/math/ - Mathematics

>>688
this is the actual mathchan curriculum: https://sheafification.com/the-fast-track/

>>689
and how do you know

>>689
>actual mathchan curriculum
>mechanics
Top kek

>>688
aim high, it doesn't just have to be a dumb desk engineering job either.
the effort doesn't just stop at reading hard books, if you just go for a programming job you're being lazy, and that's not why we're here on mathchan
it's not 'follow this hobby math curriculum and do a bunch of toy analysis proofs'
which is why our list doesn't look like a typical math or CS major, because it is not courses for courses' sake
it doesn't stop there, it continues in your work - if you know theoretical physics and a base of mathematics, you could be doing literally anything
it would be lazy and shameful to stop there
you should be working on something big and important, gather experience in a different field, transform it with mathematics, start your own company
anything less is a waste

>>694
I aim trying to aim high anon. This curriculumn looked difficult. So should I start with sheafification?

>>695
Almost all the recommendations there are great. It recommends first getting proficient at single- and multivariable calculus before moving onto analysis but I prefer books that treat both simultaneously, like Amann and Escher's three-book analysis series.

>>689
Even Urs Schreiber approves of the /mg/ curriculum:
https://nforum.ncatlab.org/discussion/15070/anisomorphism/?Focus=102597#Comment_102597

>>688
Why haven't anyone named the books yet. Just fucking read the titles. I need the names of last two books

Last book is Topics in Transcendental Algebraic Geometry by Phillip A. Griffiths and other one is Geometric Invariant Theory by Mumford.

>>758
Thanks Anon.
Its /thread/

The early curriculum is great for building a solid foundation. But it seems very single-minded on getting to abstract results in algebraic geometry. You can easily miss the trees for the forest by doing that.

>Are the books shown in the picrel enough to cover the mentioned topics.
They mostly seem to be selected for being the "hardest" book on the particular subject, which is not always the best. For instance BottTu is definitely not the hardest for anything it covers, but the clarity of exposition makes it a worthwhile read.
>how long would it take
Depends how much time you devote to it. If you spend 40-50 hours a week on studying, and you study efficiently, you could maybe finish this in five years. How much you would retain with no interaction from a mathematical community is uncertain, probably low. It takes years of being immersed in the field for knowledge to really sink in.

>>775
>If you spend 40-50 hours a week on studying, and you study efficiently, you could maybe finish this in five years.
It's Over...
I could never become a mathematician in this lifetime

>>784
>I could never become a mathematician in this lifetime

Why?
You can pubblish a unique idea that makes false all these books until 120 y.o.

>>785
Is it possible?

>>788
In my opinion, it is possible.

>>775
>Depends how much time you devote to it. If you spend 40-50 hours a week

Midwit pseud leeching off academia. Just stop. If it takes you that long to work through glorified linear algebra you might as well be doing accounting before AI takes over your pitiful breed of mentally challenged bookfags.

>>806
OP here. What should I be doing then Anon?

>>812
Do whatever you want, there's no shame unless you give a fuck.
It's been 2 months, so you must've figured something, and if it's that you genuinely enjoy being a shut-in book sniffer, then so be it.

>>815
I will tell you straight "I haven't reading anythig from that list yet. I got intereseted in computer science and right now doing a free course on coursera called "Nand2Tetris" where you build your own computer. Starting from basic logic gates then building an ALU , the memory and then an instruction set and implementing it with a control unit and an assembler your hardware part is complete. After that you build your own high level programming language and build a compiler for it and then write Tetris using it. Thus the name "Nand2Tetris". I am currently doing the first part (almost done.)

>>696
Is Amann and Escher actually any good?

>>688
http://pastebin.com/sy2MbenC

>>846
NTA but imo it's a really great introduction. I personally prefer specifically reading books on harmonic and complex analysis, measure theory, differential geometry instead of Amann Escher's later books and chapters (that is not to say their treatment is shit. It's just not deep enough for my liking) but the single- and multivariable analysis chapters are really solid.

>>846
>>849
And by "introduction" I mean introduction to proof-based math. Zorich is another book that does calculus and analysis simultaneously.

>>849
>>850
Thank you. I don't mind if it doesn't cover everything in depth. But you say that Amman and Escher is a good introduction to proof-based math and compare it to Zorich. I can't comment on that but I would be lying if I didn't say that I didn't have difficulties with Zorich. Are they comparable in diffculty? I have covered Courant's calculus vol. 1 beforehand and I regret it slightly.

>>853
Accidentaly posted that.
What I am wondering is if I should cover multivariable calculus before tackling analysis. (The problems I had with Zorich were related to lack of mathemathical maturity not multivariable calculus knowledge)

>>853
>>854
Amann Escher's problems aren't much easier than Zorich's per se but I'd still claim you'll have a much easier time. One of the reasons why Zorich's problems are difficult is because they're often based on novel examples or only tangentially related fields. Amann Escher isn't as random (or rather, the proofs they expect you to write down aren't much harder than the ones they do for you). Amann Escher also treats analysis much more formally (introduce metric spaces, normed vector spaces, and topological ones early on, then prove most of the theorems for banach spaces). So if you had issues with abstraction Amann Escher may be better. For illustration: Zorich introduces transcendental numbers in an exercise early on (may be chapter 2 IIRC), whereas in Amann Escher you first hear about them on page 300-something and not in an exercise.

>>688
What happens after you consume all of that information? How will you use it? What do you accommplish? What goal motivates it all?

>>870
I intend to revolutionize the field of mathematics supplanting my name in History.
What do you think is this the right mindset to go about with my life.

>>872
>4 months later
>still not a single book read
Ngmi

>>875
You are right , I guess.
It's over, probably never began.
Now I should devote more of my time to programming and becoming a code monkey

>>881
no dude the key is to just start as obvious as it may sound. If you want to do something, do it now.
I used to think I'd have no time to read during uni but that's all nonsense. Once I started doing my assignments immediately I had enough time to read through 4 books in one semester and that conversely helped me become really fucking good at math to the point of me going to far less lectures

>>887
Did you do the exercises? Or only read those books. If yes then what percent of exercises like 50% or 80% or each and every one(skipping the trivial easy ones of course).

>>890
Do all of them. When you get to my point in life where I've read one undergrad curriculum's worth of books, I can't remember what I need to any more. Burn it into your memory, because you can only ascend as strong as your foundation.

>>891
Can you specify which were those 4 books

>>892
Federer. Geometric Measure Theory
Kashiwara. Sheaves on Manifolds
Harthshorne. Algebraic Geometry
Hotta. D-modules, Perverse Sheaves, and Representation Theory