Anonymous at Wed, 24 Jul 2024 15:54:28 UTC No. 16294835

>>16294829
Math is empirical in nature so you should start with the basics. Geometry, algebra, calculus.

Anonymous at Wed, 24 Jul 2024 16:01:28 UTC No. 16294844

>>16294835
I thought what differentiates math from the other sciences is the fact that it's not empirical.
Sets don't exist in material reality.

Anonymous at Wed, 24 Jul 2024 17:17:17 UTC No. 16294924

Category theory is great, but tragically every person who's ever written anything about it has only written trash. MacLane was brilliant overall but he got a number of things wrong from the start and things have mostly gone downhill from there. Category Theory is only ever taught badly, so learning it properly requires a lot of patience. By the time 4 years have gone by you'll either figure it out and have better things to do than to write a book on category theory, or delude yourself that you've figured it out and waste a fuck ton of everybody's time trying to heroically write a book, which will invariably be shit.

Anonymous at Wed, 24 Jul 2024 17:33:20 UTC No. 16294941

>>16294924
I bought a book called "category theory for programmers" and it's not that bad.
The only bad part is that his code examples are in C++ but the book makes some sense.
There's not a single proof in the book tho.

Anonymous at Wed, 24 Jul 2024 17:54:01 UTC No. 16294955

>>16294829
Yes, check out Kato's "The Heart of Comohology". You'll also learn some basic sheaf theory while you're at it
>reading through categories and sheaves but it's kinda hard
that'll always be the case with higher algebra though. Takes some time to get used to

Anonymous at Wed, 24 Jul 2024 17:56:16 UTC No. 16294959

>>16294941
AH well. Anything works if you're a beginner, but it's relatively not great. It does seem like it wouldn't be very useful for mathematics.

Anonymous at Wed, 24 Jul 2024 17:58:43 UTC No. 16294966

>>16294829
Brown's book on topology is centered around groupoids and introduces cat theory early on. May want to check that out.

Anonymous at Wed, 24 Jul 2024 18:04:41 UTC No. 16294970

>>16294829
Read Lang's Algebra. He introduces categories at the end of the first chapter on groups and makes use of them throughout. You'll want to see them in context or else it's just abstract non-sense.

Anonymous at Wed, 24 Jul 2024 18:07:23 UTC No. 16294972

>>16294924
desu i never understood those massive tomes on cat theory itself. All the cat theory i ever needed for algebraic topology ive found in books on the former. Stuff like Johnstone's elephant or even borceaux's series seems heavily specialized

Anonymous at Wed, 24 Jul 2024 18:10:48 UTC No. 16294974

>>16294941
>There's not a single proof in the book
Yeah, you're not gonna become a mathematician that way. It's very important to study proofs in detail and work out techniques and ideas

Anonymous at Wed, 24 Jul 2024 18:13:40 UTC No. 16294979

>>16294844
the basic axioms were chosen based on empirical observations. you wont see anyone denying the axiom scheme of separation

Anonymous at Wed, 24 Jul 2024 18:18:26 UTC No. 16294982

>>16294829
http://arxiv.org/abs/2101.02031

Anonymous at Wed, 24 Jul 2024 18:18:54 UTC No. 16294983

>>16294924
That's because category theory really should be learned after algebraic topology. Yes, it's possible to learn it for its own sake but it just makes more sense when you understand more concretely why we care about categories, functors, and natural transformations. Mac Lane came from this background because he worked with Sammy Eilenberg (alg topist) and founded the field. After that if you want to further specialize have at it but you really need courses in algebra and topology first (at least) to begin to appreciate it imo.

>>16294972
Yeah it's for specialists, but sometimes approaching a problem categorically pays its dividends I think. If you get into topos theory or higher topos and certain extensions of homotopy theory a solid grounding in higher cat theory is basically a must. That said, you can certainly stay in algebra top and barely ever talk more than something about an object being functional etc. at most.

Anonymous at Wed, 24 Jul 2024 18:24:22 UTC No. 16294989

>>16294829
>sheaves
have you done complex analysis already? Seems to be heavily lacking in motivation otherwise

Anonymous at Wed, 24 Jul 2024 18:31:23 UTC No. 16295002

>>16294829
>it's kinda hard
It's part of the "Grundlehren der mathematischen Wissenschaften" series. That's about as hard as it gets when it comes to Springer.

Anonymous at Wed, 24 Jul 2024 18:33:50 UTC No. 16295007

>>16294829
>I'd like to start with the most abstract stuff
In that case you'll want to look at [math](\infty,2)[/math]-categories or whatever they're called.

Anonymous at Wed, 24 Jul 2024 18:48:32 UTC No. 16295020

>>16294966
great rec

Anonymous at Wed, 24 Jul 2024 18:53:54 UTC No. 16295025

>>16294941
>for programmers
Dont ever read these kinds of books. I did the same mistake when I first started. No csfag has ever written a good math book

Anonymous at Wed, 24 Jul 2024 20:14:55 UTC No. 16295168

>>16294829
>>15833839
>Reminder: /sci/ is for discussing topics pertaining to science and mathematics, not for helping you with your homework or helping you figure out your career path.

>If you want advice regarding college/university or your career path, go to /adv/ - Advice.

Anonymous at Thu, 25 Jul 2024 05:51:28 UTC No. 16295677

>>16295168
maybe read your own post fucking retarded wannabe janny. Textbook threads are on topic and always have been