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What books would you recommend to learn physics, being a a Math major, from classical mechanics, electricity, etc. to modern physics?

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This might be a better place for your question... –  J. M. Dec 30 '10 at 5:05
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This might be too: phys.uu.nl/~thooft/theorist.html –  timur Dec 30 '10 at 7:31
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I think the question is on-topic but should be clarified: lots of people study both math and physics at the undergraduate level. When you say "being a Math major", do you mean that you want books that take a more mathematically rigorous approach than most books written by physicists, or just that you know some mathematics beyond calculus so you can handle more math-intensive treatments? (Or something else?) –  Pete L. Clark Dec 30 '10 at 9:18
    
Yes, I want books that take a more mathematically rigorous approach. –  Jacques Dec 30 '10 at 16:10
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I actually suggest that to learn physics you take an advanced lab course or two! I think that if you approach theoretical physics like a mathematician you will not properly develop your physical intuition. That being said, the best books in my opinion for your purpose are the Landau series, especially books 1,2,3, and 5. Also see the three volume Feynman lectures. –  Matt Calhoun Dec 30 '10 at 17:31
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6 Answers 6

As for mechanics I'd recommend:

Stefan Banach - Mechanics (1951)

Arnold VI - Mathematical Methods of Classical Mechanics

I also recommend Griffiths books:

Griffiths - Introduction to Electrodynamics

Griffiths - Introduction to Quantum Mechanics

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+1 for Arnold's Mathematical Methods of Classical Mechanics –  Simon Dec 30 '10 at 11:52
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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).

  1. Mechanics.
  2. The Classical Theory of Fields.
  3. Quantum Mechanics: Non-Relativistic Theory.
  4. Relativistic Quantum Theory.
  5. Statistical Physics.
  6. Fluid Mechanics.
  7. Theory of Elasticity.
  8. Electrodynamics of Continuous Media.
  9. Statistical Physics, Part 2.
  10. Physical Kinetics.
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Old but definitely worth reading. It's a kind of Feynman lectures at a higher level. –  Raskolnikov Dec 30 '10 at 12:38
    
I think these are great textbooks on physics, but I wouldn't recommend them to someone who wants to start learning physics, even if he is a math major. –  becko Dec 30 '10 at 16:14
    
Landau-Lifshitz is great but somehow dated (For example no manifold is mentioned and it uses index notation for tensors). Thirring's 4 volumes seem to be more modern and I heard that in some way can replace Landau-Lifshitz. Please comment if anyone knows how close it is to the truth. –  timur Dec 30 '10 at 17:03
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These are some of the most elegant books ever written on the subject of physics. –  Zach Conn Dec 30 '10 at 18:48
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@timur - they are a little dated, but still more modern than most uni physics courses. It would be good for a math major to see and use index notation - too many have a unhealthy disrespect for it! I haven't read Thirring... –  Simon Dec 30 '10 at 23:03
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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.

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The first volume of Spivak's "Physics for Mathematicians" is already available, actually. –  Zhen Lin Dec 31 '10 at 9:49
    
Here's a link for a set of lectures of Spivak called Elementary Mechanics from a Mathematician's Point of View: math.uga.edu/~shifrin/Spivak_physics.pdf –  becko Dec 31 '10 at 22:21
    
Great! Did anyone here read Spivak's book? I like the way he writes. –  Jacques Dec 31 '10 at 23:57
    
Sounds promising. I love Spivak's other books. –  John D. Cook Jan 2 '11 at 3:23
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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.

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.

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For math rigor, I agree with the Landau & Lifshitz recommendation (which I gave +1), but I will leave this answer for others interested in a general treatment of physics. Feynman is not lacking mathematics, but it is not as rigorous. I also used both Griffiths books (E&M and quantum) and those are great. For optics consider Goodman or Gaskill - I prefer the latter, but it may be more of an EE/controls style than a math style. –  sage Dec 30 '10 at 17:08
    
My impression was that Goldstein ans Jackson were The standard textbooks for mechanics and electrodynamics, respectively. No one mentioned them here so are they not that popular after all? –  timur Dec 30 '10 at 17:15
    
I recommend avoiding University Physics by Young et al. It's not a bad book, but it's very much a heavily marketed textbook, meaning it lacks elegance and beauty and is overshadowed by other books for self-study (e.g., Landau and Lifshitz). University Physics is analogous to those massive tomes used in freshman calculus classes; L&L is analogous to Spivak's Calculus books. –  Zach Conn Dec 30 '10 at 18:55
    
I'm not as familiar with Goldstein, but Jackson is one of the strongest books on E&M and is very well known. Griffiths is popular with some professors (and I liked him) because he is more accessible. As one well-written review on Amazon (by 'Reviewer') puts it, Griffiths's E&M is "a foundation that will give [undergraduate juniors/seniors] the experience and confidence to eventually tackle more difficult texts like Jackson". –  sage Jan 1 '11 at 20:26
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  • 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).

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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)
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