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Sheafification – The optimal path to mathematical mastery: The fast track (2022)

sheafification.com

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Re: Sheafification – The optimal path to mathematical mastery: The fast track (2022)

#11

Post by graycat »

(1) Didn't see anything on the math of probability or stochastic processes, e.g., nothing from Dynkin, Neveu, Breiman, etc.

(2) That it's important to study carefully that computing is about "switches" is something like knowing the details of the amazing work in the chemistry of rubber tires is crucial for truck driving or we should all early in our education achieve good mastery of each of the proteins in our DNA.

(3) After working through all those books, cancelling nearly everything else in life for some years, just what is the result, the payoff, the reason? Academic research or something in the mainstream economy, technology, etc.?

Re: Sheafification – The optimal path to mathematical mastery: The fast track (2022)

#12

Post by jhanschoo »

3 years still sounds optimistic to me ... even full-time, if we are talking reading through the material thoroughly. I suppose the modern student knows to pick and choose the gaps that they have, that are still relevant, and that they lack under guidance in an institution.

Re: Sheafification – The optimal path to mathematical mastery: The fast track (2022)

#13

Post by asplake »

TimorousBestie wrote: post #2

Safe, conventional, non-controversial choices here. Given the domain name, I expected more category theory. I dunno about “two or three years,” though. It would take me about a year to get through all three volumes of _The Quantum Theory of Fields_ alone (~1500 pages of extremely dense physics!)

About the domain name, I don’t thought that too. But its stated intention is “to accelerate the development of prospective mathematical scientists”, hence the lean to physics and to certain authors.

Re: Sheafification – The optimal path to mathematical mastery: The fast track (2022)

#14

Post by easygenes »

figassis wrote: post #10
bbor wrote: post #7

Earlier quoted context omitted.

Oof. Not usually one to comment on technical issues, but that's a rough one to get for a (presumably) completely-static site! Dr. Sheaf, please consider serving your site via a dedicated service like S3. This is a solved problem <3

He probably doesn’t know how. This message is em from Wordpress. There are many WP providers where you just signup and start writing. They don’t tell you that if you get to HN front page, your db will die. I don’t know any static blog providers. He’d have to roll out his own or use Medium/Substack.

> I don’t know any static blog providers.

Bear Blog comes to mind (no connection): https://bearblog.dev

Re: Sheafification – The optimal path to mathematical mastery: The fast track (2022)

#15

Post by lsc4719 »

This is wrong. In Computer Science language, human learning works in greedy way. We make locally optimal decisions in life. We cannot learn something in globally optimal way. We learn something in locally optimal way. And by repeating that we can reach somewhere at some point.

Re: Sheafification – The optimal path to mathematical mastery: The fast track (2022)

#16

Post by stared »

I am not sure if I agree with the list. I mean, one red flag is the frequent mention of Landau & Lifshitz. It is considered a "standard textbook", but I feel it stuck there by inertia. There are quite a few choices of both less boring and more insightful.

(Back when I was reading such stuff, 20 years ago, the Feynman Lectures provided orders magnitude more insight. And fun.)

Re: Sheafification – The optimal path to mathematical mastery: The fast track (2022)

#17

Post by stared »

rfl890 wrote: post #3

The optimal path to mathematical mastery is "Error establishing a database connection"?

It stings be a bit that people use Wordpress in times of really wonderful static sites generators AND vibe coding. They are both pleasure to write, make it easy to tweak style however you please, can cost nothing (just host it on GitHub pages), no maintenance, and if something hits Hacker News, no risk of an outage.

Re: Sheafification – The optimal path to mathematical mastery: The fast track (2022)

#18

Post by lambdas »

stared wrote: post #16

I am not sure if I agree with the list. I mean, one red flag is the frequent mention of Landau & Lifshitz. It is considered a "standard textbook", but I feel it stuck there by inertia. There are quite a few choices of both less boring and more insightful. (Back when I was reading such stuff, 20 years ago, the Feynman Lectures provided orders magnitude more insight. And fun.)

Shivlov for the one and only text in linear algebra is rough. IMO, it’s a little terse and fast paced. Efficient if you’re already well versed enough to be dangerous, but otherwise I think might slow down the beginner to a crawl in places.

Same for Hartshorne’s Algebraic Geometry. Neither of these are bad textbooks at all, they both have a place on my bookshelf, but certainly better options have appeared through the years (for AG, I’d be remiss to mention Ravi Vakil’s fantastic The Rising Sea, due for a physical publishing October, and Ulrich Görtz & Torsten Wedhorn two part series)

Re: Sheafification – The optimal path to mathematical mastery: The fast track (2022)

#19

Post by mna_ »

lambdas wrote: post #18
stared wrote: post #16

I am not sure if I agree with the list. I mean, one red flag is the frequent mention of Landau & Lifshitz. It is considered a "standard textbook", but I feel it stuck there by inertia. There are quite a few choices of both less boring and more insightful. (Back when I was reading such stuff, 20 years ago, the Feynman Lectures provided orders magnitude more insight. And fun.)

Shivlov for the one and only text in linear algebra is rough. IMO, it’s a little terse and fast paced. Efficient if you’re already well versed enough to be dangerous, but otherwise I think might slow down the beginner to a crawl in places. Same for Hartshorne’s Algebraic Geometry. Neither of these are bad textbooks at all, they both have a place on my bookshelf, but certainly better options have appeared through the…

What would you recommend as a supplement to Shilov's LA book?
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