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I finished my first discrete math course this semester using mostly the excellent Kenneth Rosen (Discrete Mathematics and Applications) book that was a great help, especially in induction content and recurrence relations. In the meantime, I have read some criticisms of the work on Amazon and would like recommendations that would close some of the gaps that the author has opened, especially in the areas of integer partitions and generating functions, and which allow for the deepening of themes such as mathematical logic.

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  • $\begingroup$ Regarding learning about generating functions, although not only in terms of integer partitions, I suggest you at least glance through MSE's How can I learn about generating functions?. $\endgroup$ Commented Jun 30, 2019 at 1:07
  • $\begingroup$ Did you mean Kenneth Rosen? $\endgroup$ Commented Jun 30, 2019 at 1:39
  • $\begingroup$ What do you mean by "the deepening of themes such as mathematical logic"? Are you interested in the field of logic (predicate logic, first order logic, higher order logic, maybe temporal logic, combinators, etc) or is your concern more with developing your mathematical reasoning (i.e. in Terry Tao's terminology, passing from pre-rigorous to rigorous mathematics)? $\endgroup$ Commented Jul 1, 2019 at 11:02

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The book Discrete Math by Gary Chartrand and Ping Zhang would likely be an excellent resource. The ISBN-13 is 978-1577667308.

The book opens with a number of chapters on proofs in mathematics using logic and a variety of methods of proof. The book also goes into some good detail on combinatorics. I know that generating functions are included in Chapter 9.

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