Hey /sci/
What are the prerequisites or math I need to understand to get into learning differential geometry? Also what are some good text books for self teaching?
>>8163135
Differential equations and geometry.
...
Yup.
>>8163135
Multivariable calculus and linear algebra.
>>8163152
Diff eqs aren't that important. You only need to know that if everything is sufficiently well-behaved, then the equation has a unique solution.
>>8163153
Thanks! I just finished calc 1, do I need to go all the way up to multivar to understand linear algebra?
Why don't you crack open a textbook and find out
>>8163154
Is that so? I just started diff eq after finishing linear algebra...
>>8163135
It depends on the type.
Curves and Surfaces:
- Vector Calc and Linear Algebra should be fine.
Manifolds/Riemannian (at like the level of Lee/doCarmo):
- Need Topology too
Riemmanian (at the level of like Jost)
- PDE theory
>>8163156
>pick up a book on linear algebra
>read the preface
>learn what the author expects
>if it seems okay, read until you realize you don't have the background
Jesus Christ, fucking do something for yourself
Topology, multivar calculus, linear algebra, some understanding of diffeqs (but, as a person who works in complex geometry I can assure you that you do not need to stress this bit, a lot can be found in appendices of differential topology books). Aside from this you need some mathematical maturity.
>>8163159
diff eq is fun unless you're some kind of cuck
>>8163158
This.
Every fucking textbook ever lists the prereqs in the fucking preface.
>>8163189
>mathematical maturity
Buzzword.
>>8163208
Guess who doesn't have it?
>>8163232
you
>>8163156
No, only algebra of school.
What linear algebra book you recommend?
>>8163208
What perspective are you saying this from? What are your "highest" math courses?
>>8163333
I'm saying this from the perspective that "mathematical maturity" is only used by professors in a very loose and egotistical way to say "oh, you are roughly able to use the same symbols and techniques I can also use", it doesn't mean anything, there is no point where you can say one student is mathematically mature or not if he has a background in X and Y. You either have a background in something or you don't, you have either studied a research topic in depth or you haven't.
You wouldn't use terms like "chemically mature" to describe more advanced chemistry students.
>
2 semesters of abstract algebra, 1 sem algebraic toplogy course, 1 sem complex + 2 sem real analysis.
