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Intro Physics What's a good first physics book for a math major?

  1. May 31, 2015 #1
    Dear forum members,

    This is my first post on Physics Forums. I'm very happy to have found this place and to be a member.

    My question isn't very complicated. I'm a math major with a reasonable grasp of the standard undergraduate analysis curriculum (including differential equations and complex functions). But after all this math I would like to learn some (mathematical) physics.

    Of course I could just pick up a book like Sears' and Zemansky's University Physics and then move on to one of the many excellent treatises on mathematical physics. But Sears/Zemansky is rather light on mathematics and very lenghty. Besides, I simply don't have sufficient time and energy to study physics for its own sake. (Something I regret, by the way.) So: does there exist a reasonably concise book that (i) introduces all the important physics concepts from scratch, and (ii) is stimulating reading for math majors?

    The level of mathematics and exposition style used should preferably be comparable to, say, Hubbard's Vector Calculus, Linear Algebra, and Differential Forms (to name a book that I found very enjoyable). Is there such a tome?

    Georg Joos's Theoretical Physics comes close to what I want, but it's still a very hefty read (with lots of stuff that doesn't seem really essential) and perhaps a bit old-fashioned.

    Many thanks for your time and attention!
    Last edited: May 31, 2015
  2. jcsd
  3. May 31, 2015 #2
    Last edited: May 7, 2017
  4. May 31, 2015 #3


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    That's probably the one book not to read, unless one is in the mood for some humour. Spivak's calculus books are great, but in this physics book he goes out of the way to show how difficult easy things are.

    A non-rigourous but terrific book on mechanics is Landau and Lifshitz https://www.amazon.com/Mechanics-Third-Edition-Theoretical-Physics/dp/0750628960. It contains all the key physical ideas, but you have to read every sentence. For introductory mechanics, alternatives are https://www.amazon.com/Introduction-Classical-Mechanics-Problems-Solutions/dp/0521876222 and https://www.amazon.com/Theoretical-Mechanics-Particles-Continua-Physics/dp/0486432610. For mathematical mechanics, one can try https://www.amazon.com/Mathematical-Classical-Mechanics-Graduate-Mathematics/dp/0387968903 or https://www.amazon.com/Introduction-Mechanics-Symmetry-Exposition-Mathematics/dp/038798643X or https://www.amazon.com/Geometric-Control-Mechanical-Systems-Mathematics/dp/0387221956.
    Last edited by a moderator: May 7, 2017
  5. Jun 1, 2015 #4
    Last edited by a moderator: May 7, 2017
  6. Jun 1, 2015 #5
    Thanks for this list of books! I'll definitely look into it, especially Landau & Lifshitz, which I saw on one of my physicist friends' shelf.
    Last edited by a moderator: May 7, 2017
  7. Jun 2, 2015 #6
    Definitely do not get Spivak. He writes calculus books very well, and he has a nice series on differential geometry. But his physics book is definitely not good. I also recommend against learning "physics for mathematicians". You should do physics the way physicists do it, that's the only way to really get it.

    I don't get this. Why are you interested in learning mathematical physics then? It's going to be rather useless if you don't know the actual physics too.
  8. Jun 2, 2015 #7


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    Well, this just goes to show one should not use illegal free books from the internet. Probably so few people bought Spivak's books that he's too poor to get himself a copy of Kleppner and Kolenkow.
  9. Jun 2, 2015 #8
    (Thanks for your reply!)

    Because I enjoy the kind of mathematics used in mathematical physics. The more direct reason is that I'm currently reading Peter Szekeres's A Course in Modern Mathematical Physics, mainly as a preparation for more advanced courses. I think it's a great book. And as far as the mathematics is concerned I'm having a lot of fun with it. But I'm rather frustrated by not really understanding the physical portions of the book (Chapters 9 and 14 for example).

    Of course I realize that many people who like physics would object to learning the subject as merely an "afterthought". However, given the constraints of time and opportunity, one has to prioritize. My goal isn't to become a physicist (or even a mathematician specializing in mathematical physics or physical mathematics or whatever), but rather to gain a basic acquaintance with the concepts, so as not to be totally in the dark about the physical motivation behind the mathematics used.
  10. Jun 2, 2015 #9

    George Jones

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    With respect to chapter 9 of Szekeres, I recommend "The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of Special Relativity" by Naber,


    Decades ago, when I had more time and energy, I read this book cover-to-cover, and I really enjoyed it.

    With respect to chapter 14, there is "Quantum Theory for Mathematicians" by Hall,


    This looks to be a good book, but it is longer and more difficult than Naber's book on special relativity, and it omits some of the most interesting bits of quantum theory, e.g., entanglement.
    Last edited by a moderator: May 7, 2017
  11. Jun 3, 2015 #10
    Thanks! I'll certainly give both of these a try.
    Last edited by a moderator: May 7, 2017
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