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August 15, 2024

Galois Theory

Posted by Tom Leinster

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I've just arXived my notes for Edinburgh's undergraduate Galois
theory course, which I taught from 2021 to 2023.

I first shared the notes on my website some time ago. But it took me
a while to arXiv them, because I wanted to simultaneously make public
most of the other course materials. I now have, which means the
following are now available to all:

  * Notes forming a complete, self-contained account of the part of
    Galois theory that we covered.

  * About 40 short explanatory videos.

  * A large collection of problems.

  * Nearly 500 multiple choice questions.

MathML-enabled post (click for more details).

I'm a little bemused by the popularity of the Galois theory notes.
I've made quite a few sets of course notes public before, e.g.:

  * Fourier analysis
  * General topology
  * Linear algebra
  * Category theory

But the Galois theory notes seem to have caught on in a way that none
of the others have (except category theory -- but that one, I made
into a book).

It's true that I probably took a bit of extra care on them: I first
taught the course during full Covid lockdown, and I felt the students
would need more guidance than usual, given that they were deprived of
all opportunities for face-to-face interaction. But I wonder whether
the real reason is that the Galois theory notes simply look nicer,
with colour and little icons and so on.

In any case, I hope the notes, videos and questions bring people joy.

Posted at August 15, 2024 1:02 PM UTC

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5 Comments & 0 Trackbacks

Re: Galois Theory

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thank you for sharing these publicly!

Posted by: gnv on August 15, 2024 3:47 PM | Permalink | Reply to this

Re: Galois Theory

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From my biased perspective, the popularity is because Galois theory
is simply prettier than almost all the rest of undergraduate math
(with stiff competition from complex analysis and rep theory of
finite groups).

Posted by: Asvin on August 15, 2024 5:07 PM | Permalink | Reply to
this

Re: Galois Theory

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You're absolutely right; I shouldn't have overlooked that factor!
Galois theory is such an amazing story.

Posted by: Tom Leinster on August 15, 2024 5:34 PM | Permalink |
Reply to this

Re: Galois Theory

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The hackers are interested..

Posted by: Simon Burton on August 15, 2024 6:38 PM | Permalink |
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Re: Galois Theory

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the popularity has to do with the cachet the name brings. If it was
called Smith Theory or even Leinster Theory, nobody would care. But
Galois Theory - please tell me more!

Posted by: ag on August 15, 2024 11:32 PM | Permalink | Reply to this

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