[stodor89]

I went through Algorithm Design Manual before learning Discrete Math[0]. Suffices to say, I had plenty of these "always has been" moments you're talking about :) The book is great at explaining algorithms, math prerequisites and all. Then you try the exercises, and they leave you with a subtle feeling of "hmm, perhaps there's more to this algorithms stuff". As an example, perhaps the first time I got this was in chapter 1, when I encountered the greedy pirates puzzle[1].

[0] Had plenty of books to select from. Kenneth Rosen's was the only one I liked. Knuth's Concrete Mathematics is great if you decide to give a subject a second go -- the material is somewhat different, more abstract, and the side notes by his students are hilarious.

[1] https://www.mathsisfun.com/puzzles/5-pirates-solution.html