I would recommend Combinatorics and Graph Theory, 2nd ed. by Harris, Hirst and Mossinghoff link to publisher's page. It presupposes little more than some knowledge of mathematical induction, a modicum of linear algebra, and some sequences and series material from calculus. The book is divided into three largish chapters: the first on graph theory, the second on combinatorics and the third (more advanced) on infinite combinatorics. Your course sounds like it might cover much of chapter two (sum rule, product rule, binomial and multinomial coefficients, the pigeonhole principle, the principle of inclusion and exclusion, generating functions, Pólya's theory of counting, Stirling numbers, Bell numbers, stable marriage, etc.). There's even a brief introduction to combinatorial geometry. Furthermore, the exposition is clear, with a touch of humour.
J W
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