Methods of mathematical physics

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• enriquto · Jan 19, 2023 · Recommends

  The classical stuff is great: * Geometry and the imagination by Hilbert and Cohn-Vossen * Methods of mathematical physics by Courant and Hilbert * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on manifolds) * Fourier Analysis by Körner * Arnold's books on…

  on “Ask HN: Math books that made you significantly better at math?” ↗
• enriquto · Jul 3, 2020 · Recommends

  …swim. EDIT: Also, some books by Hilbert are breathtakingly beautiful: Geometry and the Imagination (just the chapter on synthetic differential geometry is worth more than 10 other great books), and the Methods of Mathematical Physics is also great. It begins by giving three proofs of cauchy-schwartz inequality, and then goes on to give several different definitions of the eigenvectors of a matrix. Both of those make great beach…

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• mjreacher · Dec 9, 2022 · Mentions

  …functions, integral equations, calculus of variations, quadratic forms and of course partial differential equations. Hilbert himself actually wrote a textbook with Richard Courant covering these topics: Methods of Mathematical Physics. As such I don't really think many physicists of Einstein's generation knew lots of mathematics simply because it wasn't taught at the time. In the decades since physicists gradually has generally become…

  on “The Sad Story of Heisenberg's Doctoral Oral Exam (1998)” ↗
• jasomill · Nov 16, 2021 · Mentions

  …applications if not in their presentation, as the interplay between pure mathematics and its applications was always an important subject to him (see also the introduction to his [and, nominally, Hilbert's] Methods of Mathematical Physics [4], the address he gave on variational methods in PDEs [5], often cited as a foundational work in finite element analysis, and, well, pretty much the entirety of What is Mathematics?[6]). [1] https://en.wikipedia.org/wiki/Nonstandard_analysis…

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• oddthink · Feb 18, 2020 · Mentions

  Yeah, I have a physics / GR background, so MTW is the lens through which I see all of this. That and Schutz's Geometrical Methods of Mathematical Physics. I agree that we don't need coordinates. Things are things. But what always got me about the geometric algebra stuff was that they used bivectors for areas, which seems like the wrong thing. If you're…

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• hintymad · Jan 19, 2023 · Critical

  For what level and in which area? Books like _Methods of mathematical physics_ can be both too hard and irrelevant to your needs. For starters, To become a better problem solver with high-school level maths: - Polya's How to Solve It. - Books of your choice about math contests.…

  on “Ask HN: Math books that made you significantly better at math?” ↗
• oddthink · Aug 27, 2024 · Mentions

  I always come back to Schutz's Geometrical Methods of Mathematical Physics as my reference for notation, but I agree. I came to this by way of General Relativity, so that colors my perceptions. The few treatments of GA that I've looked at (briefly) weren't very clear about the…

  on “Poor Foundations in Geometric Algebra” ↗