Summer 2008 Workshops
All workshops will run for approximately 4 weeks, meeting daily for 2 hours in the morning with the professor and 2 hours in the afternoon with graduate student mentors. Students will be placed in a workshop depending on their background and research project choice.
Workshops are as follows:
Linear Algebra, Markov Chains, and Graphs
Instructor: Asst. Prof. Victor Vega, St. Ambrose University
Pre-requisite: One year of calculus. Some experience with matrices desirable but not required..
The overall plan is to integrate at an elementary level the concepts of probability, finite Markov chains, and graphs, using tools from linear algebra.
Part 1. Present relevant topics from linear algebra, including matrix algebra, linear transformations, eigenvectors.
Part 2. Introduce probability, leading to Markov chains.
Part 3. Study finite Markov chains in terms of graphs and transitions matrices.
Students will be encourages to participate in developing and/or presenting material.
Permutations and Braids
Instructor: Asst. Prof. Holly Mosley, Grinnell College
Pre-requisite: One year of Calculus, one semester of linear algebra. (These prerequisites are for general level of mathematical maturity rather than specific content.)
Introducing students to ideas from abstract algebra using groups of permutations and braid groups, continuing to "tangles" and related algebra structures.
The workshop will combine lecture and discovery-learning. Students will be asked to make their own observations about these mathematical objects and their relationship, and then follow this up by lecturing on formal definitions and theorems related to the phenomena that they have discovered themselves.
Combining Geometry and Algebra: SL_2(R) and Automorphisms of the Upper Half-Plane
Instructor: Assoc. Prof. Brian Birgen, Wartburg College
Pre-requisite: One year of Calculus, one semester of Linear Algebra.
Assuming a basic background in linear algebra, the workshop will introduce complex variables and abstract groups to study the geometry and algebra of linear fractional transformations (Mobius transformations) and relations to the matrix group SL_2(R). May extend to higher dimensions, e.g. SL_2(C) and upper half-3-space.
Students will be encouraged to participate in various ways, including developing a Wiki-type web site.