Which order of Mathematics is correct?

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.

>>8680555
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

>>8680562
I would have recommended you to not waste your money in books at all but you already did so whatever.

>>8680563
Ah, Thank you. I knew my friend was talking out of his ass when he said that. Much appreciated! Are you in college?

>>8680555
no all you literally need is serge langs basic mathematics and then you can start calculus

>>8680571
>Are you in college?

Yeah, for pure mathematics.

>>8680566
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.

>>8680580
THAT'S INCREDIBLE! I hope you're loving it so far, and I hope you get everything that you need from it.
Also, is >>8680579 right when he mentioned Serge Langs basic Mathematic? Is that all I really needed to learn all the concepts that I needed?

>>8680583
>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.

>>8680590
>Also, is >>8680579 right when he mentioned Serge Langs basic Mathematic? Is that all I really needed to learn all the concepts that I needed?

I've never read any book in that topic. I've never had to review basic mathematics as I was doing well enough in high school and I moved to university immediately so I already knew all the algebra, geometry and trig someone needed to know for university.

But before you go buying more books, simply take it for a test ride... or just use it from here and never buy it:

https://www.docdroid.net/K1VENuF/basic-mathematics-serge-lang.pdf.html#page=15

>>8680591
Like I stated, I just have a difficult time learning from online textbooks. I much rather have a physical copy. But I see your point. Some of the prices for these books would cost an arm and a leg to some. So I see no problem with someone getting them for free.

>>8680579
Are you memeing or are you being serious? I have no idea. I went through all these different sites where people recommended these books. Are you sure that's literally all I need? I saw someone made a thread about it earlier and thought nothing of it.

This is going to cover EVERYTHING in great detail? Alg-Geo-Alg2-Trig? It just sounds too good to be true.

>>8680555
>learning trig before algebra 2
>learning geometry before algebra

this is dumb

>>8680611
it's a 469(?) page book by a really good mathematician that explains all of the math before calculus so you're ready for it. I read it in the month before university started and had no problem in any of my math classes.

Algebra -> Geometry -> Pre-Calc

>>8680590
>>8680596
>>8680611
i'm the same anon but yes it will cover everything i'm not memeing

that's literally what he means by basic mathematics; he made the book to cover everything before calculus

>>8680674
the most mind boggling thing is that high school math for most students myself included took 3-4 years to cover all of basic mathematics when it could be covered in like a year tops

>>8680680
I NEVER understood that concept. Why does it literally take years to cover the basics? When it seems you can learn it in several months. On top of that, Most of my teachers throughout my life have been complete ass at teaching which severely fucked up the entire class's curriculum.

Why do high schools allow teachers straight out of college teach subjects that they barely care to know of!? Plus their emotionally unstable. I had my chem teacher break out in tears and had to take several days off because she couldn't "handle it" my math teacher did the same shit. She was just a complete bitch to the whole class, Skipped lessons that she deemed "unfit" for us, Then bitched why all of her students were failing tests.

>>8680712
this just makes me feel like i have some sort of duty to teach high school plebs

im never going to do it but i feel bad that there's people like OP (and me a couple years ago) that thought basic mathematics is this massive thing that takes years when it can literally be finished over a summer with a good beginner book like serge lang or maybe even morris kline

>>8680712
>Why does it literally take years to cover the basics?
because the classes are for a wide range of students and are required. if it was for the smart kids, the classes would obviously move faster.

>>8680724
>takes a summer to read 475 pages

brainlet detected

geometry is unnecessary

>>8680728
people actually believe this, that a "wide range of students" justifies taking 3+ years to cover basic mathematics

yes students are retarded, everyone is retarded, but if you introduce math with historical context and don't spend 3 months on a single topic using a dry textbook 1000x longer than it needs to be then math wouldn't be so cancerous to everyone
>>8680731
>spending ur summer learning math
bet u had a lot of friends

OP here, I have read and responded. This has been alot of help. I appreciate all your help. I've only purchased one book so far and that was Serge Lang-Geometry. Should I just return it? Since the other book basically covers everything?

Also, What book should I get after Serge Langs basic Mathematic?

And what Chemistry book should I get? I was thinking of Nivaldo J. Tro-Chemistry: A Molecular approach. IS this good?

>>8680761
his geometry book isn't necessary but i'd keep it, it's certainly going to be good; from the reviews i read it's like a modern euclid's elements and it will be a good reference regardless at some point if you continue with math

with that said, after you finish basic mathematics and maybe geometry:

as i posted in another thread there's 3+ options..

Spivak's Calculus (i dont recommend this personally unless you're a pure math grecian god)

Morris Kline's Calculus: Intuitive Approach (my favorite calculus book)

or if you liked those serge lang books you can continue with him by reading Serge Lang's First Course in Calculus and then his multivariable/intro linear algebra books


also that's the book i used for my chemistry class, it was good

What is the best way to study and absorb all of the information in a text book? My chemistry teacher recommended copying the entire Text book word by word by hand.

>>8680820
That is a really dumb strategy, unless you have absolutely zero ability to determine what parts of the book are important and/or difficult to remember.

Do the exercises, especially if it's math or physics. Biology and chemistry are more dependent on memorization so I would recommend flash cards.

>>8680820
just do the reading, maybe write down the important parts if you arent a lazy pos

you are more liable to remember things you've written down usually

Algebra 1 -> Trig -> Algebra 2 -> Calc 1-4 -> Geometry

(Not even memeing)

>>8680563
This is the true path for someone interested in pure mathematics. By the sounds of what this guy is talking about, he's interested in getting up to speed with calculus.

>>8681318
Also how did you not learn this stuff in high school? (No offense. I have a lot of respect that you are teaching this to yourself when most have given up)

PS Drill the shit out of Algebra + Algebra 2. You need to be able to do that stuff fast as well as fast mental arithmetic if you want to get good.

>>8681324
OP here, Like I stated before. I had terrible teachers throughout my life. They couldn't teach to save their own skin. I was basically self-teaching myself anyways to pass those damn classes.

Basically I just want to have a stronger grasp on some concepts that I struggled with. Plus, brush up on my math. I've always loved math, It's a language to me.

I'm at the end of my Algebra Demystified book and I've started to be able to do most of what I've learned off the top of my head. Without putting anything to paper and I've started dreaming up equations as of last night. Where's my next step? I've downloaded the PDF already and plan to study that book and hopefully memorize and be able to mentally do all basic math. How viable is it to self study (maybe hiring a tutor upon reach calculator ii or as the need arises ) all of the maths by year's end? I'm pretty sure I can start on Calc before March. From there I can't really scale until I have a frame of reference for my own understanding of the subject but I have skipped ahead a bit to get basic notions of what I can expect and I'm honestly excited to get learning

>>8680555
You're really fucking up your algebra choice, you need something with category theory. Try Hungerford.