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Course Information: 700 level

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MATH 793A SPTP: Math Systems Biology

Credit Hours: 
3
Syllabus: 
Semester Offered: 
Comments From Graduate Director: 
This course studies dynamical systems that arise in the modeling of biological systems and how these systems can result in fundamental biological phenomena, including stable equilibria that arise in complex systems, and bistable states. We expect to offer a three semester sequence in systems biology, with the second course emphasizing simulation of complex biological systems and the third semester devoted to the role of random effects.

Math 793E. SPTP: Combinatorial Optimization

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
This course is generally offered every other year, alternating with the Matroids sequence. This is a full-year course, with research-level topics in the spring.

Math 793F. SPTP: Introduction to Infinite Combinatorics

Credit Hours: 
3
Semester Offered: 

Math 793G. SPTP: Research in Undergraduate Mathematics Education 4

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
The fourth in a series of courses on the research literature and practice in undergraduate mathematics education.

MATH 793H. SPTP: Injective Choice Functions.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
The goal is to prove the following result for arbitrary bipartite graphs without any cardinality restrictions. This result is a generalization of König's Theorem which has the same statement but is restricted to finite bipartite graphs. Theorem (Aharoni): For every bipartite graph there exists an independent set of edges and a vertex cover containing exactly one vertex of each edge. The algebra content of this course will concern ideals in boolean rings, and in particular the nonstationary ideal in the boolean ring consisting of all subsets of a regular cardinal number. The operation of multiplication in such a ring is the intersection and the operation of addition is the symmetric difference. The course will include introduction to ordinal and cardinal numbers. For Ph.D. students, this course would be suitable as part of a minor or major in either Algebra or Discrete Mathematics.

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