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I am an undergraduate pure math student at UC Berkeley. I am in a class which is meant to work on problem solving, particularly with regards to Putnam style questions. My only problem thus far has been my own forgetfulness with regards to some discrete math topics, such as graph theory, and discrete probability.

The analytic topics and linear algebra topics have been significantly easier. In the interests of properly learning some of this material, can anyone recommend me a good "encyclopedia" for Discrete Math? I have used Rosen's book for an introductory class, but the depth of coverage was not sufficient for what I need now.

Some topics I would like to properly learn are:

1) Generating Functions

2) Recursion Theory

3) Intermediate Combinatorics

4) Graph Theory

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    $\begingroup$ Try A walk through combinatorics - by Miklos Bona $\endgroup$ – Anurag A Nov 3 '15 at 7:35
  • $\begingroup$ Thanks for the suggestion. Looks like a good reference. $\endgroup$ – Antonios-Alexandros Robotis Nov 3 '15 at 7:49
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I highly recommend Discrete Mathematics by Norman L. Biggs.

You can also try checking out An Invitation to Discrete Mathematics by Jiří Matoušek and Jaroslav Nešetřil.

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