Re: prerequisite to Differential Geometry

On Sat, 07 Jul 2007 09:20:37 -0400, vartkar@xxxxxxxxxxxxx wrote:

Stephen:
The reason I want to learn differential geometry is that I am trying
to pave the way to studing general relativity. So you are saying
that if I am on sold ground with linear algebra and multivariable
calculus, the book "Calculus on Manifolds" by Spivak should provide me
with the rest of the preparation to differential geometry?

Saghatiel

On Fri, 06 Jul 2007 22:54:56 -0400, "Stephen J. Herschkorn"
<sjherschko@xxxxxxxxxxxx> wrote:

vartkar@xxxxxxxxxxxxx wrote:

Could someone tell me what are the prerequisites to differential
geometry.
Is it just plain geometry and differential equations?



It depends at what level you will be studying it, and with which
textbook. At the undergraduate level, you might just need a could
multivariable course. Linear algebra would help. Really nothing else
was a prerequisite for my undergraduate course, which used the text by
Millman and Parker, though some topology and real analysis might help.

For a graduate level course, you certainly need topology and analysis.
Algebraic topology (for which you need some abstract algebra) would help.

You do not need differential equations anywhere, really. And I agree
with quasi that physics might provide motivation for some of the subject.

However, I respectfully disagree with quasi when he mentions

Differential Equations
Abstract Algebra
Tensor Analysis
Complex Analysis
Modern Geometry (especially Non-Euclidian geometry)
Lie Groups & Lie Algebras


Differential equations don't show up much, if at all. My impression is
you need only a few basic concepts from abstract algebra and complex
analysis; if you haven't seen these before, you can pick them up along
the way. I consider vector analysis included in multivariable
calculus. You will learn what you need of the rest in the course of
studying differential geometry.

Most of the calculus, analysis, topology, and linear algebra you will
need for a first course is contained in Spivak's Calculus on Manifolds.
.

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