I begin talking about error-correcting codes. Remember that I listed a few references to consult.
I plan to sometimes use the computer-algebra system sage-math to
accompany the lectures/presentation.
Example of ternary code, in
sage-math[viacocalc] [download notebook]