Physics books for a pure math student

[Gingia]

Hi all; firstly, I thank all of you who respond to my question in advance.

I'm a mathematics student with an advanced undergraduate background in most of what's associated with 'pure math', and my particular interest is in mathematical logic. I'd really like to teach myself physics - I have taken a year's worth of university physics and I did quite well; however, I feel as if I didn't really learn very much at all beyond how to manipulate particular formulas, as the course was generally populated by pre-med students and thus geared more towards rote memorization than understanding.

Unfortunately, I haven't the credit-space to take more advanced courses in physics, so I'm hoping I can teach myself some.

I would like some book recommendations - ideally I'd like to 'do over' the material I covered in my year of physics and start from scratch. So this means something that would constitute a 'first course in physics', except taught in a way that assumes a relatively strong (in undergraduate terms) mathematical background. After I get my way through this first material, then I'd like to approach modern physics, although I do have some of the requisite mathematical background in differential geometry, abstract algebra, etc.

What books would you recommend?

Thank you all very much.

 

[marcusl]

Take a look at vol. 1 (Mechanics) of Landau and Lifgarbagez's course in theoretical physics. They assume a reasonably high degree of mathematical sophistication, are rigorous, and provide beautiful insight into physics principles.

If you like it, subsequent volumes will take you as deeply into physics as you care to go.

 

[Gingia]

Thanks very much!

After reading the first few pages of 'Mechanics' online, this series of books looks perfect. Thanks a lot!

 

[Frimus]

Another hint: Take a look at https://www.amazon.com/dp/1441930876/?tag=pfamazon01-20 by V.I. Arnol'd. You may see from reviews whether it matches to your needs.

 

[Daverz]

If you want some insight into how physicists think, I'd start with the Feynman Lectures. The Landau series is also a good recommendation, but requires much more than Freshman physics.

 

[qspeechc]

Spivak has recently released his first book in the series of physics for mathematicians, which covers mechanics:
https://www.amazon.com/gp/product/0914098322/?tag=pfamazon01-20
I haven't read it though.

You may want to look at physics books written by applied mathematicians. V.I. Arnold is one such author. There's also Jerrold Marsden, John Baez...eh, can't think of any others, sorry.

Just looking around on amazon.com I found "Geometry, Topology and Physics" by Nakahara, and "The Geometry of Physics" by Frankel.

None of these books are at an elementary level, though, so you may just have to start with ordinary physics books.

 

[yenchin]

For general relativity, you may want to read:
https://www.amazon.com/dp/0125267401/?tag=pfamazon01-20

And since you have some knowledge in differential geometry, this should not be a hard read.

 

[Gingia]

Thanks very much for the recommendations, everyone.

@qspeechc: I should have been more specific, sorry about that. What I meant by 'starting from scratch' was to go over the material I already knew from elementary physics texts and courses more rigorously. Thanks for the recommendations!