The Center for the Study of Complex Systems offers a Graduate Certificate in Complex Systems. Students who wish to enroll can do so by contacting firstname.lastname@example.org. (Linked course names will take you to the LSA Course Guide page.)
CMPLXSYS 501: An Introduction to Complex Systems --- This course covers a broad range of fundamental topics relevant to the study of complex systems. The course work involves weekly readings focus on "classics" in the complex systems literature, in order to give students a broad, general understanding for the variety of work that falls under the rubric of complex systems. Topics to be covered will include evolutionary systems, self-organized criticality, measures of complexity, approaches to modeling complex adaptive systems, and emergence. Authors to be covered include Holland, Axelrod, Kaufmann, Bak, and Gell-Mann. Grading will be based on the participation in the discussions and on two or three term papers.
CMPLXSYS 510 / MATH 550: Introduction to Adaptive Systems --- This course is an introduction to applications and integration of dynamical systems and game theory to model population and ecological dynamics and evolutionary processes. Topics include Lotka-Volterra systems, non-cooperative games, replicator dynamics and genetic mechanisms of selection and mutation, and other adaptive systems.
CMPLXSYS 530: Computer Modelling of Complex Systems --- Introduces students to basic concepts, tools , and issues which arise using computers to model complex systems. Emphasis is placed on the modeling process itself, from model design through implementation to analyzing, documenting, and communicating results. Case studies of computer models of complex systems, including adaptive and non-adaptive complex systems drawn from economics, ecology, immunology, epidemiology, evolutionary biology, political science, and cognitive science.
CMPLXSYS 535/PHYS 508: Theory of Social and Technological Networks --- Introduce and develop the mathematical theory of networks, particularly social and technological networks; applications to important network-driven phenomena in epidemiology of human infections and computer viruses, cascading failure in grids, network resilience and opinion formation. Topics covered: experimental studies of social networks, WWW, internet, information, and biological networks.
CMPLXSYS 541/PHYS 541: Introduction to Nonlinear Dynamics and the Physics of Complexity --- An introduction to nonlinear science with an elementary treatment from the point of view of the physics of chaos and fractal growth.
While the following are 400 level courses, they are open to graduate students and are valid as credit toward the Complex Systems Graduate Certificate:
CMPLXSYS 425: Evolution in Silico While every population of living organisms is evolving, not everything that evolves is alive. Nature’s success at finding innovative solutions to complex problems has inspired many computational implementations of the evolutionary process. Philosophically, this is possible because evolution is itself a substrate neutral process (i.e., evolution can occur regardless of what particular substance makes up the individuals in a population). This fundamental property of evolution creates a deep connection between computational implementations and the biological process responsible for the diversity of life on Earth. We will highlight this connection and the possibility of two-way interdisciplinary discovery through regular readings and discussions. Some of the various implementations of evolution we will learn about include approaches to solve optimization problems, building controllers and/or bodies for robots, and using computational instances of Darwinian evolution to study fundamental questions in biology.
CMPLXSYS 435: Ecological Networks Networks have revolutionized the way we understand, represent and analyze complex systems. In particular, Ecology has greatly benefited from network theory to analyze the (inherently complex) structure and dynamics of ecological systems. This course introduces fundamental concepts and recent ecological theory on the structure and dynamics of networks composed by species connected via antagonistic (e.g. who eats whom) and/or mutualistic (e.g. plant-pollinator) interactions. These concepts and theories will be introduced via lectures and regular reading of primary literature, and actively learned via individual and group analysis of empirical data, mathematical models and computational tools. We will also elucidate how to use ecological networks to inform real-world problems such as the current environmental crisis.
CMPLXSYS 489-002: Applications of Entropy and Information in the Natural Sciences --- As a general measure of uncertainty, Entropy finds diverse applications in numerous disciplines, such as physics, chemistry, and biology. This course will highlight many of these applications. After introducing the basic notions of entropy and information, we will study the theoretical underpinnings of its many interpretations. Illustrations of these ideas will be drawn from information theory, statistical inference, statistical mechanics, network theory, and biophysics.