What books would you recommend to learn physics, being a a Math major, from classical mechanics, electricity, etc. to modern physics?
If you want a solid and consistent approach to physics from the theoretical point of view (I assume that as a mathematician you don't want an experimentalist's point of view) then you can't go past the series by Landau and Lifshitz - "Course of Theoretical Physics" (Amazon).
- The Classical Theory of Fields.
- Quantum Mechanics: Non-Relativistic Theory.
- Relativistic Quantum Theory.
- Statistical Physics.
- Fluid Mechanics.
- Theory of Elasticity.
- Electrodynamics of Continuous Media.
- Statistical Physics, Part 2.
- Physical Kinetics.
Michael Spivak gave me a small volume he wrote on mechanics from the mathematicians perspective, and he is said to be preparing to release a longer book on physics explicitly for mathematicians. In the meantime you might like Max Born's Atomic Physics. I myself enjoyed, and learned from, at least looking at J.C.Maxwell's E&M.
I will assume you are getting started - once you finish the equivalent of the first year of calculus-based physics, then you should dig in / branch out depending on your interests (optics, dynamics, modern physics - i.e. 20th century - E&M, etc.)
For an overview of it all, I recommend the Feynman Lectures on Physics, supplemented liberally with any of the solid textbooks (such as the following) and I suppose some Wikipedia. I like the Feynman lectures because they are entertaining, conversational, and provide a great insight into physics. Here are some example introductory texts - I can personally vouch for HLR.
- Fundamentals of Physics - Halliday, Resnick, & Walker. Link is to current edition, but this is the book that many of us have used for decades, including myself at a small liberal arts school. It's also the book used at Stanford. I think you can use any edition from the last 10-20 years...
- Physics for Scientists and Engineers - Serway and Jewett (CalTech's intro book)
- University Physics - Young, Hugh, Ford and Freedman (one of MIT's intro books)
Frankly, I recommend you go to the syllabus of the introductory, calculus-based physics from a school you respect and select that textbook as a reference.
I did a physics major as an undergraduate, in addition to my studies in mathematics and engineering. I still find that the first year's material is the most useful content, although I think that the concepts covered in introductory Modern Physics courses are really cool. If you are interested, in addition to the Feynman lectures that I have read on the side, I was quite impressed with the text we used: Modern Physics - Serway, Moses, Moyer. While remaining very readable, it provides more of a textbook approach, whereas Feynman is a lecture style.
I started in math as an undergrad (topology/geometry) and then went into physics for grad school. I know your pain... :) Most of the books people have suggested already are excellent works that provide physical intuition and if you're going to do some physics for real then make sure you read 'em. That said, most of what was mentioned does NOT present stuff the way a math guy likes so -- assuming you are a junior or senior in a math undergrad program -- my recommendations are,
For geometry and dynamical systems as applied to Classical Mechanics:
- Classical Dynamics: A Contemporary Approach Jorge V. José (Author)
For (functional) analysis applied to Quantum Mechanics:
- Quantum Mechanics in Hilbert Space: Second Edition (Dover Books on Physics) [Paperback] Eduard Prugovecki (Author)
For Lie Groups and using them like a physicist:
Lie Groups for Pedestrians [Paperback] Harry J. Lipkin (Author)
Lie Algebras In Particle Physics: from Isospin To Unified Theories [Paperback] Howard Georgi (Author)
For understanding quantum and path integrals:
Quantum Mechanics and Path Integrals Richard P. Feynman (Author), Albert R. Hibbs (Author), Daniel F. Styer (Author)
Modern Quantum Mechanics (Revised Edition) [Hardcover] J. J. Sakurai (Author)
You gotta understand rotation stone cold:
Rotations, Quaternions, and Double Groups [Paperback] Simon L. Altmann (Author)
The Theory of Spinors by Elie Cartan
Clifford Algebras and Spinors (London Mathematical Society Lecture Note Series) by Pertti Lounesto
And differential forms are required:
- Differential Forms with Applications to the Physical Sciences [Paperback] Harley Flanders (Author)
For general relativity:
Gravitation (Physics Series) [Paperback] Charles W. Misner (Author) Kip S. Thorne (Author) John Archibald Wheeler (Author)
Advanced General Relativity (Cambridge Monographs on Mathematical Physics) [Paperback] John Stewart (Author)
For stat mech:
- Equilibrium Statistical Physics (3rd Edition) [Paperback] Michael Plischke (Author) (Author), Birger Bergersen (Author)
and for a final one-shot book that tries to hit everything under the sun:
- The Geometry of Physics: An Introduction, Second Edition [Paperback] Theodore Frankel (Author)
- Kleppner/Kolenkow's An Introduction to Mechanics
- David Morin's Introduction to Classical Mechanics
- Purcell's Electricity and Magnetism
- A.P. French's Principles of Modern Physics
These books have more math than the typical introductory physics textbooks. But they also introduce the "physicists" way of thinking (e.g. how to gain physical intuition).
I would suggest the following books in addition to several good recommendations above :
1.) Classical Dynamics : A Modern Perspective by E.C.G. Sudarshan and N.Mukunda . You may like Arnold's book mentioned above.
2.) For Quantum Mechanics, I would recommend Merzbacher's and Weinberg's books in addition to Sakurai's book suggested above.
3.) Advanced Classical Field Theory by G. Sardanashvily,G.Giachetta,L.Mangiarotti. This requires lots of mathematical prerequisites. A lighter introduction to some topics would be 'Gauge theory and variational principles' by D. Bleecker
4.) General Relativity by R. Wald