- February 20, 2007

**Valerie Peterson**(UIUC Math)

**Title:**Plaiting Polyhedra

**Abstract:**There are all kinds of methods for constructing polyhedra out of strangely shaped pieces of heavy paper, but in 1983 J. Pedersen discovered an ingeneous one using only n congruent flat strips. Given a Platonic solid, if one assumes that (1) every edge in the model is crossed at least once, and (2) every color used has an equal area exposed on the model's surface, then the number of necessary and sufficient strips to plait the tetrahedron, cube, octahedron, icosahedron, and dodecahedron are, respectively, 2, 3, 4, 5, and 6. We will discuss these constructions as well as embark on a few. Materials and instructions will be provided, and no previous plaiting experience will be assumed.

- March 6, 2007

**Jennifer Paulhus**(UIUC Math)

**Title:**Using Algebra to Study Points on Curves

**Abstract:**Points on elliptic curves have a natural group structure on them which allows us to use algebraic techniques to study the curves. While other curves do not have such a natural structure, we can define a special object associated to the curve which is a group and use this group to study these curves. We give a gentle introduction to this field, assuming no more than an undergraduate course in algebra.

- April 3, 2007

**Nil Sirikci**(UIUC Math)

**Title:**The group of Hamiltonian diffeomorphisms

**Abstract:**We will introduce the group of symplectomorphisms and the group of hamiltonian diffeomorphisms on a closed symplectic manifold and discuss how they relate. This will be an introductory talk on the subject and the basic definitions we need will be provided, including the definition of a symplectic manifold.

- April 17, 2007

**Melissa Simmons**(UIUC Math)

**Title:**Bow & Stern Sequences

**Abstract:**I will compare my recent results on the recursive bow sequence with the famous Stern sequence. Specifically, I will introduce the generating function for the general bow sequence, and the bow sequence modulo 2. I will also discuss properties of b(7n+k) and other interesting facts. The talk should be accessible to all graduate students.

- May 1, 2007

**Martha Makowski**(UIUC Math)

**Title:**Problem solving and gender: An introduction to the issues surrounding girls and mathematics education.

**Abstract:**Teaching through problem solving has many interpretations. Most however, agree that problem solving itself is the process by which students apply knowledge they have learned to solve new problems. Research increasingly shows that girls struggle more with problem solving by the time they get to high school than boys of the same age. Part of this may be the result of the testing format, although there is evidence to suggest that girls simply learn or choose to solve problems differently than boys at a very early age--a difference that creates a performance gap by the time these students reach high school. Teaching through problem solving does not necessarily close the gap as much as would be hoped by the reform oriented population. While I do not believe this difference comes from the fact that girls are less inclined or able to solve problems, it does seem that many factors contribute to the education of girls in mathematics.