M615 Combinatorics and Graph Theory (3 cr.)
This course provides an introduction to combinatorics and graph theory, including the Pigeonhole Principle, generating functions, permutations, combinations, principle of inclusion-exclusion, recurrence relations, Ramsey theory, graphs and directed graphs, paths, trees, and graph coloring.
Upon completion of the course, students are expected to be able to do the following:
- Apply counting techniques including permutations, combinations, the Pigeonhole Principle, and the principle of inclusion-exclusion to solve a variety of problems. (3.c)
- Construct and use generating functions to solve problems, including recurrence relations. (3.b)
- Use graphs and directed graphs to model given situations. (3.d)
- Prove and present theorems using combinatorial and graph theoretic techniques. (4.b)
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