a question about differential geometry

[Al]

As a high shcool student, Which are the branches of math that I have to learn in order to be able to start studying Differential Geometry? Do I need some physics?

Thanks in advance, I ll appreciate any comment.

[Narcoleptic Insomniac]

I haven't taken differential geometry myself. From
the what I've seen, though, you'd at least need a
good knowledge of calculus and linear algebra. Beyond
that, exposure to (real and/or complex) analysis and
topology would be benefical.

In general, I've heard good things about the Schaum's
Outline series:

http://www.amazon.com/Schaums-Outline-Differential-Geometry/dp/0070379858

..I'm sure others will have better references.

However, as a high school student, differential geometry
would probably be a little too advanced at the moment...

but it never hurts to try, and reading ahead will make
things more clear when you come back to them in the
future. ^_^

My suggestion to you would be to spend a good deal of
time right now learning the fundamentals like calculus
and linear algebra.

Good Luck,
Kyle Czarnecki

P.S. You do not need to know any physics, unless of
course you plan on doing physics.

[Joshua Zucker]

> On May 16, 2008 7:35 PM CT, Al wrote:
>

>> As a high shcool student, Which are the branches of
>> math that I have to learn in order to be able to
>> start studying Differential Geometry? Do I need some
>> physics?

Real analysis is probably the most useful prereq. I suppose you'd
also need some calculus on manifolds. Usually calculus and linear
algebra are required for real analysis, and real analysis is required
for manifolds, and then manifolds for differential geometry. Some
topology doesn't hurt but probably isn't required.

I'm sure if you're sufficiently bright you can skip some or all of the
prereqs. But I agree with the advice of mastering calculus and linear
algebra first.

--Joshua Zucker

[Walter Whiteley]

Interesting that a background in geometry is not seen as necessary!

There are a pair of books which will give an introduction which is
more geometric, less analysis.
These are by David Henderson.
His first book is Experiencing Geometry on Plane and Sphere (it has
further editions with varying titles), which explores geometry
through symmetry - but with an underlying flavour of differential
geometry (e.g. how does a bug know it is walking straight, holonomy
on they sphere, ... )
His second book is Differential Geometry. A few chapters overlap.

I agree that linear algebra and calculus are needed to go very far -
but there are ways to approach the subject visually and sensibly.

Walter Whiteley