I have NEVER taken a combinatorics course, outside of what one covers in a calculus-based probability course.

I would be interested in knowing what would be a suitable combinatorics text for studying for the Math GRE Subject Test. Specifically, I'm interested in a text which goes through combinatorics in tandem with linear algebra, abstract algebra, and real analysis (e.g., see this question: How many distinct partials of order $k$ for a function $f: \mathbb{R}^{n}\rightarrow\mathbb{R}$?), and has many practice problems.

Maybe what I'm hoping for doesn't exist. But I have some hope. I've considered Concrete Mathematics, but I'm not sure if it has what I'm looking for.


Having studied for the math GRE two years ago with good results, I'd suggest that you don't need any such text. There won't be more than two or three such problems on a usual test, so it's a highly inefficient use of your time if you don't want the combinatorics for its own sake.

EDIT: the official breakdown is here. Combinatorics is one of five subjects mentioned in three bullets making up together a quarter of the test.

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    $\begingroup$ I second this. As long as you are comfortable with the basics of binomial coefficients (pascal's triangle) and you know some common counting techniques (maybe a couple of intro theorems from graph theory), it shouldn't be an issue. I had very good results on the math GRE without taking a class in probability or combinatorics. The most important things are calculus I,II,III, analysis (real and complex, but frankly they tend to be problems that build on common ideas or theorems), and some linear algebra. For all the other topics, make sure to be familiar with the basics, but more is not needed. $\endgroup$ – J. David Taylor Nov 12 '14 at 6:32
  • $\begingroup$ Going off @J.DavidTaylor's comment, the questions on abstract algebra and general topology actually were so basic they threw me off, initially: they use nothing but the definitions, so that to compensate they have to ask rather weird questions. $\endgroup$ – Kevin Carlson Nov 12 '14 at 6:38

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