Classroom:    Maryland 104

Course Web Page:    http://www.ams.jhu.edu/~eyink/Advance-Param

Text:   The notes of the lecturer and cited journal articles will constitute the primary source for the course.

Overview:   This course is a continuation of 560.702, ``Modeling Complex Systems Colloquium.''
(See also 560.700, ``Applications of Science-Based Coupling of Models'', linked on the main page.)
Although not strictly a prerequisite, the IGERT Colloquium 560.702 shares the main subject and goals
of the present course. The basic topic is the coupling of multi-scale/multi-physics models in the context of
a broad range of science and engineering applications, emphasizing calculable approximation schemes.
The course is fundamentally interdisciplinary. Two of its key objectives are to help students to develop an
appreciation for the many disciplines in which science-based coupling of models is important and also to
help students communicate with researchers in other areas, in order to share and cross-fertilize ideas
and methods.

The principal difference of this course from 560.702 is methodological. In the Colloquium, Hopkins IGERT
faculty from diverse fields present a series of broad themes in modeling complex systems together with
sample applications, discussing the problems, methods, and prospects in those several areas. In our
discussions, however, the emphasis will be on unity as well as diversity. An attempt will be made to
identify common mathematical structures and methods that cut across the several fields of research.
A deeper understanding of the shared mathematics and tools should permit more effective communication
between researchers and better ability to adapt and exploit new approaches.

Topics Covered:

I.    Dynamics.

II.    Coarse-Grained Dynamics.

III.    Ensembles & Probability.

IV.    Moment Closure.

V.    Statistical Estimation & Uncertainty Quantification.

VI.    Hybrid/Multiscale Algorithms.

Grading:

Your final grade in this class will be determined from homework and from participation in scheduled
classroom conference sessions.