What pre-requisites are required to understand algebraic geometry, I was planning on buying the two books from the /sci/ wiki, and I only have a mathematical understanding up to calculus 2.
>>8146657
Topology and Commutative Algebra.
k
try learning real analysis, abstract algebra to a graduate's understanding, algebraic topology, and commutative algebra first
>>8146659
fuck
>>8146662
>real analysis
>algebraic topology
Neither of these are necessary if you avoid complex geometry and cohomology.
>>8146657
Commutative algebra is most important. In particular the chapter about rings and ideals. You'll need a shitload of that. Basic topology is also something you should know. If you want to go deeper, differential geometry and algebraic topology can help you see and understand a lot of stuff you'll encounter in AG.
>>8146670
>algebraic geometry
>avoid cohomology
>>8146671
what backgrounds do I need for those?
>>8146675
linear algebra and multivariable calculus
>>8146675
you finish your calculus education then learn real analysis for maturity and then you do algebra. that will give you the fundamentals
>>8146675
Undergrad Algebra should prepare for commutative algebra.
Take a look at these for an overview of what the subject looks like.
http://wwwf.imperial.ac.uk/~apal4/commalgnotes.pdf
>>8146678
>>8146678
>>8146679
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.
>>8146680
I'll get started on this today.
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.
>>8146688
ODEs are part of calculus, but they're not important for algebraic geometry.
>>8146692
but they're important for real analysis, no?
>>8146689
This is true.
I live in my parents loft.
>>8146696
Yeah, kinda. Just convince yourself that solutions exist. The rest is trivial computation.
>>8146688
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
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 >>8146719
>>8146719
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.
For a book with minimal requisites, pick up Shafarevich's basic algebraic geometry book.
You just need to know what rings and ideals are. All the baby commutative algebra you need, it goes over.
And honestly, if you can't get through the first few chapters of that on your own (supplemented by an algebra text as needed), algebraic geometry probably isn't the right field for you.
>>8146763
I've never read Linear Algebra Done Wrong so I cant really comment. Linear Algebra Done Right however is a standard text and you can likely pick up any pieces you have missed from your subsequent formal abstract algebra education.
as for books for commutative algebra and algebraic topology, you can find recommendations everywhere but often the books are more geared towards reference rather than education, that is to say these books do not have the finesse and motivation of books such as spivak's calculus. thus there is no go to book for these topics, just like how there is no go to book for alot of more advanced mathematical topics.
nonetheless:
for commutative algebra, try macdonald's introduction to commutatitive algebra and eisenbud's commutative algebra: with a view towards algebraic geometry
for algebraic topology I can only recommend Hatcher's algebraic topology, although I have not actually gone through it thoroughly, as it is the only book ive read on the topic. its free online though
>>8146805
For algebraic topology, you're better off with Peter May's Concise Course.
>>8146657
Older books only; nothing with schemes at first. Shafarevich volume 1 is perfect. You should have the equivalent of a first course in ring theory under your belt -- this will suffice for now. You need to be incredibly comfortable working with ideals in polynomial rings. Every so often you will need to reference something in commutative algebra or use some algebraic fact to prove something you're stuck on, so keep a book nearby. Atiyah & MacDonald is very concise and covers a lot of ground. Eisenbud goes very in depth and ties everything back to geometry. If you want anything resembling motivation guiding you, you're going to want to be comfortable with basic notions of smooth manifolds. These are the guiding principle behind most constructions in algebraic geometry. As you get going, complex analysis will also be a crucial guiding hand.
>>8146831
Oh, and if you don't know anything about point-set topology (most of the first few chapters of Munkres) as well, then just fucking quit. You're not ready and you just want to study something you heard was hard.
>>8146766
Rings and ideals are quite a jump for someone who only knows calculus. You're glossing over the ideas of algebraic structures and group theory which lead to constructing ring theory. Maybe not because of the conceptual difficulty but because of the inability to appreciate abstract concepts.
>>8146877
He said Dummit and Foote or Artin for abstract algebra and macdonald for commutative algebra. Read the thread
>>8146671
>In particular the chapter about rings and ideals
Uh, you mean every chapter?
>>8146719
Why take spivak's 3rd edition over his latest?
>>8146914
because as far as I can tell the 4th edition solution manual is not online for free. on the other hand the 3rd edition book and solution manual can be found instantly.
>>8146928
kahn is nice to recap, but bad to learn, at least with math, the problems are too similar.
>>8146921
Also, you didn't seem to put any books on analysis, are those simply optional, or are they included in those works?
>>8146940
That's a shame, I spent 3.5 weeks learning all of the multivariable calculus content on khan academy.
>>8146984
advanced calculus by loomis and sternberg is sufficient work in analysis to begin more sophisticated topics
>>8146928
khan academy will not teach you proofs or heuristics of problem solving or an ability to comprehend the abstract that is all necessary for study in advanced math topics. its purpose was always as a middle school and high school online tutor repository
>>8146995
None of that is wasted you just need more than this to progress in study of mathematics. khan academy is almost exclusively computational, this is not enough, at its core math is logic not number crunching. your previous study will simply accelerate your understanding of analysis on manifolds (multivariable calculus with rigor)
>>8147201
I thought the more intuition based videos that were theory heavy were rigorous.
>>8147201
Yeah... not everything is freely available online, only people who can really learn you proper are b grade State Employees
>>8147683
>not everything is freely available online,
Becoming less true by the year.
>only people who can really learn you proper are b grade State Employees
I hope that's sarcasm. Just buy books.
>khan academy will not teach you proofs or heuristics of problem solving or an ability to comprehend the abstract that is all necessary for study in advanced math topics.
Do you think a "higher-level" alternative is feasible? I've thought about attempting to code a math sandbox that in some sense only allows you to apply algorithms and operations that have been preprogrammed, attempting to avoid the possibility of ever having an incorrect step. Seems like such a system could be modified to be educational for more formal material. Of course, everything I say is bullshit without a proof of concept. And that's part of why I'm asking what other anons think.
>>8147356
If you mean the videos were they explain the idea behind the definite integral and the like, no hardly. What is considered rigorous by khan academy is just a chapter introduction in spivak.
>>8147702
A math sandbox that can verify proof? I think you might make some revolutionary discoveries in AI before that takes off, or rather before it could take off.
