Book recommendations on geometrical methods for physicists

[Joker93]

Hello,
I would like to obtain a book that has to do with geometrical methods/subjects for physicists. When i say geometrical methods/subjects i mean things like Topology, Differential Geometry etc.

Thanks!

 

[ShayanJ]

https://www.amazon.com/dp/0750306068/?tag=pfamazon01-20

https://www.amazon.com/dp/0521298873/?tag=pfamazon01-20

https://www.amazon.com/dp/1107602602/?tag=pfamazon01-20

 

[NumericalFEA]

Differential geometry is a huge subject; different branches of physics use different parts of that subject. There is a variety of books covering this topic, as stated by one of our colleagues above. In case if you are looking for really working algorithms and software implementing methods of differential geometry for physical problems, they are hard to come by. Are you looking for such practical sources ?

 

[The Bill]

Burke's Applied Differential Geometry and Baez & Munian's Gauge Fields, Knots and Gravity are good "extra" texts to have for what you're looking for, because of their insightful treatments of the material they cover.

 

[Joker93]

Differential geometry is a huge subject; different branches of physics use different parts of that subject. There is a variety of books covering this topic, as stated by one of our colleagues above. In case if you are looking for really working algorithms and software implementing methods of differential geometry for physical problems, they are hard to come by. Are you looking for such practical sources ?

No, i want to learn the underlying mathematics with some applications(which do not use algorithms and stuff)

 

[Joker93]

Burke's Applied Differential Geometry and Baez & Munian's Gauge Fields, Knots and Gravity are good "extra" texts to have for what you're looking for, because of their insightful treatments of the material they cover.

Why did you add the word "Extra"? One can not learn by only using those books?

 

[The Bill]

Why did you add the word "Extra"? One can not learn by only using those books?

Because they aren't as comprehensive as the books I'd recommend as primary sources for learning modern differential geometry, and their pedagogy is aimed in a different direction.

For primary books, I'd recommend John M Lee's three textbooks on manifolds. Topological, then Smooth, then Riemannian.

 

[Joker93]

Because they aren't as comprehensive as the books I'd recommend as primary sources for learning modern differential geometry, and their pedagogy is aimed in a different direction.

For primary books, I'd recommend John M Lee's three textbooks on manifolds. Topological, then Smooth, then Riemannian.

But going through three books will be very time depleting, especially for self study. The reason that i want a book on these subjects that is aimed at physicists is because physicists only learn the stuff that they need, so i would conserve time by reading a book like that. Otherwise, i would learn those subject in the deepest way, in a way that might contain your three books.

 

[ShayanJ]

But going through three books will be very time depleting, especially for self study. The reason that i want a book on these subjects that is aimed at physicists is because physicists only learn the stuff that they need, so i would conserve time by reading a book like that. Otherwise, i would learn those subject in the deepest way, in a way that might contain your three books.

All the books I mentioned are famous in their class and are usually recommended. But I think Schutz's is more proper for you.

 

[micromass]

You can't have it both ways. Either you learn the underlying mathematics, which will take several books. Or you take the physicists approach which will teach you how to teach the computations but not the underlying math.

 

[jbergman]

I'd recommend Tu's Introduction to Manifolds and then his Differential Geometry book. Lee's books are the best but they are pretty exhaustive. Tu's are much more streamlined, and, IMO, clearer and you can probably learn 80% of what is in Lee's books.

 

[jbergman]

I would also recommend Barrett's Semi-Riemannian Geometry. The nice thing about that book is that it deals with the Geometry of General and Special Relativity. It also covers much of what is in Lee's and Tu's books but at a much more rapid pace.