MURPHYS-HSFS-2014 - 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems, April 7-11, 2014 - Abstract
Kalachev, Leonid
The complexity of mathematical models in current real life bio-medical applications brings forward the need for specialists in particular applied areas of science to work closely together with mathematicians to produce meaningful results and reliable predictions of possible outcomes of various processes described by these models. Communication skills play an important role in such collaborations and teaching such skills evidently must be an essential part of the applied mathematics and statistics students? training. Taking responsibility for the results of the applied research which, e.g., may lead to new medical devices and treatments and could strongly affect the lives of the future patients, must also be emphasized. The recent experience with teaching ?practical? applied mathematics projects courses at the University of Montana indicates that the students who work in these courses in groups on modeling studies that involve real data and, often, their own experimental designs gain very valuable experience which cannot be otherwise obtained in the ?theoretical? courses. Asymptotic methods also become an important tool and intrinsic part of the professional training of neuroscience, physics, chemistry and biology students at the University of Montana. Asymptotic methods play increasingly significant role in identification of cases where the originally proposed complex models are over parameterized, in constructing models? reductions which allow one to produce new model formulations containing fewer reliably identifiable parameters, and in producing new ?effective? models that are optimal with respect to available data. Surprisingly, the role of asymptotic methods in the age of growing computing power is only increasing. In the current presentation some ?hands-on? applied courses taught at the University of Montana and the examples of applied projects from these courses involving asymptotic reduction of models will be discussed.