What are some good math books for upper HS AP math/first year

>>9102669
>Book of Proof
Read this if you think you need help understanding proofs
>Rudin's Principals of Mathematical Analysis
A rigorous derivation of Calculus. Truth be told, I thought this book was very good but also a bit antiquated. The notation used is kind of crappy since it was published before LaTeX existed.
>Algebra by Micheal Artin
This will teach you everything you could need to know about Linear Algebra at the undergraduate level.

There does not exist a good ODEs book with proof for undergrads. Rigorous ODEs is a fucking nightmare. Combines Analysis, Topology, and Algebra into a very messy indiscernible clusterfuck. There are some easy applied books though.

Don't be a nigger. Get a nice Real Analysis textbook instead of calculishit.
God Tier: H. Amann, J. Escher "Analysis", V.A. Zorich "Mathematical Analysis"

>>9102669
>Any proof book
How to Prove It: A Structured Approach by Velleman
How to Read and Do Proofs: An Introduction to Mathematical Thought Processes by Solow
Book of Proof by Hammack
A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre

>Any precalculus book
Precalculus with Unit Circle Trigonometry by Cohen
Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by Simmons (review/refresher)
Basic Mathematics by Lang (proofy)

>Calculus
1st place: Introduction to Calculus and Analysis, Volume I by Richard Courant and Fritz John
2nd place: Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra by Apostol
3rd place: Calculus by Spivak
Bohemian tier: Elementary Calculus: An Infinitesimal Approach by Jerome Keisler + Infinitesimal Calculus by Henle and Kleinberg
Actually, I just wanted a few proofs: A First Course in Calculus by Lang
On second thought, I just want the regular class: Calculus With Analytic Geometry by Simmons
Um... brainlet tier plz: Calculus: An Intuitive and Physical Approach by Kline

>>9102684
Another memer suggesting Rudin to not even a freshman but a highschool senior. Don't listen to this douchebag, no college on earth will ever use Rudin to teach an analysis class. If you've already done analysis, understand most of the concepts, there's some good exercises in there, but you're not gonna understand a whole lot if it's your first text. Go for something introductory like Abbott or Apostol.

>>9103347
I know for a fact that honors analysis at UCLA uses Rudin, also some regular courses at Berkeley use Rudin. Granted it's not suitable for freshman nor for normal high school students, but still a decent text

>>9102684
shut the fuck up
>>9103357
>it's not suitable for freshman nor for high school students
>it's not suitable for freshman nor for high school students
>it's not suitable for freshman nor for high school students
so fucking stop giving it to them. it's not a good book for anyone to read it by themselves at all, it's a great book to give lectures from and that's the reason it's used.

>>9102669
do you really need a calculus book with proofs? ask that first. it might be worth it to just go through watered down calculus and after that to analysis if you want more. ocw.mit.edu 18.01SC / 18.02SC is a great soft calculus sequence offering some intuition, i'd say do that and afterwards grab a book of proof and go for analysis