Physics and engineering, and some related fields, have a well-established type of course and book which teaches "mathematical methods" for the field. This means it covers ideas, results and techniques of branches of advanced mathematics which are widely used in the field. (Here "advanced" means something like "beyond basic calculus and linear algebra.") These typical have no pretense of rigor, and lots of examples illustrating the intended applications. (This is not what is usually meant by "applied math", for complicated historical reasons.) I liked these courses as a physics student, and wish we had more of them in statistics. This notebook is for collecting relevant references.
What would go in a "mathematical methods for statistics" class? (Again, I exclude basic calculus and finite-dimensional, vectors-and-matrices linear algebra.) Combinatorics, of course, but what else? My off-the-cuff, unordered list for a course for beginning graduate students would be:
I'm sure this list is open to many objections and corrections! If anyone can point me to a math-methods-for-stats book, I'd appreciate it; I very much do not want to write one. (I have too many unfinished book projects as it is.)