# Course Information: 700 level

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## 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.

## Math 793I. SPTP: Spatial Simulation in Bio-Molecular Systems

Credit Hours:
3
Syllabus:
Semester Offered:
Comments From Graduate Director:
A course on spatial stochastic (Monte Carlo) simulations of molecular processes in living cells. The course might be of interest to those who took one or both semesters of Mathematical Systems Biology in the past years. However, this course is meant to be self contained, and pre-requisite knowledge is some familiarity with dynamical systems, basic multivariate calculus and probability. We will spend a few classes on basic models in systems biology and (a superficial) summary of chemical reaction systems. The core course focuses on the connection between the continuum picture (reaction-diffusion systems represented by PDE) and the behavior of individual particles. The ideas behind these simulation methods are quite general, and might be useful in other applications. Students proficient in programming will have the option of choosing projects that center on writing simulation programs.