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I graduated with an undergraduate mathematics degree this past May, but I had never taken a Discrete Mathematics course. I took the usual years' worth of Algebra and Analysis.

I am interested in a discrete mathematics text (with challenging problems) that covers all of the topics on the Math GRE Subject Test, i.e.,

Discrete mathematics: logic, set theory, combinatorics, graph theory and algorithms

and won't be boring for me to read, given my math background.

(I have heard that I would be bored in such a class, as I once spoke to a Discrete Math professor about taking her class, and she told me it would be a waste of time.)

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    $\begingroup$ Seems awfully similar to your previous question on GRE prep, to which you accepted my answer that no textbook reading in these subjects was necessary. Have you looked at past GREs? There's really very little of this stuff on them! Again, if you're just interested in learning some of this material, then this may be answerable. math.stackexchange.com/questions/1018105/… $\endgroup$ – Kevin Carlson Nov 18 '14 at 1:46
  • $\begingroup$ @KevinCarlson - Awfully similar, but I'm not focusing on solely combinatorics. $\endgroup$ – Clarinetist Nov 18 '14 at 2:09
  • $\begingroup$ @KevinCarlson - FWIW, I took it last October. $\endgroup$ – Clarinetist Nov 18 '14 at 2:20
  • $\begingroup$ And you're really feeling like you need to focus on discrete math review? Well, OK-that surprises me, but maybe someone will have a suggestion. $\endgroup$ – Kevin Carlson Nov 18 '14 at 2:25
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What you probably want is the MIT Course Notes for CS Math (Discrete Mathematics). It is used at Harvard and MIT, as well as my local university and it is Creative Commons Licensed (The specific license for the course notes are Attribution+Noncommercial+ShareAlike).

The "book" is: Mathematics for Computer Science

BY:
Eric Lehman, Google
F Thomson Leighton, MIT
Alebert R Meyer, MIT

With your math background though you should be fine without perusing it for the Math GRE as others have pointed out.

Creative Commmons License for Reference

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If I had one book to recommend covering the topics you mentioned, it would be

Discrete Mathematics and Its Applications by Kenneth Rosen.

The only problem with it is that it's aimed towards new computer science undergraduates, so it may not be as challenging. As recommended in the comments, you could work through it without looking at any of the proofs and figure them out on your own, and don't do any of the tedious exercises, just the challenging ones (starred and double-starred).

But here are some other recommendations:

  1. For Set Theory & Logic
    • Set Theory and Logic by Robert R. Stoll
    • Theory of Sets by E. Kamke
    • Axiomatic Set Theory by Paul Bernays
    • Axiomatic Set Theory by Patrick Suppes
  2. For Graph Theory
    • Schaum's Outlines: Graph Theory by V.K. Balakrishnan
    • First chapter of Pearls in Graph Theory by N. Hartsfield & G. Ringel
  3. For Algorithms
    • My first recommendation, Rosen's book, should suffice; you shouldn't need more than that, but if you want to practice writing algorithms, I'd recommend checking out project euler and learning some basic python
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  • $\begingroup$ Rosen would probably be boring to read for him, as it's likely to be at the level he said was too low. If he does use it, I think he should just read the statements of the theorems and only stop to read the text where there are theorems or definitions he's not familiar with. Also, only do the starred and double-starred problems. $\endgroup$ – Mike Nov 22 '14 at 20:13
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If your interest is computing The Art of Computer Programming by Donald Knuth covers a wealth of discrete Mathematics. If your interest is more mathematical then try generatingfunctionology by Herbert S. Wilf, and Enumerative Combinatorics by Richard P. Stanley. All of these texts are appropriate for graduate level inquiry. These texts would not be a waste of your time.

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