Combinatorics (the mathematics of counting things) is a relatively new field in math, and one brimming with research potential and fascinating applications.
Though it is college-level mathematics, it relies entirely on basic principles and problem-solving, making it an ideal topic for students who love math and are looking for a challenge, regardless of the background they might have.
In this course, we will begin with basic methods of proof (the most fundamental aspect of all advanced mathematics) and counting simple structures and move into partitions, compositions, lattice paths, pattern avoidance, and elementary graph theory.
If time permits, we may even reach generating functions and chromatic polynomials!
The course will be formatted similarly to a college class with weekly homework.