This course will be an exposition to the beautiful subject of knot theory. While knot theory first attracted interest due to an outdated atomic model, it is now a central topic of study in low-dimensional topology with connections to several other fields. Furthermore, it is easy and fun to experiment with - we'll provide the string! However, you may be surprised at how difficult it is to tell if your friend's knot is the same as yours. Topics will be tailored to the audience. Likely ones include: examples of knots and links, Reidemeister moves, prime knots, knot invariants (particularly knot polynomials), Seifert surfaces, braid groups. You may even learn a couple of party tricks and some knot-so-great puns!

Learn about splay trees: the elegant and effective self-adjusting binary search tree! Topics covered include the construction of the data structure, runtime analysis, and discussion of performance in practice. Also will briefly discuss the dynamic optimality conjecture if time allows.

Can you cut a square in pieces and rearrange them to form an equilateral triangle of equal area? Of course! Can you cut a cube in pieces and rearrange them to form a regular tetrahedron? Of course not! Come to this class to learn: why you can cut and rearrange any polygon into another of equal area, but you can't do the same with polyhedra; why you can evenly cut sandwiches with as many as $$n$$ ingredients in $$n$$ dimensions in two equal parts with a single cut; and maybe even why you can cut one 3-D ball into two identical copies of it. For a demonstration, we may even have ham-sandwiches. They'll be 3-dimensional, we promise!

This class will not be like your average high school math class. We will explore topics that include algebra, number theory, combinatorics, and geometry. The problems will range from advanced to math olymipad level and might include one or two International Math Olympiad problems.