Geometry, topology, and physics

What Hacker News says

1. senorcrabJan 2026
   Freshman university textbooks have what you need. Two of the most popular are:

   - University Physics by Young and Freedman

   - Fundamentals of Physics by Halliday, Resnick, Walker

   - Modern Physics by Krane

   You might guess that real physics is not actually in freshman textbooks, and you are right. Modern physics requires rigorous mathematics.

   For a nonrigorous introduction/overview:

   - The Road to Reality by Roger Penrose

   If you want to actually learn almost all of physics at a high level:

   - Course of Theoretical Physics by Landau

   Note that Landau is extremely difficult.

   If you want to learn the math needed for modern physics (topology) in the context of physics, nonrigorously:

   - Geometry, Topology, and Physics by Nakahara

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2. tMcGrathAug 2018
   I think the standard reference is probably Spivak's 'Calculus on Manifolds' but this never really did it for me.

   If you have a background in physics then some combination of Nakahara's 'Geometry, Topology and Physics' and Baez and Muniain's 'Gauge Fields, Knots and Gravity' might be good (I haven't included relativity textbooks as I assume it you have a background in GR then you have enough differential geometry).

   An unusual recommendation that I think is really nice is 'Stochastic Models, Information Theory and Lie Groups' by Chirikjian. It covers a few other topics mentioned in this thread and is really nice. It's _extremely_ concrete and spells out a lot of calculations in great detail. Plus, the connection to engineering applications is much more obvious.

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