Which order of Mathematics is correct?

Hey Veeky Forums I'm curious about what is the correct order in learning Mathematics?

My friend mentioned that Geo-Alg-trig-Alg2-Cal is correct. Instead of the traditional sense of Alg-Geo-Alg2-Trig. Is this correct?

Also, I purchased several books to help me relearn some basic subjects. Did I do good?

Serge Lang-Geometry (2nd addition)
S.L. Loney-Plane Trigonometry (Scholar's Choice)
Gelfand's-Algebra

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Additional Information-
I'm going to college to become an Aerospace Engineer. Starting off at community before transferring over to Embry. (Maybe MIT) Are these books sufficient enough to learn from? (I know I need more) But what else do you guys recommend to help me along my journey? Any help would be appreciated.

You need to know algebra before you can do geometry, at least in the sense you are talking about.

Anyways, the true path is

First order logic
Set Theory
Algebra
Analysis
Geometry

I would have recommended you to not waste your money in books at all but you already did so whatever.

Ah, Thank you. I knew my friend was talking out of his ass when he said that. Much appreciated! Are you in college?

no all you literally need is serge langs basic mathematics and then you can start calculus

>Are you in college?

Yeah, for pure mathematics.

What do you recommend then? The reason why I paid for physical copies of these books is because, for me, It's easier to learn from.

THAT'S INCREDIBLE! I hope you're loving it so far, and I hope you get everything that you need from it.
Also, is right when he mentioned Serge Langs basic Mathematic? Is that all I really needed to learn all the concepts that I needed?

>What do you recommend then?

Well, at the level you are at there are a billion books online for free.

And even if you want those specific commercial books, there are places for that too. I get all of my books online.

And this is better because what I have found is that when you are in undergrad, books are highly disposable. Back when I was doing calculus, the professor was using like 4 different books that she would get from the department's library. If I wanted to have the books I would have had to buy 4 books all on the same topic, simply because of how disposable they are in university.

Maybe at the grad level when there is at most one decent book in a topic you will stay longer with books, but at the undergrad level? Nah. There are like 50 books for everything and your professors will use all 50 simultaneously.

But you already have the book so it is okay. Try to get your money's worth, I guess.

>inb4 but isn't that stealing

I'll pay them back with my contributions to humanity from what I learned with their books.