In Summer 2018, we will hold some classes for the Advanced Group only. Classes will meet in Phillips Hall from 10:30 – 12:00. Dates, room numbers, and topics will be posted below on an ongoing basis.
This schedule is tentative and may be changed.
|Saturday, Jun 16||Phillips Hall 381||Taxicab Geometry||UNC grad students (Paul Kruse and others)|
|Saturday, Jun 30||Phillips Hall 381||Steiner Symmetrization||Wesley Hamilton||Steiner symmetrization is a useful tool for proving facts about “optimal” shapes by rearranging shapes in a way that preserves area. This week we’ll explore this tool, and see how it can be used to prove that, for a fixed perimeter, a circle enclosed the largest area.|
|Saturday, July 14||Phillips Hall 381||Axiomatic Systems||Hunter Dinkins||During the 19th and 20th centuries, mathematicians began to notice problems and paradoxes that resulted from shaky foundations. As a result, it became a high priority to make concrete and definite sense of the work that they were doing. The solution they came up with was to base mathematics on axiomatic systems. We will look at what an axiomatic system is and study several thought-provoking examples.|
|Saturday, July 28||Phillips Hall 381||Symmetry Groups||Marc Besson||We will study the symmetry groups of objects in the plane and objects in space like the Platonic solids. We will discuss and use (but not prove) Lagrange’s theorem, the Orbit-Stabilizer theorem and possibly Burnside’s Lemma to compute orders of symmetry groups.|
|Saturday, August 11||Phillips Hall 381||Group Actions and Symmetric Polynomials||Paul Kruse||We will discuss what the symmetric group is and what group actions are. Then, we will explore examples of groups actions, namely how the symmetric group acts on polynomials. Finally, we will talk about symmetric polynomials and a few interesting properties and applications.|