经典著作太棒了：* 希尔伯特和康福森的《直观几何》（Geometry and the imagination）* 柯朗与希尔伯特的《数学物理方法》（Methods of mathematical physics）* Spivak 的《微分几何综合引论》（A comprehensive introduction to differential geometry，以及它的小兄弟《微积分》和《流形上的微积分》）* Körner 的《傅里叶分析》（Fourier Analysis）* Arnold 关于常微分方程、偏微分方程和数学物理的书，美得令人窒息。* 《…的形状》…
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…
…举个例子，我以前一直对多变量微积分用“具有物理意义”的微分算子这种传统讲法很头疼，直到业余时间啃完了 Spivak 的《微分几何综合引论》（Comprehensive Introduction to Differential Geometry）前几卷，那一瞬间很多东西一下子就豁然开朗了。要不是我大学微积分入门课恰好碰上一位微分几何出身的教授，喜欢在讲基础概念时…
…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…
…一位数学教授的指点。我没读过 Spivak 的《微积分》，但他那些进阶著作（由 Publish or Perish 出版）非常出色，所以我猜他的微积分教材应该也差不到哪去。尤其是《流形上的微积分》（Calculus on Manifolds）和《微分几何综合引论》（A Comprehensive Introduction to Differential Geometry）。任何想理解高维微积分的人都该读读《流形上的微积分》。如果你想向大师学习，而且你足够自信、大胆且聪明，我会…
…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…
经典著作太棒了：* 希尔伯特和康福森的《直观几何》（Geometry and the imagination）* 柯朗与希尔伯特的《数学物理方法》（Methods of mathematical physics）* Spivak 的《微分几何综合引论》（A comprehensive introduction to differential geometry，以及它的小兄弟《微积分》和《流形上的微积分》）* Körner 的《傅里叶分析》（Fourier Analysis）* Arnold 关于常微分方程、偏微分方程和数学物理的书，美得令人窒息。* 《…的形状》…
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…
…举个例子，我以前一直对多变量微积分用“具有物理意义”的微分算子这种传统讲法很头疼，直到业余时间啃完了 Spivak 的《微分几何综合引论》（Comprehensive Introduction to Differential Geometry）前几卷，那一瞬间很多东西一下子就豁然开朗了。要不是我大学微积分入门课恰好碰上一位微分几何出身的教授，喜欢在讲基础概念时…
…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…
…一位数学教授的指点。我没读过 Spivak 的《微积分》，但他那些进阶著作（由 Publish or Perish 出版）非常出色，所以我猜他的微积分教材应该也差不到哪去。尤其是《流形上的微积分》（Calculus on Manifolds）和《微分几何综合引论》（A Comprehensive Introduction to Differential Geometry）。任何想理解高维微积分的人都该读读《流形上的微积分》。如果你想向大师学习，而且你足够自信、大胆且聪明，我会…
…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…