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🧵 Untitled Thread

Anonymous No. 16260091

Scientifically, what is the fastest way I can learn math (from elementary algebra to college math) through books, and be able to solve hard, olympiad-level questions?

Anonymous No. 16260114

>>16260091
just solve a shit ton of problems.

Anonymous No. 16260116

>>16260091
If you have to ask you already failed.

Anonymous No. 16260193

>>16260091
Make sure you don't have missing links. Your understanding of base concepts must be rock solid before going forward into more complex subjects.

Anonymous No. 16260199

>>16260116
I find it easy to solve normal-difficulty basic math problems. What I want to know is how to reach a level where I can solve olympiad questions comfortably.

Anonymous No. 16260206

>>16260199
Most professors can't solve olympiad questions. Olympiad questions are a different kind of math. They're not about knowledge. Either you have the right IQ for them or you don't. This is a skill that can't be trained.

Anonymous No. 16260236

>>16260206
>This is a skill that can't be trained.
some of these tudents here didn't have that skill at all at the beginning, atleast according to their own admission which may be out of humility
https://www.youtube.com/watch?v=OSVhVydtN_w&list=PLUYNlNeaj8WsshtLvVye6-yFBD8XSCqmZ&index=10

Anonymous No. 16260822

>>16260091
go through the fast track https://sheafification.com/the-fast-track/

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Anonymous No. 16260825

>>16260091

Anonymous No. 16260826

>>16260822
this

Anonymous No. 16260832

>>16260091
most books waste too much time on irrelevant garbage. Just read http://arxiv.org/abs/2101.02031

Anonymous No. 16260844

>>16260091
>>16260199
nobody cares about the high school olympiad scam. Any problem in any GTM book blows your precious olympiad problems out of the fucking water in terms of difficulty and creativity required

Anonymous No. 16261464

>>16260091
Follow Dieudonné's 5 year 'How to be a Mathematician, not a mathematician' plan (published as "A Letter from
Dieudonne")

>1st year (Elementary algebraic geometry)
Borel and Bass - Linear algebraic groups (first part)
Cartan-Chevalley Seminar 1955
Chevalley Seminar 1956 'Classification des groups algébriques'
Mumford - Introduction to algebraic geometry (chapter 1)
Semple and Roth's - Algebraic geometry
Serre - Faisceaux algébriques cohérents (cohomology parts)
Serre - Géométrie Algébrique et Géométrie Analytique
van der Waerden - Algebraische Geometrie

>2nd year
Borel and Bass - Linear algebraic groups (the rest)
Borel-Tits - Groupes réductifs
Serre - Groupes algébriques et corps de classes

>3rd year
Borel-Harishchandra - Arithmetic subgroups of algebraic groups
Borel - Introduction aux groupes arithmétiques
Weil - Adeles and algebraic groups
Seminaire Borel-Serre - Complex multiplication notes

>4th year
Mumford - Introduction to algebraic geometry (chapters 2-3)
Read Elements de géométrie algébrique until Mumford's 'Abelian varieties' makes sense
Mumford - Geometric invariant theory
Serre - Algèbre locale
Samuel Ergebnisse - Méthodes d'algèbre abstraite en géométrie algébrique

>5th year
Abelian varieties over finite fields, formal groups
Automorphic functions, modular functions
Jacquet-Langlands theory
Algebraic geometry of surfaces
Advances theory of schemes (Grothendieck topologies, étale cohomology...)

Anonymous No. 16261555

>>16260091
Read Precalculus by Stitz and Zeager, available for free online. Unironically the best way

Anonymous No. 16261560

>>16261555
His goal is college math though

Anonymous No. 16261567

>>16261560
A lot of people consider advanced algebra and trigonometry to be college math, and to my understanding, "olympiad" stuff doesnt involve calculus

Anonymous No. 16261575

>>16261555
>1000 pages
>starts with set theory and treats it like the reader is a preschooler
Holy shit, what a retarded recommendation. Just read an analysis book like Amann Escher. No prereqs

Anonymous No. 16261578

>>16261555
Lang's basic mathematics is better

Anonymous No. 16261583

>>16261567
maybe in papua new guinea or whatever shithole you're from

Anonymous No. 16261590

>>16260822
actually not bad

Anonymous No. 16261608

>>16261575
>>16261578
Skip the sections you already know well obviously
>1000 pages!!
Being in depth is good and necessary
>>16261583
USA

Anonymous No. 16261623

>>16261608
>Being in depth
The book isn't in-depth retard. Its treatment of set theory is incredibly shallow despite being long. Look at Bogachev's series on measure theory if you really want to see what 1000 pages of an in depth treatment of a topic looks like.
Just read Shilov for fuck's sake. There are NO prerequisites. Analysis books like Amann Escher or Zorich also treat all the topics contained in your abortion of a textbook and more all while introducing you to proofs

Anonymous No. 16261640

>>16261555
>1000 pages
>all problems are trivial computations
surely this will help OP solve olympiad problems...

Anonymous No. 16261667

>>16260832
Based!

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Anonymous No. 16261990

Start with this problem that I created in microsoft paint

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Anonymous No. 16262015

>>16260822
I thought the list was serious until I saw Landau & Lifschitz on it. Good meme.

Anonymous No. 16262186

>>16260822
Doesn't mention olympiad math at all

Anonymous No. 16262474

>>16262186
>implying you won't find olympiad math trivial after going through the fast track
God you're retarded
>>16262015
Filtered

Anonymous No. 16263376

>>16262474
You might want to read the op again

Anonymous No. 16263393

Do not bother posting on /sci/ ever again. You're more likely to get helpful answers through Google or even Youtube and TikTok.
You get good by practicing, researching a topic as you need and watching other people solve problems.
https://artofproblemsolving.com/wiki/index.php/Olympiad_books