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I know most of a standard US undergrad math degree - multi-variable calculus, real and complex analysis, point-set topology, basic abstract algebra, etc. etc. I know very little about physics beyond F=ma, but I want to learn the basics.

I have found any "introductory" book I look at bothers me for a few reasons:

  • It is written in typical non-serious "American college freshman textbook" style - lots of colorful, distracting sidebars and boxes, links to online exercises, pop science digressions, motivational speeches about how cool it is to be learning physics, etc. Many dozens of extremely easy exercises after every section, when I would have gotten the point after two or three and wanted something more deep/challenging.

  • It assumes the reader is learning basic mathematics at the same time as physics, so it spends way more time than I need explaining concepts like vectors, derivatives, integrals, linear transformations, etc.

On the other hand, any more advanced book I looked at assumes prior physics knowledge.

Does anyone have any recommendations that do not suffer from these flaws?

(For the purposes of this question, let's define "basic physics" as things that were discovered before the year 1900).

Qmechanic
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Brennan Vincent
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    Try an older introductory book, like Halliday, Resnick, and Krane (5th edition). It doesn't have the extra distractions you talk about, and it has a few neat problems. You could also go with the 'honors-level' introductory books, such as Kleppner and Kolenkow (mechanics) plus Purcell and Morin (E&M). These will all introduce some basic math, but it's not hard to skim over. – knzhou Dec 20 '18 at 01:35
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    There are also books aimed at the pure mathematician, such as Spivak's Physics for Mathematicians, but I've generally found that mathematicians educated exclusively by these books cannot answer even the simplest questions about the real world, which is presumably the point of learning physics. It is certainly clear and precise, though. – knzhou Dec 20 '18 at 01:36
  • @knzhou thanks for the recommendations. I will take a look.

    As for "physics for mathematicians" -- first of all I am not a mathematician; I just know some basics :). Second, I am interested in knowing physics for its own sake. I don't want something that is just a bunch of theorems for the sake of doing math -- on the other hand, I don't need to read 10 pages about what dot products are :)

     – Brennan Vincent Dec 20 '18 at 01:38
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    I second the recommendation for Kleppner and Kolenkow. And, of course, the Feynman lectures, although these have no exercises. – d_b Dec 20 '18 at 01:40
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    https://manyebooks.org/download/theoretical_physics_georg_joos.pdf. perhaps have a look at this, it's old but covers far more physics than maths. I agree with the comments above, you will need an old book –  Dec 20 '18 at 01:46
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    Landau and Lifshitz if you are a bit masochistic... – Jon Custer Dec 20 '18 at 01:59
  • I want to recommend The Feynman Lectures. As far as I recall, the treatment doesn't emphasize mathematical manipulation but qualitative understanding. On the other hand, I'm not sure how completely they cover the usual frosh/soph material, since I never read them through. – The Photon Dec 20 '18 at 02:32
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    I generally will always recommend any of Morin's writing, especially his mechanics book and E&M one with Purcell. – Aakash Lakshmanan Dec 20 '18 at 03:08
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    Related: A soft introduction to physics for mathematicians who don't know the first thing about physics – Alfred Centauri Dec 20 '18 at 03:20
  • I think V. Arnold's book "Mathematical Methods of Classical Mechanics' could be quite illuminating. He covers Newtonian mechanics, then moves to Lagrangian, and finally to Hamiltonian mechanics. Alongside examples of physical systems he also talks about how these topics link with manifold theory, vector fields, forms, symplectic geometry and so on. He sketches the theory without too much detail and nitpicking. Uses relatively abbreviated notations, so you may have to "unpack" some of them if you feel uncertain about the details. – Futurologist Dec 20 '18 at 03:22
  • Tune into Dr. PhysicsA (Pr. Bob Eagle) on youtube, you won't need a book. – PhysicsDave Dec 20 '18 at 05:33
  • https://www.google.com/url?sa=i&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjHpP-Bl6_fAhXvqIsKHXV-AHAQjRx6BAgBEAU&url=https%3A%2F%2Fwww.amazon.com%2FSolutions-accompany-Mechanics-Berkeley-Ruderman%2Fdp%2FB0007H2R6Q&psig=AOvVaw1uIMDxd0HrKQeNbxMynU-e&ust=1545421807568889 – Žarko Tomičić Dec 20 '18 at 19:50
  • This res. recom. post (v1) is too broad topic-wise to be allowed on Phys.SE. – Qmechanic Dec 20 '18 at 20:03

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Honestly, I think that the Yale Courses found here is really a great serious introduction to physics. Prof. Shankhar expects a lot from his students, and has fantastic lectures. The link contains problem sets and solutions (which are also very instructive), and you really don't need a textbook to follow them. Just sit down, take notes and take the course seriously.

InertialObserver
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