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Courses in LSA Complex Systems
Complex Systems (CMPLXSYS)
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 470 / PHYSICS 470. Experiments in Nonlinear Dynamics
One of: PHYSICS 125 or 135 or 140; and one of MATH 115 or 185; each with a minimum grade of C. (Prerequisites enforced at registration.) (3). (BS). May not be repeated for credit. Rackham credit requires additional work.

The ideas of nonlinear science are essential to the modern scholar with beneficial applications ranging from economic forecasting, climate modeling and social networking. This course introduces the core concepts of nonlinear dynamics through laboratory experiments on physical systems.

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 531. Basic Computing Skills for Programming Agent Based Models
(1 - 2). (BS). May not be repeated for credit.

This course covers the basic computing skills which are required for implementing again-based models using Swarm (and other similar packages) in a LINUX/UNIX environment, including (a) basic LINUX/UNIX commands, (b) basic programming concepts (variables, operators, flow-control), (c) creating simple C and objective C programs and (d) basic Object-Oriented Programming concepts. For students intending to take CMPLXSYS 530.

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.) (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 608 / SI 708. Networks: Theory Complex Systems
Doctoral student status. (3). May not be repeated for credit.

This course will cover topics in network analysis, from social networks to applications in information networks such as the internet. We will introduce basic concepts in networks theory, discuss metric and models, use software analysis tools to experiment with a wide variety of real-world network data, and study applications to areas such as information retrieval. For their final project, the students will apply the concepts learned in class to networks of interest to them.

CMPLXSYS 899. Special Topics in Complex Systems
Graduate standing. (1 - 3). May be repeated for a maximum of 9 credits. May be elected more than once in the same term.

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