Beginner's foray into Diff Geometry

[tade]

I would like to learn DG so I picked up "Differential Geometry" by Erwin Kreyszig.

I'm finding it too difficult to understand, especially the notation. What books on DG would you guys recommend to beginners?

 

[WannabeNewton]

That book is horrible and extremely outdated. Get O'Neill "Elementary Differential Geometry" or Do Carmo "Differential Geometry of Curves and Surfaces".

 

[theoristo]

My brother loves this book https://www.amazon.com/dp/0471504033/?tag=pfamazon01-20

 

[lurflurf]

What are your goals and background? Differential geometry books with different goals are quite different. Are you most interested in applications to physics, chemistry, biology, engineering, mathematics, or something else?
I would say if you know some topology (or want to learn some) you could go with the John Lee trio
Introduction to Topological Manifolds
Introduction to Smooth Manifolds
Riemannian Manifolds: An Introduction to Curvature

If you like some physical stuffs and know a little calculus and linear algebra a good start would be
Curvature in Mathematics and Physics by Shlomo Sternberg. I have only read a bit of it but the price, quality, and minimal required background make it a good choice for a first exposure.

A supplement of some interest is Riemannian Geometry: A Beginners Guide Frank Morgan

Some times people suggest something like Elementary Differential Geometry by Pressley. I do not care much for that book. It is easier because it is so limited in scope. I do not think time with it is well spent.

Yes old timey books can be challenging due to the notation and approach.

 

[Daverz]

Here's a free online text:

http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

The notation used is the classical notation.

 

[WannabeNewton]

By the way tade, is this for GR?

 

[tade]

By the way tade, is this for GR?

Initially, yes. But I would like to learn DG in general too.

 

[tade]

And preferably something noob-friendly. :tongue2:

 

[WannabeNewton]

Initially, yes. But I would like to learn DG in general too.

Ah ok. That's cool. I was going to say that if this was for GR specifically then most GR texts by themselves offer good introductions to tensor calculus and differential geometry as used in GR. What's your background in math by the way?

 

[tade]

Ah ok. That's cool. I was going to say that if this was for GR specifically then most GR texts by themselves offer good introductions to tensor calculus and differential geometry as used in GR. What's your background in math by the way?

12th grade AP calc.

 

[WannabeNewton]

Ok well you will need to know linear algebra and multivariable calculus first before jumping into either classical differential geometry of surfaces or GR.

 

[micromass]

If your single-variable calculus is good, then I really recommend this book: https://www.amazon.com/dp/0130414085/?tag=pfamazon01-20

It is a solid intro to multivariable calculus, linear algebra and diffential forms. I think it perfectly fills up the gaps that still Lie between you and differential geometry.

 

[tade]

Do you think Gravity: An Introduction to Einstein's General Relativity by James B. Hartle is a good book for noobs?

Though I probably need to finish Hubbard's book first.

 

[WannabeNewton]

If you know LA and Calc 3 then yes, I would highly highly recommend that book. It's brilliant.