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?
>>16260091just solve a shit ton of problems.
>>16260091If you have to ask you already failed.
>>16260091Make sure you don't have missing links. Your understanding of base concepts must be rock solid before going forward into more complex subjects.
>>16260116I 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.
>>16260199Most 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.
>>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 humilityhttps://www.youtube.com/watch?v=OSVhVydtN_w&list=PLUYNlNeaj8WsshtLvVye6-yFBD8XSCqmZ&index=10
>>16260091go through the fast track https://sheafification.com/the-fast-track/
>>16260091
>>16260822this
>>16260091most books waste too much time on irrelevant garbage. Just read http://arxiv.org/abs/2101.02031
>>16260091>>16260199nobody 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
>>16260091Follow Dieudonné's 5 year 'How to be a Mathematician, not a mathematician' plan (published as "A Letter fromDieudonne")>1st year (Elementary algebraic geometry)Borel and Bass - Linear algebraic groups (first part)Cartan-Chevalley Seminar 1955Chevalley Seminar 1956 'Classification des groups algébriques'Mumford - Introduction to algebraic geometry (chapter 1)Semple and Roth's - Algebraic geometrySerre - Faisceaux algébriques cohérents (cohomology parts)Serre - Géométrie Algébrique et Géométrie Analytiquevan der Waerden - Algebraische Geometrie>2nd yearBorel and Bass - Linear algebraic groups (the rest)Borel-Tits - Groupes réductifsSerre - Groupes algébriques et corps de classes>3rd yearBorel-Harishchandra - Arithmetic subgroups of algebraic groupsBorel - Introduction aux groupes arithmétiquesWeil - Adeles and algebraic groupsSeminaire Borel-Serre - Complex multiplication notes>4th yearMumford - Introduction to algebraic geometry (chapters 2-3)Read Elements de géométrie algébrique until Mumford's 'Abelian varieties' makes senseMumford - Geometric invariant theorySerre - Algèbre localeSamuel Ergebnisse - Méthodes d'algèbre abstraite en géométrie algébrique>5th yearAbelian varieties over finite fields, formal groupsAutomorphic functions, modular functionsJacquet-Langlands theoryAlgebraic geometry of surfacesAdvances theory of schemes (Grothendieck topologies, étale cohomology...)
>>16260091Read Precalculus by Stitz and Zeager, available for free online. Unironically the best way
>>16261555His goal is college math though
>>16261560A lot of people consider advanced algebra and trigonometry to be college math, and to my understanding, "olympiad" stuff doesnt involve calculus
>>16261555>1000 pages>starts with set theory and treats it like the reader is a preschoolerHoly shit, what a retarded recommendation. Just read an analysis book like Amann Escher. No prereqs
>>16261555Lang's basic mathematics is better
>>16261567maybe in papua new guinea or whatever shithole you're from
>>16260822actually not bad
>>16261575>>16261578Skip the sections you already know well obviously>1000 pages!!Being in depth is good and necessary>>16261583USA
>>16261608>Being in depthThe 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
>>16261555>1000 pages>all problems are trivial computationssurely this will help OP solve olympiad problems...
>>16260832Based!
Start with this problem that I created in microsoft paint
>>16260822I thought the list was serious until I saw Landau & Lifschitz on it. Good meme.
>>16260822Doesn't mention olympiad math at all
>>16262186>implying you won't find olympiad math trivial after going through the fast trackGod you're retarded>>16262015Filtered
>>16262474You might want to read the op again
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
