Reddit reviews Student's Solutions Guide to accompany Discrete Mathematics and Its Applications
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Here is a reading list:
Good Introductory Books:
Some free resources: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2005/readings/
Most Discrete Math courses in the US will use the Rosen textbook: http://www.amazon.com/dp/0073229725/ with the solution manual http://www.amazon.com/dp/0073107794/. You should read this to get a head start.
The Rosen book is a bit dry and may be hard to understand at first so I'd look at the Epps book: http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/. The Epps book does a better job at explaining combinatorics and a few other topics. I've read both. Rosen assumes more mathematical understanding and will definitely be better for understanding proofs.