A good introductory discrete mathematics book. I am professor of mathematics and I am scheduled to teach a newly designated discrete math class for computer science majors.  The prerequisite for the class is only Calc 1 and Id like a book that isnt too expensive, has a chapter on logic and proofs, and isnt too difficult but addresses some modern concepts.
Any suggestions?
If I can get a book that addresses all of these criteria except price, then that would work too.
 A: Given that it’s for computer science majors, my first choice would be Susanna S. Epp, Discrete Mathematics with Applications, which meets all of your criteria except price. Among the standard discrete math texts it offers one of the gentler introductions to reading and writing proofs. Unfortunately, it’s obscenely expensive. Edward R. Scheinerman’s Mathematics: A Discrete Introduction is merely expensive and is in my opinion a significantly better book, but it’s aimed more at math majors than at computer science majors; still, I recommend taking a look at it. It also makes a serious effort to accustom the neophyte to reading and writing proofs.
I’ve also used the notes by Lovász & Vesztergombi mentioned in another answer; they have the great virtue of being free, and in general they’re well written, but there are few exercises, and they lack coverage of a number of topics that are pretty standard in discrete math courses for computer science students. You would probably have to supplement them fairly extensively. Here are some other freely available texts and lecture notes; I’ve not used them, so I prefer not to offer any judgements.


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*Marcel B. Finan, Lecture Notes in Discrete Mathematics.

*WWWL Chen, Discrete Mathematics.

*C.D.H. Cooper, Discrete Mathematics: Notes for DMTH137 $-$ suitable only as supplementary material.
Added: In my experience Graham, Knuth, & Patashnik, Concrete Mathematics, is pretty much out of the question for students with no more background than Calc 1. I used it several times in an upper division course, with students who had had at least some exposure to theoretical mathematics, and a majority of them had trouble with it. The coverage is also rather idiosyncratic for a discrete math course for computer science students, and it certainly doesn’t include a chapter on logic and proofs.
Do you know yet what topics are to be central to the course?
A: I am in a similar boat, with a couple of differences.  First, I've taught the course previously, but am looking for a free alternative to the rather expensive text I've used in the past. Second, our course requires only pre-Calc, and will have a mix of Math & CIS students so the math abilities will vary.  I have perused free texts by Finan as well of those by Chen and Lovasz posted in this thread.  Right now I am leaning toward Chen, which has a nice selection of topics from which to choose or omit as you see fit.  A clearing house of free texts is here.  Best of luck.
A: I like these lecture notes, though they may be too elementary:


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*László Lovász, Katalin Vesztergombi, Discrete Mathematics, Lecture Notes, Yale University, Spring 1999.

A: My colleagues have written some notes which you might find suitable, available here and here. Before we had these notes, I used the text by Grimaldi, which I thought was pretty good. 
