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Discrete Mathematics and Its Applications?
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Don't get me wrong, he was a very sharp guy. He and I took 256AB in senior year, and I was always amazed by his facility with these things. However, you'll learn a lot of proof techniques along the way in each class.
55 usually uses Ken Rosen's Discrete Mathematics and Applications. If you look at the table of contents, I'd say the relevant bits are Chapters 1.1-1.6 and 3.1-3.2. Chapter 6.1-6.6 would be helpful for 113, but not necessary for 110/104/185. (Well, 6.6 might be slightly useful in the beginning of 104.) There's a student solution manual, so you could probably work through these sections and be good to go.
You're very welcome. The standard and pretty good textbook for this stuff is Discrete Mathematics and its Applications by Rosen. There are newer more expensive editions, but the one I linked to is about $15 on Amazon. You can probably also find it online.
You might also like to check out combinatorics on Art of Problem Solving.
I've used Rosen's Discrete Math text for a few courses. It also features a lot of applications to CS.
https://www.amazon.ca/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0072899050
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