I think it's a good time to mention a couple of nice books (related)
1. Elementary intro to math of machine learning . Its style is a bit less austere than that of OP's. It also has a chapter on probability. It could possible serve as a great prequel to the book linked in the OP.
2. The book on probability related topics of general data science: high-dimensional geometry, random walks, Markov chains, random graphs, various related algorithms etc 
3. Support for people who'd like to read books like the one linked in the OP, but never seen any kind of higher math before . This book has a cover that screams trashy book extremely skimpy on actual info (anyone who reads a lot of tech books knows what I am talking about), but surprisingly,it contains everything it says it does and in great detail. Not even actual math textbooks (say, Springer) are usually written with this much detail. Author likes to add bullet point style elaboration to almost every definition and theorem which is (almost) never the case with gazillions of books usually titled "Abstract Algebra", "Real Analysis", "Complex Analysis" etc. Some such books sometimes attach words like "friendly" to their title (say, "Friendly Measure Theory For Idiots") and still do not rise to the occasion. Worse yet, a ton (if not most) of these books are exact clones of each other with different author names attached. The linked book doesn't suffer from any of these problems.
 Mathematics For Machine Learning by Deisentoth, Faisal, Ong
 Foundations Of Data Science By Blum, Hopcroft, Kannan
2] Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra by Steve Warner