The Variational Principles of Mechanics

Among technical books, books by Cornelius Lanczos are some of the best (less popular) books I've read. Some quotes from his "The Variational Principles of Mechanics": From the Preface: Many of the scientific treatises of today are formulated in a half-mystical language, as though to impress the reader with the uncomfortable feeling that he is in the permanent presence of a superman. The present book is conceived in a humble spirit and is written for humble people. From Chapter 8: Put off thy shoes from off thy feet, for the place whereon thou standest is holy ground. -- EXODUS III, 5 We have done considerable mountain climbing. Now we are in the rarefied atmosphere of theories of excessive beauty and we are nearing a high plateau on which geometry, optics, mechanics, and wave mechanics meet on common ground. Only concentrated thinking, and a considerable amount of recreation, will reveal the full beauty of our subject in which the last word has not yet been spoken.…

For mathematics, I would recommend: 1. "What Is Mathematics? An Elementary Approach to Ideas and Methods" by Courant and Robbins -- a general book on mathematics in the spirit of Feynman lectures. 2. Strogatz's "Nonlinear Dynamics and Chaos" -- it's a bit narrow in scope (mostly dynamical systems with a little bit of chaos/fractals thrown in) but very good nonetheless. 3. Tristan Needham, "Visual Complex Analysis", beautiful introduction to complex analysis. 4. Cornelius Lanczos, "The Variational Principles of Mechanics" -- this is a physics book, but one of the classics in the subject, and as Gerald Sussman once remarked, you glean new insights each time you read it. 5. Cornelius Lanczos, "Linear Differential Operators" -- an excellent treatment of differential operators, Green's functions, and other things that one encounters in infinite-dimensional vector spaces. This book has some very intuitive explanations, e.g., why d/dx is not self-adjoint (i.e., Hermitian), whereas d^2/dx^2 is. For chemistry, I would recommend "General Chemistry" by Linus Pauling, even though it's a bit outdated.