[0] https://www.amazon.com/Pure-Mathematics-Beginners-Rigorous-I...
I think it's a good time to mention a couple of nice books (related)
1. Elementary intro to math of machine learning [0]. 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 [1]
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 [2]. 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.
[0] Mathematics For Machine Learning by Deisentoth, Faisal, Ong
https://mml-book.github.io/book/mml-book.pdf
[1] Foundations Of Data Science By Blum, Hopcroft, Kannan
http://www.cs.cornell.edu/jeh/book%20no%20so;utions%20March%...
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
https://www.amazon.com/Pure-Mathematics-Beginners-Rigorous-I...
One of the dirty little secrets of studying CS and math is that truly understanding 2 problems of the kind you've never seen before in 1 day is OK and expected. Hell, sometimes mere understanding of one single solution to a problem can take a week or longer. Most anyone who does better has either studied the (adjacent) material before or just trudging along half-understanding this bit and that piece hoping that sometime in the future it might all come together. And that's exactly what happens after you stick with it for awhile (often several years). Your job is to understand the thought process and philosophy of math. It's usually called "math maturity". Math/CS people reuse the same tips and tricks over and over again under many different guises and after a while you'll start seeing this repetition and even start using them yourself. It's very similar to how you learned your own native tongue. Luckily, math folk have methods to rein in this madness.
Check out [0]. It's free and teaches you some basics of structured thought. Then check out [1], [2], [3] to expand on what you've learned.
One really good unpretentious algo book that shows you how to do problems is [4].
[0] BOOK OF PROOF by Richard Hammach
https://www.people.vcu.edu/~rhammack/BookOfProof/
[1] Discrete Mathematics with Applications by Susanna Epp
https://www.amazon.com/Discrete-Mathematics-Applications-Sus...
[2] Pure Mathematics for Beginners by Steve Warner
https://www.amazon.com/Pure-Mathematics-Beginners-Rigorous-I...
[3] Mathematical Proofs by Gary Chartrand et al
https://www.amazon.com/Mathematical-Proofs-Transition-Advanc...
[4] Data Structures and Algorithms: Concepts, Techniques and Applications by G.A.V. Pai
https://www.amazon.com/gp/product/0070699577/ref=ppx_yo_dt_b...
Good Luck and don't f*ck it up!