KAM theory and semiclassical approximations to eigenfunctions Book

An absolute treat to those who are tired of just intuitive explanations in their statistics classes – but have also struggled with the heavy mathematics that is used in the development of statistical theories. That is not to say that the textbook does not rely on intuitive explanations. Instead, it beautifully connects the mathematical ideas with the elements of serious analysis. The book never assumes a pure mathematical background or even a course in measure theory, but it still steers through complex topics with clarity.

The pure mathematician may be uneasy with many of the theorems being stated without proofs, but the book always either sketches a proof or provides a counter-example to explain why the math proceeds the way it does. This makes the text far better than the recipe-based books that have littered the literature. Instead of using software solutions and graphical explanations, the book attempts to provide the reader an ability to develop the concepts from the ground up. That this can be achieved without a rigorous proof-based approach is in itself an achievement (although the reader is referred to more advanced books - particularly Billingsley and Feller - throughout the book).