Comprehensive Introduction to Differential Geometry
by Michael Spivak · first published 1970
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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 ODE, PDE and mathematical physics are breathtakingly beautiful. * The shape of…
on “Ask HN: Math books that made you significantly better at math?” ↗…For example, I struggled with the traditional presentation of multivariable calculus in terms of "physically meaningful" differential operators until working through the first couple books of Spivak's Comprehensive Introduction to Differential Geometry after-hours, at which point everything sort of clicked. Had my intro (college) calculus course not coincidentally been taught by a differential geometer with a habit of presenting some of the basic ideas…
on “When did computer science theory get so hard?” ↗…direction from a math professor. I do not know Spivak's Calculus but his advanced books (by Publish or Perish) are excellent, So I assume his calculus book is also. Especially Calculus on Manifolds and A Comprehensive Introduction to Differential Geometry. Anyone who wants to understand calculus on higher dimensions should read Calculus on Manifolds. If you want to learn from the masters and you have the confidence, audacity and intelligence. I would…
on “Learning Math” ↗