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I am an undergraduate, studying physics. I have studied maths courses like Groups, Linear Algebra, Real analysis, Differential geometry and probability. I wish to get into mathematical physics, similar to what Arnold's book has to teach. But i find it a really difficult read since it's a graduate text in mathematics. Can anyone suggest me what stuff do i need to study before getting a good intuitive picture of Arnold's book. Or any resources that provide a road map, intuitive picture of the maths used in physics.

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  • $\begingroup$ Question seems more appropriate for Academia community. It is not really about physics. $\endgroup$
    – Roger V.
    May 27, 2023 at 12:41
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    $\begingroup$ @RogerVadim I think this question is only for people interested in Physics and reasonably fits with the possibility of asking for resources. $\endgroup$ May 27, 2023 at 15:38
  • $\begingroup$ I didn't feel the book was that difficult, I feel that it would actually be seen as trivial with someone who has a background as you've described. Are you sure you spent enough time with the fields you mentioned? $\endgroup$ May 28, 2023 at 3:57
  • $\begingroup$ @HopefulWhitepiller I didn't get to go in much depths of the subjects. We had a one semester course for each of the above. Wasn't too rigorous though. $\endgroup$
    – Rice Field
    May 28, 2023 at 5:24
  • $\begingroup$ Eh, then I'd say just read it and ask as you get difficutlies. If it's too hard, find an easier book. Focusing on the preq-requisites too much is not useful $\endgroup$ May 28, 2023 at 5:47

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It is difficult to answer if the question is how to make intuitive the content if that book. The point is that, the goal of that book is just to make rigorous some important arguments and topics of classical mechanics.

A form of mathematical-physics intuition can be developend only after one managed to rigorously deal with all that mathematical formalism.

To be completely frank, that book is not completely rigorous from a strict mathematical perspective, because it avoids some mathematical subtleties which do not enter the physical reasonings. However, Arnold's viewpoint is mathematical not physical.

From your post it seems that you are already familiar with all mathematical tecnology necessary to understand the book. Maybe a more physically minded perspective is necessary.

My suggestion is to try to get acquainted with basic constructions of elementary differential geometry but from a physically oriented point of view. Maybe by reading Arnold's book simultaneously to a well written, physically minded, mathematical text on differential geometry. There is a useful book by von Westenholz entitled something like "differential forms for mathematical physics".

I found it very useful when I was student, though it has some defects (as incomplete proofs).

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  • $\begingroup$ Thank you for the reply. I will look into the book by von Westenholz. $\endgroup$
    – Rice Field
    May 27, 2023 at 12:48
  • $\begingroup$ This review ( ams.org/journals/bull/1979-01-06/S0273-0979-1979-14697-4/… ) that appeared in the Bulletin of AMS does not look very encouraging. $\endgroup$ May 27, 2023 at 15:43
  • $\begingroup$ The (relatively recent) book by Godinho, Natario is nice. This book filled in some nagging issues I’ve had since studying Landau-Lifshitz. Though, it should be noted that this only treats physics in the last 2 chapters (but very clearly, with instructive exercises and also has some partial solutions, so it’s great (if used wisely) for students self-studying). $\endgroup$
    – peek-a-boo
    May 27, 2023 at 18:39
  • $\begingroup$ @GiorgioP yes it is not very encouraging, but it is because the review is written from the viewpoint of a rigorous pure mathematician. My impression is that it is a good text for passing from elementary mechanics to a more advanced formalism. $\endgroup$ May 27, 2023 at 20:16
  • $\begingroup$ (My book on analytical mechanics, the English version, is in print) $\endgroup$ May 27, 2023 at 20:18

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