Each semester, faculty propose some 600-level courses to possibly be offered to graduate students, primarily doctoral students. Some of these courses follow up on 500-level courses, and some are primarily focused on current research. Depending on several variables, including student interest, these courses may be offered as regular courses, or they may be offered by faculty as independent study courses, or the course may be withdrawn (i.e., cancelled).
| The following 600-level courses are proposed for the Fall 2006 semester: |
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Instructor: Harvey Blau
CRQ: Math 520
The use of linear algebraic methods to study combinatorial problems has produced some striking results and has generated algebraic systems that raise new questions and are of interest in their own right. This course will focus on the structures variously known as hypergroups, fusion rule algebras, C-algebras, and table algebras. We will define them, motivate their existence via permutation groups and association schemes, study their basic properties, survey some known results, and see how these objects may be applied to combinatorial configurations such as distance-regular graphs. We will sketch some open research problems which seem fairly accessible to the interested student. The necessary background from the theory of algebras and of nonnegative matrices will be covered in the course.
Text: Notes by the instructor
References:
Instructor: Dan Grubb
Prerequisite: Math 431, Math 450
Differentiable manifolds are topological spaces with enough structure that calculus can be done on them. Their study provides fundamental examples and results that are useful across mathematics and its applications. This course will cover the basis of these objects including such topics as the tangent and cotangent bundles, differential forms, orientation, integration, Stoke's Theorem, and flows of vector fields.
Recommended Text: To be announced
For updates of the description of this course, please check here.