An Infinitely Large Napkin [pdf] (2019) • Hacker News Board

This is a fantastic resource, and I used it heavily in 2018 before starting my BSc in Math while still in school to learn the stuff that interested me a bit in advance (and to some extent as a familiar reference for a few years afterwards).

I can only recommend this as a good starting point for anyone without the time for a full scale education, or in preparation for such, especially if you have some experience with math olympiads (as mentioned also in the introduction).

I only wished I had spent some more time with stuff like category theory before starting my studies, and had had the guts to take more advanced courses directly in my first semester.

With just a bit of prep from these notes I'm pretty convinced that it's possible to directly take e.g. Algebraic Topology, Differential Geometry, Category Theory, or Algebra during the first semester (don't know about number or measure theory, or anything requiring lots of functional analysis, have not engaged enough with those topics to know how good these notes would be as prep).

Re: An Infinitely Large Napkin [pdf] (2019)

#26

Post by Mithriil » Thu, Feb 13, 2025, 4:06 PM UTC

fbn79 wrote: post #5

How many of you upvote this pretenting to find some day the time and spirit to read and learn from it, but perfectly knowing that will never happen. I'm one of them unfortunally, gosh!

I'm reading it while waiting for the compiler.

Re: An Infinitely Large Napkin [pdf] (2019)

#27

Post by mauvehaus » Thu, Feb 13, 2025, 4:48 PM UTC

Technically, napkin is a diminutive of "nape" with the suffix "kin" meaning small[0]. So really the title probably ought to be "An Infinitely Large Nape". Unless the author is going for an oxymoronic use of napkin like "jumbo shrimp".

[0] https://www.etymonline.com/word/napkin

Re: An Infinitely Large Napkin [pdf] (2019)

#28

Post by skrebbel » Thu, Feb 13, 2025, 5:42 PM UTC

r0uv3n wrote: post #25

This is a fantastic resource, and I used it heavily in 2018 before starting my BSc in Math while still in school to learn the stuff that interested me a bit in advance (and to some extent as a familiar reference for a few years afterwards). I can only recommend this as a good starting point for anyone without the time for a full scale education, or in preparation for such, especially if you have some experience with…

> With just a bit of prep from these notes I'm pretty convinced that it's possible to directly take e.g. Algebraic Topology, Differential Geometry, Category Theory, or Algebra during the first semester

Why is it important/useful to take advanced classes so early on?

Re: An Infinitely Large Napkin [pdf] (2019)

#29

Post by JadeNB » Thu, Feb 13, 2025, 6:53 PM UTC

reikonomusha wrote: post #15

This document reminds me of the kinds of things I wrote at a smaller scale when I'd self-teach math. The usual pattern was: Step 1. I don't know how X works. Step 2. I collect several sources about X and try to understand it. Step 3. I put in a lot of effort to understand X by reading all these sources repeatedly. I try to do exercises, do calculations, etc. I'm desperately seeking the moment it "clicks". Step 4. I f…

In theoretical CS, I've seen Steps 4–8 called "the monad tutorial fallacy."

https://byorgey.wordpress.com/2009/01/12/abstraction-intuiti...

Re: An Infinitely Large Napkin [pdf] (2019)

#30

Post by JadeNB » Thu, Feb 13, 2025, 6:53 PM UTC

gorlilla wrote: post #18

bheadmaster wrote: post #10

Earlier quoted context omitted.

No. Nuh-uh. Not me. I'll definitely find some time to read and work through this. As soon as I finish a few of these things I still have on my TODO list... Just a few more days...

You said that a few days ago.... And a few before that... And a few....

> You said that a few days ago.... And a few before that... And a few....

Aha, so already they're studying induction.