This is a junior-senior level course in enumeration, that is, the art of counting the size of various finite sets. It assumes that the student has taken single-variable calculus, as well as linear algebra (e.g. determinants occasionally come up). Precise statements and theorems are a part of this class, and it is assumed that the students can occasionally prove things, rigorously.
Topics include elementary counting techniques, including the principle of inclusion-exclusion, along with with more sophisticated techniques, such as generating functions and Polya theory.
Because Polya theory requires a very small amount of group theory, and due to some of the other mildly algebraic topics, this course is among those that can be counted toward a math major's algebra requirement (part of "Column Y") as described here .
Note that Math 4707 is a class which covers some of the material of Math 5705 at a slightly lower-level, as well as some of the graph theory covered in Math 5707.
To suggest some flavor of Math 5705, a student might learn how to ...