Applications of difference equations in problem solving and modeling, especially in the area of chaos. The notion of proof, first order logic, set theory, ordinals, cardinals and an overview of the most important recent results in the field. A survey of topics in arithmetic and analytic number theory, such as Eulers' function, quadratic reciprocity, continued fractions and the distribution of prime numbers. Repeatable, may be taken two times under different subtitles. An advanced seminar in an active area of mathematical research.
Content depends upon instructor's choice.
Repeatable, may be taken two times under different subtitles. Emphasis is on group representations. A broad yet deep survey of current topics in combinatorics and graph theory essential for teachers k-16, including applications to probability, coding theory, sorting and matching algorithms and optimization. Primarily for doctoral candidates preparing to teach in colleges or community colleges. Repeatable, may be taken two times.