[madhadron]

That's rather like saying that a Java book should include a section on processor architecture so you can design your own chips. Plus, what's in this book isn't really enough to do probability and statistics at any but the most basic level.

The path to a deep understanding of inference that makes most modern ML seem straightforward goes through measure theory, Lebesgue integration, some functional analysis, a smattering of topology, and an intuition around dynamical systems. Then you go do probability and random processes, detour into game theory for a bit, learn decision theory, and at that point it all goes from mystical to bleedin' obvious.