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Anonymous at Tue, 19 Mar 2024 22:05:20 UTC No. 16087130
In what order do you learn mathematics? I want to learn, but I'm unsure where to start and what to freshen up on.
Anonymous at Tue, 19 Mar 2024 22:10:01 UTC No. 16087143
>>16087130
Read the Éléments de mathématique books by Nicolas Bourbaki in order.
Anonymous at Wed, 20 Mar 2024 00:43:47 UTC No. 16087357
>>16087145
This is the shittiest guide i've ever seen OP do not do this. Look at any college's curriculum for a start
Anonymous at Wed, 20 Mar 2024 01:06:07 UTC No. 16087395
>>16087130
you pick an application you are interested in and learn the math necessary for analyzing it
Anonymous at Wed, 20 Mar 2024 01:14:21 UTC No. 16087414
Basic Mathematics by Serge Lang, simple as.
Anonymous at Wed, 20 Mar 2024 01:47:50 UTC No. 16087460
>>16087414
Lang is a meme.
Anonymous at Wed, 20 Mar 2024 02:32:15 UTC No. 16087495
>>16087130
There's no definitive order, but I am going to give you a pretty typical order for an American mathematics student, starting from the first year of high school. Once you get to a topic you're not comfortable with, go find a textbook (and no, it doesn't have to be Lang).
>High School Algebra
>High School Geometry
>Trigonometry
>Precalculus
>Calculus I & II
>Proofwriting / Introductory Set Theory
>Multivariable Calculus & Linear Algebra
>Differential Equations (ODEs)
>Abstract Algebra & Real Analysis
>Complex Analysis
>Point-set Topology
This is ignoring what would generally be considered elective courses, but it should give you a solid foundation. Start small, do exercises, and don't get discouraged. If you need guidance about what topics in these courses are important to understand, college curricula and syllabi are good places to look. Good luck OP.
Anonymous at Wed, 20 Mar 2024 04:07:47 UTC No. 16087568
>>16087130
There really isn't any real ordering once you get to higher level mathematics, but there's a pretty typical sequence people follow for the starting points.
1) Basic Mathematics. This includes your geometry, pre-algrebra, high school level algebra and pre-calculus..
2) Calc sequence. Calc 1 (differential calculus), Calc 2 (integral calculus, sequences and series), Calc 3 (parametric equations and multivariable), ODE's and linear algebra.
The next two could really be done in any order and some could be ignored based on your desires.
3 a) Fundamental applied math courses: Calculus based probability, linear algebra and calculus based statistics, numerical analysis, calculus based Fourier analysis (as opposed to higher level measure theoretic Fourier analysis), functions of complex variables.
3 b) Fundamental pure math courses: Introductory proofs course, basics of real analysis (e.g., baby Rudin), basics of measure theory (e.g., Royden), Abstract Algebra, Introductory Topology, introductory mathematical logic.
After you've got a good set of fundamentals in pure and applied math, you've got your bases covered to start graduate level materials.
Anonymous at Wed, 20 Mar 2024 16:43:53 UTC No. 16088284
>>16087130
I simply learned it in bulk and withdraw it from the aether like some sort of wizard, as God intended. ~.~
Anonymous at Wed, 20 Mar 2024 18:01:08 UTC No. 16088368
>>16087143
fucking retarded Nigger! Even Grothendiek though there is an elemental problem with N.Bourbaki and they should restart it over, I bet you are a retarded professor from an African University. sauce: https://en.wikipedia.org/wiki/Nicol
Now for an actual answer: Try the high school mathematics books of you country. Seriously, this is were I think I started to get interest in mathematics. I think highschoolers are retarded in math cuz teachers ommit the proofs of theorems, the extremely theoretic point and hardest problems from the textbooks. You just don't do that. Start from the very fist book in the math curriculum of a first year sci highschooler and move on, then move to college books.
Another two suggestions that I unironically have:
https://zr9558.files.wordpress.com/
https://lms.umb.sk/pluginfile.php/1
both are great books starting from scratch and moving to advanced shit
Anonymous at Thu, 21 Mar 2024 00:34:56 UTC No. 16088886
>>16088368
>>16087143
>Even Grothendiek thought there is an elemental problem with N. Bourbaki and they should restart it over
Yes, he thought the Elements had to include category theory from the start.
Anonymous at Thu, 21 Mar 2024 05:24:21 UTC No. 16089080
>>16087414
>>16087460
So I actually went through the book. As the other guy said it's a meme. It doesn't do a good job to prepare you for a proper calculus course. It's a very quick overview, kinda shallow, despite formatted/type-setted like a real math text. And the "problems" are very trivial.
Even springer has washed their hand of the book. https://link.springer.com/book/9780
I think they'll stop selling the garbage soon.
>>16087130
AOPS' Intro Algebra and Intermediate Algebra. Unfortunately the pirated copy on the internet aren't that good, and their books are expensive.
From there, you can start with normal calculus books, like Spivak or Apostol.