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The class number formula (
3 points by oxide to math 33 days ago | 5 comments

Neat stuff ... it would be interesting to see a minimal "Tree of Concepts" to get one from school arithmetic to an understanding of this.


2 points by oxide 31 days ago

it would be! meanwhile, here's a bare sketch of the prerequisites needed to understand the theorem statement (the proof needs some more):

1. elementary algebra (functions, graphs, etc)

2.1. single variable calculus (limits, derivatives, integrals, series)

2.2. elementary number theory (modular arithmetic, euler's and fermat's theorem, etc)

3. abstract algebra (groups, rings, fields, and homomorphisms between them), abstract alg. also clarifies a bunch of elementary number theory.

4. the very basics of algebraic number theory (ideal class group, discriminant of number fields)

it may seem like a lot (especially to a school child who just learned arithmetic!) and in some sense it certainly is, but many of these concepts reinforce and build upon each other, so when you've understood them, it doesn't seem like much at all.


2 points by oxide 31 days ago

ah, i just checked out your profile and realised you have a PhD in apologies for misinterpreting your original comment :p


2 points by shawn 30 days ago

I couldn't help but notice that you've created a fork of Gwern's website. That's so cool! It seems to be an independent implementation too.

I wanted to invite you to come say hello in #lesswrong on freenode sometime, or to DM me on twitter:

What caught my attention about your site is that I know from experience how hard it is to create a fork of I noticed lots of little details in yours, like the fact that the anonymous feedback form is different, and that you exported your logo with potrace. (Killer logo by the way!) All of that took a lot of thought and effort, and it was a delightful surprise to see that someone else did it independently. It'd be neat to compare notes with you!

Thanks a lot for the thoughtful content, and the tree of concepts. I don't have nearly as much training in math, so it was quite helpful. :)


Not a problem ... I'm involved with outreach, enrichment, and enhancement, so creating a DiGraph or concepts, although impossible, would be an excellent goal. I know groups that are making progress towards it for the UK school curriculum, but it's hard, and I'm not entirely sure that what they're doing will turn out to be useful in the way(s) I'd hope.


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