week05--rep-theory-conclusion-ec-start.md

---

title: |
 Week05 -- conclusion of rep theory;
 begin error-correcting codes
author: George McNinch  
date: 2024-02-12

---

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...).

• [GAP notes]

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!).

• [The number of irreducible representations - 2024-02-12] [pdf]

On Wednesday, I begin talking about error-correcting codes. Remember that I listed a few references to consult.

• [Overview on linear codes - 2024-02-14] [pdf]

I plan to sometimes use the computer-algebra system sage-math to accompany the lectures/presentation.

• [suggestions for using / installing sage-math]

• Example of ternary code, in sage-math [via cocalc] [download notebook]