How to find suitable exercises to practice on (in physics geometry) ?

[camel_jockey]

I am currently studying geometry and topology (with applications in physics) from the books

T. Frankel "The Geometry of Physics"

and

M. Nakahara "Geometry, topology and physics"

Both these books work pretty fast up to a sophisticated level, and I am lacking in practice. I can easily read the beginning chapters, but then when these concepts and tools are applied in later chapters - I see that I lack familiarity with the details, calculations and intuition with these objects.

So I was wondering if someone would be kind enough to recommend a good source of EXERCISES WITH SOLUTIONS in these fields, aimed at physicists. I am not completely without mathematical competency, so the occasional pure-proof derivations and proof-exercises wouldn't hurt either.

The exercises in these books are quite awful and useless, and lack solutions. SOME examples are worked through in the text, but many of the more basic things (like giving concrete examples of vector fields, pull-backs and diffeomorphisms etc) are ignored. Although I am in general very appreciative of these books, I would like to complement with something that has 1) more exercises 2) easier exercises, of "drill" type and 3) covers many topics.

Many thanks my fellow physicists :D

 

[MathematicalPhysicist]

I am not sure if I know similar textbooks like Nakhara with solutions to its exercises.

But if you want textbooks with solutions in the sepcific topics of differential geometry, GR and QFT, there are textbooks like Maggoire's QFT and some professor from Oxford Springer edition GR (both have solutions and hints to problems in them), and for differential geometry there's the textbook by O'neal (not sure about my spelling).

Most advanced textbooks such as Nakhara's don't include solutions and rarely even hints, it's really rare to find advanced textbook which include solutions.

 

[quantumkiko]

I suggest "Classical Mathematical Physics" by Walter Thirring.
https://www.amazon.com/dp/0387406158/?tag=pfamazon01-20

The book is dense but makes up with the rigor by providing lots of diagrams and examples. It contains problems and solutions to all the problems. Pretty amazing book if you ask me. ^^

You can also try the latter part of "Mathematical Physics: A Modern Introduction to its Foundations" by Sadri Hassani. I'm specifically talking about parts 7 and 8 ("Groups and Manifolds" and "Lie Groups and Their Applications" respectively). The book is laden with end-of-chapter problems that are less sophisticated than Nakahara's.

https://www.amazon.com/dp/0387985794/?tag=pfamazon01-20

Goodluck! =)

 

[George Jones]

Have a look at Differential Geometry and Lie Groups for Physicists by Marian Fecko,

https://www.amazon.com/dp/0521845076/?tag=pfamazon01-20,

and at the review

http://www.cap.ca/BRMS/Reviews/Rev857_554.pdf

of this book.

This is still a tough go, and will not be everybody's cup of tea.

 

[camel_jockey]

Wow, thank you so much!

It is true that most books at the level of Nakahara don't have many problems, exercises let alone solutions.

What I was hoping on was that somewhere on the internet there would be a good source from some professors course, some researcher's note or some PDF, or past exam papers with solutions.

Again, thanks a lot!

 

[Sara Oal]

Hi,

Could you help me with the Geometry ,''the same book'' in case you have found useful Pdf's or may be yours notes.I have started the Geometry this year and it seems exactly as you said.

Thanks in advance

Sara