Undergrad Algebra should prepare for commutative algebra.
Take a look at these for an overview of what the subject looks like.
wwwf.imperial.ac.uk
What pre-requisites are required to understand algebraic geometry...
Thomas Powell
Jonathan Richardson
Does calculus include ODE's as well? Also, exactly how much of linear algebra do I need to understand since I haven't started it on kahn academy.
I'll get started on this today.
Andrew Richardson
Just some words of advice for the newfags: Algebraic geometry might sound cool and you should certainly know the basics, but the more advanced stuff in AG is mostly memes and autism. So don't dedicate your career to it, unless you're the next Memechizuki.
William Anderson
ODEs are part of calculus, but they're not important for algebraic geometry.
Liam Bell
but they're important for real analysis, no?
Noah Clark
This is true.
I live in my parents loft.
Xavier Peterson
Yeah, kinda. Just convince yourself that solutions exist. The rest is trivial computation.
Jacob Stewart
i make this simple for you.
level 1: foundations
>read spivak calculus 3rd edition, solutions and book can be found in pdf online
>read linear algebra done right, solutions can also be found in pdf online. you should read this concurrently with spivak, start once you feel comfortable with spivaks style
level 2: we getting there
>read Advanced calculus by loomis and sternberg. it is the most comprehensive analysis on manifolds text out there. this will cover real analysis, multivariable calculus, and differential geometry.
>read Artin's algebra or dummit and foote's algebra. at this point you can decide for yourself which book you prefer but im not sure dummit and foote has solutions online
level 3: direct preparation
>commutative algebra
>algebraic topology
level 4:
You may now begin studying the basics of algebraic geometry and at least know what the words mean. if you made it this far and perservere a bit longer you will be ready for the language of schemes
Tyler Scott
Go ahead and throw that Khan academy stuff in the trash bin because more important then specific knowledge at this stage is an ability to do proofs and understand abstractions which is what is referred to as "mathematical maturity" which is why I upquote this
Carter Carter
Rando here, any input on LADR vs LADW? Suggestions for books in commutative algebra & algebraic topology? Thanks for everything! It helps to have someone more experienced set out a logical path rather than looking at lists of books in subjects you don't have a great grasp on and trying to choose yourself.