The University of Montana

Department of Mathematical Sciences

Technical report #27/2010

Integrals don’t have anything to do with discrete math, do they?

**Kal M. Karply***

*correspondence to mark.kayll@umontana.edu

**Abstract**

Most people think of integration as belonging to the realm of continuous mathematics, far removed from its ‘polar opposite’, discrete mathematics. We present a few examples illustrating the ubiquity of integration, even in the discrete world. Our goal is to convince students to keep up on their analysis, even if they lean more to the mathematically discrete. One never knows when an integral might rise seemingly out of nowhere and play an interesting role in a discrete problem.

**Keywords:** gamma function, perfect matching, graph, bipartite graph, rook polynomial,
derangement

**AMS Subject Classification:** Primary 05C70 Secondary 05A15 33B15 05A05

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