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I realise that this question has been asked many times before, but none of those could answer my situation, so here I am.

I am a high school student with a keen interest in mathematics and physics. I want to be a mathematician and as such I have studied some undergraduate books on mathematics. I am listing my background in maths and physics.

I am very comfortable with calculus, both single variable and vector calculus. I have also read some calculus of variations, but I am not very good at it. I have studied linear algebra at the level of Hoffman and Kunze, and also some abstract algebra at the level of Serge Lang’s undergraduate algebra. I have also studied geometry, Euclidean, affine and projective from Brannan’s book ( I don’t have a very in depth understanding of affine or projective geometry however, just what is written in Brannan’s book ) However I do not have any experience with analysis or topology or differential equations ( I only know how to solve first order homogeneous differential equations ) or manifolds and other advanced stuff.

As of physics, I have studied classical mechanics roughly at the level of the freshman course in any American university.

I am now interested in deep diving into classical mechanics. I want to understand it from a mathematician’s perspective, in a rigorous manner. I have read ( at least tried to ) the typical recommendations for it, such as Spivak’s physics for mathematicians, or Arnold’s mathematical methods, and even Goldstein’s book and Landau. However, I found all of these to be too advanced for me, and as such I couldn’t really understand them.

Also, please do not recommend Taylor or Morin, as I have read those and I found them pretty easy to go through, but they don’t address the subject in the same way I want - in a rigorous and mathematical manner.

So, my question is this:

  1. Assuming that I have enough background in math and physics, which book do you think would be best suited for me?

  2. If I do not have enough background, then what do you suggest the path for me moving forward should be?

Any answer is highly appreciated.

Qmechanic
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Srinidhi kabra
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1 Answers1

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The most approachable is "Mathematical Methods of Classical Mechanics" (Graduate Texts in Mathematics, Vol. 60) by V. I. Arnold.

More advanced (at least notationally) is "Foundations of Mechanics" by Ralph Abraham and Jerrold E. Marsden.

Another book that goes from undergrd to research level is "Symplectic Techniques in Physics" by Victor Guillemin and Shlomo Sternberg

mike stone
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