The Center for the Study of Complex Systems offers an academic minor in Complex Systems. Students who wish to enroll can do so by contacting email@example.com (Linked course names will take you to the LSA Course Guide page.)
CMPLXSYS 250/ENVIRON 250/PUBPOL 250: Social Systems, Energy & Public Policy Energy is an incredibly complex topic by virtue of the inter-linkages of science, technology, public policy, economics, and human behaviors. This course will examine all aspects of energy: supply and demand, technical and social, with a concerted look at the natural place of social science (behavior, pricing, externalities, social norms) in the energy sphere.Every aspect of present-day society depends on the continuing availability of clean, affordable, flexible, secure, and safe energy resources. Yet nearly 90% of our current energy needs are met by fossil fuels. Our reliance on fossil fuels has led to declining supplies, rising prices, global climate change, and security concerns. The current global energy economy is not sustainable. The technological challenges are formidable; but they cannot be considered solutions without considering the human and social behavioral side of energy demand.The quest for solutions to "The Energy Problem" is dominated by technology "fixes". The visions of practical technological fixes, whether electricity energy generation, oil exploration and extraction, pollution mitigation, automobile fuel efficiency and alternatives to combustion engines, etc., necessarily build on what we know today and presume that we can achieve in a couple of decades or so, through sufficient R&D, an energy supply-demand balance that fulfills a wide range of incompatible requirements — cheap, environmentally benign, politically secure, unconstrained supply, convenient, and safe. While we expect technology to come to our energy-rescue and support our established patterns of economic growth and energy-intensive lifestyles, we tend to expect very little from the human and social behavioral side of energy use and demand. In some ways the Energy Problem is yet another version of C.P. Snow's Two Cultures — parallel technology and social cultures with little mutual understanding and rare cross-over exchange.The Complex Systems view would hold that society and Energy technologies have coevolved through the actions of individual agents (inventors, scientists, entrepreneurs, financiers, writers, politicians, kings and queens, dictators, and statesman), learning, adapting, selecting, exchanging information, and interacting through transactions of many kinds. At every stage, the social, economic, and technological systems were tightly coupled. It is not possible to understand Energy Problems without framing them in a systems context.
CMPLXSYS 260/SOC 260: Tipping Points, Bandwagons and Cascades: From Individual Behavior to Social Dynamics --- In this class, we examine how interdependent behaviors of individuals can lead to some surprising and unexpected social outcomes. We will explore both theoretical models and empirical applications of social dynamics, including sexual networks and marriage markets, the formation and transformation of neighborhoods, the success or failure of social movements, and the diffusion of innovation.
CMPLXSYS 270: Agent-Based Modeling (ABM) Many systems can be modeled as being composed of agents interacting with one another and their environment. As a method, agent based modeling (ABM) can explain phenomena in the biological and social sciences, ranging from evolution to epidemic spread to flocking to cooperation to racial segregation in neighborhoods. Very simple rules governing agent behavior can lead to complex and emergent phenomena. In this course students will use NetLogo to examine and modify well-studied agent based models of complex systems, as well as formulate models of their own.
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.
While the following are graduate level courses, they are open to undergraduate students and are valid as credit toward the Complex Systems Minor:
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.