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Fall 2016

Math 733 RUME 3: Advanced Learning Theories

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
This is one of four graduate courses covering research in undergraduate mathematics education that form the basis of a specialization area in our Ph.D. program.

MATH 593G. SPTP: Applied Dynamics/Chaos.

Credit Hours: 
3
Syllabus: 
Semester Offered: 
Comments From Graduate Director: 
This is a special topics class in dynamical systems, an important and evolving area within applied mathematics. The pre-requisite is an undergraduate course in differential equations. Topics include stability, bifurcations, catastrophe theory, chaos, the butterfly effect, strange attractors, fractals. There are diverse applications to biology, physics, chemistry and engineering. The course is cross-listed with Math 493H.

MATH 747. Advanced Topics in Modern Algebra

Credit Hours: 
3
Course coordinator: 
Professor Wojciechowski
Semester Offered: 
Comments From Graduate Director: 
Provides, in essence, a “third semester” of modern algebra after Math 541-641. This course can be used with Math 641 to make a minor area in algebra for Ph.D. students. It is offered every one or two years and sometimes continues in the spring. The course can be repeated for credit, as the topics will change from year to year. Please contact the instructor for further information on the topics to be covered this year.

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 771. Matroid Theory 1.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
This course usually follows with a second semester, Math 772, in the spring. Matroid theory emergies from the studies of graph theory, combinatorial optimization, industrial engineeringand studies of certain algebraic structures (linear independence and algebraic independence, for example) and has become an important and attractive branch of mathematics, both in theory and in applications. The objective of this sequence is to introduce to students the basics of matroid theory, including the following topics in the first semester: Independent sets and circuits, other matroid axiom systems, representations, duality theory, matroid minors, connectivity, and constructions. The second semester will be devoted to more advanced topics, including matroid connectivity, algebraic matroids over finite fields, decomposition of matroids, among others. Research front problems will be discussed. Research problem discussions will be focused on supereulerian matroids, and optimal matroid circuit covers

MATH 751. Functional Analysis 1.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
This course is offered in alternate years, alternating with Math 757 Partial Differential Equations. It is intended to be followed in the spring with Math 752 and so would be suitable for either a minor sequence or as part of a major area in analysis for Ph.D. students.

MATH 555. Complex Variables 1.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
This course is offered every other year and provides a graduate-level introduction to complex variables. Math 451 is generally an expected prerequisite. A basic knowledge of complex variables, at least at an undergraduate level, is essential in many areas of pure and applied mathematics so if you have no prior background and you have taken a course similar to Math 451, you might want to consider taking this course. Otherwise, we offer an undergraduate course Math 456 each spring which in most cases does not count toward course work requirements but will give you a working knowledge of the area. Also Math 568 covers basic complex variables from an engineering mathematics viewpoint.
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