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This is literally all you need.

>>16921892
>What is THE DEFINITIVE GUIDE/PATH/INFOGRAPH to continue study mathematics for someone who's only taken Calculus I with Optimizations in college maximum
There should be different guide/infograph for the analyst path, the algebrist path, the geometer path, number theorist path and so on. General guides shouldn't be that long and unconnected, only the basics common to all aforementioned paths

>>16921892
>doesn't start with the geeks
Dopped.

>>16921909
>analyst path, the algebrist path, the geometer path, number theorist path and so on
No such thing any more. You're expected to know everything.

>>16921892
which of those books teaches me normal algebra?

>>16921892
I'm halfway through that Elements of Set Theory book and they've yet to explain how set theory is anything more than academic masturbation. It's honestly kind of extraordinary, I don't think I've ever seen a field so vague on its application.

>>16922120
>I don't think I've ever seen a field so vague on its application.
The application is right below in OP's guide, there's no reason to use set theory outside of understanding other mathematical textbooks. And almost all higher mathematical textbooks use set theory.

>>16921905
>forgotten books
why are you giving your money to Ayndryl and the FL crew?

>>16922202
AI can't surpass humans in mathematics if all they can do is memorize the answers to homework problems.

>>16922120
I read that a while back and all I got out of it was that they invented an entire field just to define things in the most obtuse way possible

like, literally, 99% of the book is just
>introduce concept
>spend 5 pages telling you how to define it using set theory notation
maybe that's the entire point, idk

>>16922120
>Reading book for no apparent reason
>Complains that the book feels unmotivated
The problem is (you).

>>16921892
>Learn enough naive set theory so that you understand the language. Whenever you feel concerned about logical issues, go back and learn enough axiomatic set theory to quell your concerns.
>Learn linear algebra (from the correct perspective, e.g. Lang, Shilov or Axler)
>Learn some basic linear differential equations (applying what you learned from linear algebra). Literally just go through the linear differential equations chapter of a ODEs textbook, ignore any technical proofs, and accept any results from complex analysis.
>Learn some Fourier theory (related to linear differential equations)
>Learn some complex analysis, up to say Picard theorem.
>Take a glance at some multivariable calculus if you want, but don't waste much time on it. You'll see it from the correct perspective soon enough.
This puts you on a decent footing to start learning some actual math, and it becomes a lot less ordered.
>Basic algebra, analysis and point-set topology
It doesn't matter what order you go through these. Algebra is the best to start with, as it gives a good feel for what math is, and introduces you to proofs very slowly. Analysis is tedious and becomes a real headache. The only issue with point-set topology is that it feels unmotivated, so you might want to learn it alongside analysis.
Once you have the basics, it becomes much wider, and there are various places you can go within each broader topic. You kind of just follow what you enjoy. As you learn more, you'll see that various topics are interconnected, and will lead you elsewhere.
Algebra
>Representation theory
>Galois theory
>Commutative algebra
>Non-commutative algebra.
Analysis
>Measure theory
>Functional analysis
>Differential equations
>Non-commutative geometry
Topology
>Algebraic topology
>Manifolds
>(Co)homology
Geometry
>Differential geometry
>Algebraic geometry
>Non-commutative algebraic geometry
Each of these topics is extremely vast. On the way, you'll realize you should pick up some category theory.