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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.

I dont know about a definitive guide, but here are books that will set you straight:

intro proofs: chartrand, loehr, velleman are all good books, choose 1

analysis: tao analysis i and ii; amann and escher analysis i, ii, iii; Simon analysis series; courant and John calculus/analysis series if you need something little lower level

topology: john lee manifolds series

abstract algebra: aluffi chapter 0

linear algebra: greub linear algebra, axler or friedberg linear algebra

misc: lawveres 2 books (conceptual math, sets for math), conjecture and proof (just a fun book)

from there you can pretty easily branch off into studying whatever you want, e.g. probability theory or whatever

>>16922202
Ted K is a retard that threw his life away to fight a battle that could've been won if he weren't an asocial retard and knew even the basics of convincing people that the modern world is a behavioral sink-trap hellhole (which everyone knows deep down but won't admit it because our addiction to technology outweighs out natural social, environmental, spiritual, physical and mental needs in our calculus). Don't post anything he says as if it is worth shit.

>>16924309
Hello CIA, now give me a bullet point list of reasons why we need to slaughter Iranians

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>>16924316
Iranians are Turk owned. Their Ayran sissy bussies belong to Helleno-Mongol chads

>>16921892
Are the books in this guide actually good?

>>16925523
There are, but not beginner friendly at all

This is crap. I don't recommend using a proofs or set theory book, it will bore you and it's a waste of time. Spivak's calculus is basically an introduction to analysis, and it's written to teach the basics of pure mathematics. From there you should study linear and abstract algebra and point-set topology, and they're self contained and won't require higher math knowledge. I'd recommend you watch a video on proofs and start with an easy abstract algebra book like Pinter. From there, work through Topology like Munkres. This should give you the mathematical maturity you need to further approach math topics.

From there, do a pure math linear algebra book, like Axler, or Hoffman & Kunze, and an analysis book like Pugh. Avoid Walter Rudin Principles of Mathematical Analysis unless it's for the exercises, which you should do, but the chapters themselves are very poorly written. Then read a higher-level abstract algebra book. I think Topics in Algebra by Herstein is quite good but it's not very comprehensive, but you don't need that if you will go onto grad level algebra since it will introduce what you missed. From there you can approach first year graduate level analysis and algebra, which are the building blocks of advanced mathematics. Then you can study whatever you want.

So my advice is to speedrun this sequence, it will be a better ramp up in difficulty and it won't be as frustrating and annoying.
>watch a lot of youtube videos on proofs
>work through Spivak's calculus book
>Pinter abstract algebra, watch lots of videos about abstract basic algebra there are a lot
>Munkres topology, and you should know enough group theory to work through the chapters on algebraic stuff now
>Pugh analysis and a linear algebra book of your choice, and do the exercises in Walter Rudin's book
>Herstein Topics in Algebra
>now you can work through the standard grad level analysis and algebra books, Lang/Jacobson/Hungerford and Folland

>>16922218
buy bitcoin when it drops below $20k in 2022, then sell it above $100k in 2025

>>16927013
What do you recommend for linear algebra?

>>16927039
I like Hoffman and Kunze, but it's challenging. However you should be well prepared by that point. H&K is pretty old school. Axler is a newer, popular book which avoids using the determinant because it trivializes many proofs. But maybe that would be good for you to force you to develop more mathematical maturity and force you to think by not just blasting away problems with determinants. Maybe you should use Axler.

Maybe you should read a basic proofs and set theory book if you feel unprepared with Spivak. But I would avoid these old meme books. A popular one used in a lot of universities is How to Prove It. I've given you the best advice so far and this should actually be manageable for you. Also make use of youtube videos for further clarification, there are a lot now on pure math and a lot of them are good unlike when I was learning this stuff.

>>16927050
Axler is easier read and a better intro to proofs compared to Spivak

>>16927013
>This is crap
>Proceeds to suggest a worse version of the same thing

>>16927755
kek

>Measure theory, topology, differential geometry, category theory
This is the perfect roadmap for someone who wants to study abstract bullshit and secure a lucrative career as a community college professor.

>>16921892

What a waste of fucking time.

If you genuinely work with numbers youll be learning matlab and numerical methods

Learning RK4 to solve odes in 10 minutes is more convenient than reading a 400+ page book