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Courses in LSA Complex Systems
Complex Systems (CMPLXSYS)
CMPLXSYS 425. Evolution in Silico
MATH 115; Comfort with Probability/Statistics; and Proficiency with Programming (e.g., CMPLXSYS 270 or MATH 463/BIOPHYS 463 or CMPLXSYS 391 or CMPLXSYS 530, etc.). (3). May not be repeated for credit.

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. Some of the various implementations we will learn about with hands-on exercises include approaches for solving optimization problems, building controllers and/or bodies for robots, and using computational instances of Darwinian evolution to study fundamental questions in biology.

CMPLXSYS 430 / EEB 430. Modeling Infectious Diseases
Consent of instructor required. MATH 115 or 120. (3). (BS). (QR/2). May not be repeated for credit. Rackham credit requires additional work.

Understanding the spread, evolution and control of infectious diseases requires integrating processes that occur at many scales: infection and pathogenesis within a host, transmission among hosts and long-term evolutionary forces. Mathematical and computational models provide a unique perspective for understanding disease dynamics at these scales individually, but also within an integrated framework. By combining lectures and computer labs, we formulate and analyze various models relating to infectious disease biology, with particular attention to their management control.

CMPLXSYS 489. Advanced Topics in Complex Systems
Advanced standing. Technical prerequisites vary with topic. (3). May be elected three times for credit. Rackham credit requires additional work.

This course covers a broad range of advanced topics relevant to the study of complex systems. Topics include evolutionary systems, self-organizing criticality, measures of complexity, collective intelligence, approaches to modeling complex adaptive systems and emergence.

CMPLXSYS 501. An Introduction to Complex Systems
Graduate standing or permission of instructor. (3). (BS). May not be repeated for credit.

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
MATH 215, 255, or 285; MATH 217; and MATH 425. (3). (BS). May not be repeated for credit.

CMPLXSYS 511. Theory of Complex Systems
(3). (BS). May not be repeated for credit.

This course is a math-based introduction to the theory and analysis of complex systems. Methods covered will include nonlinear dynamics, both discrete and continuous, chaos theory, stochastic processes, game theory, criticality and fractals, and numerical methods. Examples studies will include population dynamics, evolutionary theory, genetic algorithms, epidemiology, simple models of markets, opinion formation models, and cellular automata.

CMPLXSYS 530. Computer Modeling of Complex Systems
Enrollment in certificate program or permission of instructor. (3). (BS). May not be repeated for credit.

CMPLXSYS 535 / PHYSICS 508. Theory of Social and Technological Networks
Calculus and linear algebra; some computer programming experience recommended. (3). (BS). May not be repeated for credit.

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 / PHYSICS 413. Introduction to Nonlinear Dynamics and the Physics of Complexity
PHYSICS 401 or Graduate Standing. (Prerequisites enforced at registration.) An intermediate mechanics course (such as PHYSICS 401) and/or a course in introductory differential equations. (3). (BS). May not be repeated for credit. F.

An introduction to nonlinear science with an elementary treatment from the point of view of the physics of chaos and fractal growth.

CMPLXSYS 599. Independent Study of Complex Systems
Graduate standing and permission of instructor. (1 - 3). (INDEPENDENT). May not be repeated for credit.

This course provides an opportunity for students to pursue independent study and research projects in the area of complex systems, e.g., for use in fulfilling one of the requirements for the Graduate Certificate offered by the Center for the Study of Complex Systems.

CMPLXSYS 899. Information Diffusion in Social Networks
Graduate standing. (1 - 3). May be repeated for a maximum of 9 credits. May be elected more than once in the same term.

Social networks play a crucial role in the diffusion of information and behaviors through society. Multiple effects are involved in the diffusion process. We will focus on three important aspects that play a key role in the diffusion process: Network structure, the cascading mechanics, and communities and clustering. The course will hence focus on three main topics: (i) Models of random network generation, (ii) Models of information diffusion, and (iii) Community detection in networks.

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