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Dynamics of Complex Systems is an introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions will be in context of contemporary experimental or observational data.

This seminar will focus on dynamical change in biogeochemical cycles accompanying early animal evolution -- beginning with the time of the earliest known microscopic animal fossils (~600 million years ago) and culminating (~100 million years later) with the rapid diversification of marine animals known as the "Cambrian explosion." Recent work indicates that this period of intense biological evolution was both a cause and an effect of changes in global biogeochemical cycles. We will seek to identify and quantify such coevolutionary changes. Lectures and discussions will attempt to unite the perspectives of quantitative theory, organic geochemistry, and evolutionary biology.


Differential Equations (18.03), Physics II (8.02)


Students are expected to come to each class prepared to discuss the readings. At the culmination of the course, students present recent papers in the subject to their classmates.


Grading for this course is based 100% on class participation and presentations.