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I am searching for book on discrete mathematics which is suitable for self study. This mean I want it to have exercises with answers (It would be ideal if it had solutions). I have already read "Discrete Mathematics" of Kenneth Ross. I have also partially read "Concrete Mathematics" of Knuth but I didn't like the style much. I am searching for next book to read. I do not have any requirements on topics I just want it to cover few of them like combinatorics and counting, recurrences and probably generating functions.

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    $\begingroup$ You can try with David Gries & Fred Schneider, A Logical Approach to Discrete Math (1993). $\endgroup$ – Mauro ALLEGRANZA Feb 12 '14 at 15:47
  • $\begingroup$ Discrete Math with Applications by Epp I don't believe it covers generating functions though. $\endgroup$ – John Habert Feb 12 '14 at 15:50
  • $\begingroup$ Bona's book "A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory" has a good chapter on generating functions. The exercises are split into two categories, one with full solutions and the other without. amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration/… $\endgroup$ – Joel Feb 12 '14 at 15:53
  • $\begingroup$ @MauroALLEGRANZA Title sounds like it connects more rigorous logic and discrete mathematics which is what I may like. Could you write few sentences about this book? $\endgroup$ – Trismegistos Feb 12 '14 at 15:53
  • $\begingroup$ Ch.1 - Textual Substitution, Equality, and Assignment; Ch.2 - Boolean Expressions; Ch.3 to 9 - Logic; Ch.11 - A Theory of Sets; Ch.12 - Mathematical Induction; Ch.13 - A Theory of Sequences; Ch.15 - A Theory of Integers; Ch.16 - Combinatorial Analysis; Ch.17 - Recurrence Relations; Ch.19 - A Theory of Graphs; Ch.20 - Infinite Sets. $\endgroup$ – Mauro ALLEGRANZA Feb 12 '14 at 16:03
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Epp's text on Discrete Mathematics is a very nice read. Johnsonbaugh is good as well, but is more technical and more geared towards computer scientists.

Nicholas Loehr's text Bijective Combinatorics is a great read for the topics you listed, which fall in the realm of combinatorics. Loehr's text is rigorous and thorough, but it is also very well written and intuitive. I did my undergraduate work at Virginia Tech where he teaches, and he has a reputation for being both brilliant and a fantastic instructor. His book lives up to that reputation, in my opinion.

Make sure you avoid Alan Tucker's Applied Combinatorics textbook. It's a horribly written book, and the only redeeming quality are the exercises.

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"generatingfunctionology" by Herbert S. Wilf and "A=B" by Marko Petkovsek, Herbert Wilf and Doron Zeilberger.

These are available as free downloads at https://www.math.upenn.edu/~wilf/DownldGF.html and https://www.math.upenn.edu/~wilf/AeqB.html

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I'm taking a Discrete Mathematics course right now, using Applied combinatorics by Roberts and Tesman. It does have some good 'real life' examples and applications.

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  • $\begingroup$ Table of contents looks very promising but it is very expensive book. $\endgroup$ – Trismegistos Feb 12 '14 at 19:35
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    $\begingroup$ @Trismegistos, It's an expensive book indeed, but I'm sure there are ways to get it if you know the right sources. $\endgroup$ – Ragnar Feb 12 '14 at 20:37
  • $\begingroup$ What do you mean Ragnar, do you mean an electronic version? $\endgroup$ – Jorge Fernández Hidalgo Aug 24 '15 at 1:24
  • $\begingroup$ Most likely the pdf of the book. $\endgroup$ – nodel Aug 24 '15 at 1:42
  • $\begingroup$ If you search for a title, sometimes you get interesting results. $\endgroup$ – marty cohen Aug 24 '15 at 1:49
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Here are very complete notes and problem sets from Jacob Lurie's (Harvard) combinatorics course (Harvard).

http://www.math.harvard.edu/~lurie/155.html

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