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# Minor: Complex Systems

Effective Fall 2011

Over the past twenty years, the ideas and methodologies that underpin the science of complex systems have gained a foothold in the research agendas of many of the world's leading universities. This trend can be explained by the resonance of the complexity paradigm and its focus on core concepts of networks, nonlinear interdependence, adaptation, and diversity to current scientific and social challenges and opportunities. These include climate change, epidemics, ecosystem and financial system robustness, genetic engineering, sustainability science, health sciences and ethnic conflict.

Academic research on nonlinear systems, networks, evolutionary and adaptive systems, emergence, and diversity using mathematics, agent based models, and numerical computation increases with each passing day at think tanks, universities, and laboratories. Most leading graduate programs in physical, biological, and social sciences now include courses that fall under the rubric of complexity science. Many of these courses involve agent based modeling and numerical analysis. At the same time, government and private sector demand for students with skills in modeling, understanding of systems level thinking, and deep understandings of the roles of networks and diversity grows.

The academic minor in Complex Systems is designed to give students an understanding of the basic concepts of complexity science and to learn how those concepts can be applied within a functional area. It provides an opportunity for concentrators in other departments to take a coherent curriculum in complexity and modeling that complements their major field of study. This academic minor requires foundational courses in complex systems theory and modeling. Students are encouraged to attend research seminars and book club meetings run by CSCS. This will provide an opportunity for undergrads to engage intellectually with students and faculty from a range of fields.

**Prerequisites to the Academic Minor**

There will be no formal prerequisites but students who have not taken calculus may find some of the courses difficult. Therefore, previous experience with calculus is strongly recommended.

**Academic Minor Program**

Students are required to elect 15 credits (5 courses) including upper-level courses in complex systems within one of four areas of focus: (1) social sciences, (2) biological science, (3) physical science and engineering or (4) complex systems theory and methods.

**Core Courses**(Take 2 of 4). We require students to take at least one of the modeling courses so that students develop the skills necessary for the upper level classes.- CMPLXSYS 270: Introduction to Agent-Based Modeling (ABM)
- CMPLXSYS 281 / POLSCI 381: Applied Complex Systems: Emergent Challenges
- CMPLXSYS 501: An Introduction to Complex Systems
- CMPLXSYS 511: Theory of Complex Systems

**Elective Courses.**Students must take two courses from one section and one course from another section. The final course can be from this list or a course not on this list as long as it is approved by the CSCS Director. Additional cross-cutting courses such as MATH 295: Honors Mathematics I can also be taken as an elective and will count for any of the four areas, with approval from the CSCS Director.**Physical Science & Engineering**- BIOINF 463 / MATH 463 / BIOPHYS 463: Mathematical Modeling in Biology
- BIOPHYS 463 / MATH 463 / BIOINF 463: Mathematical Modeling in Biology
- CMPLXSYS 470 / PHYSICS 470: Experiments in Nonlinear Dynamics
- CMPLXSYS 520 / PHYSICS 580: Empirical Analysis of Nonlinear Systems
- CMPLXSYS 535 / PHYSICS 508: Network Theory
- CMPLXSYS 541 / PHYSICS 413: Introduction to Nonlinear Dynamics and the Physics of Complexity
- EECS 492: Introduction to Artificial Intelligence
- EECS 587: Parallel Computing
- EECS 598: Special Topics (section titled "Algorithms for Robotics")
- ENGR 371 / MATH 371: Numerical Methods for Engineers and Scientists
- HONORS 493: College Honors Seminar (section titled "Introduction to Networks")
- MATH 176: Explorations in Topology and Analysis (Nonlinear Systems and Chaos)
- MATH 371 / ENGR 371: Numerical Methods for Engineers and Scientists
- MATH 463 / BIOINF 463 / BIOPHYS 463: Mathematical Modeling in Biology
- MATH 471: Introduction to Numerical Methods
- PHYSICS 413 / CMPLXSYS 541: Introduction to Nonlinear Dynamics and the Physics of Complexity
- PHYSICS 470 / CMPLXSYS 470: Experiments in Nonlinear Dynamics
- PHYSICS 508 / CMPLXSYS 535: Network Theory
- PHYSICS 580 / CMPLXSYS 520: Empirical Analysis of Nonlinear Systems

**Social Science**- CMPLXSYS 250: Social Systems & Energy
- CMPLXSYS 260 / SOC 260: Tipping Points, Bandwagons and Cascades: From Individual Behavior to Social Dynamics
- EECS 594: Introduction to Adaptive Systems (section titled "Complexity & Emergence")
- HONORS 493: College Honors Seminar (section titled "Complexity & Emergence")
- MATH 217: Linear Algebra
- MATH 425 / STATS 425: Introduction to Probability
- NRE 550: Systems Thinking for Sustainable Development
- POLSCI 598: Mathematics for Political Scientists
- POLSCI 793: Methods Seminar (section titled "Advanced Modeling in Political Science")
- PSYCH 447: Current Topics in Cognition and Perception (section titled "Complexity & Emergence")
- PUBPOL 513: Calculus for Social Scientists
- SOC 260 / CMPLXSYS 260: Tipping Points, Bandwagons and Cascades: From Individual Behavior to Social Dynamics
- STATS 425 / MATH 425: Introduction to Probability
- STRATEGY 566: Systems Thinking for Sustainable Development

**Biological Science**- BIOINF 800: Special Topics (section titled "Computation and Neuroscience")
- BIOINF 463 / MATH 463 / BIOPHYS 463: Mathematical Modeling in Biology
- BIOPHYS 463 / MATH 463 / BIOINF 463: Mathematical Modeling in Biology
- CMPLXSYS 430 Modeling Infectious Diseases
- CMPLXSYS 510 / MATH 550: Introduction to Adaptive Systems (section titled "Introduction to Dynamics for Biocomplexity")
- EEB 315 / ENVIRON 315: The Ecology and Evolution of Infectious Diseases
- EEB 401: Advanced Topics in Biology (section titled "Interrogating Data with Models")
- EEB 466 / MATH 466: Mathematical Ecology
- ENVIRON 315 / EEB 315: The Ecology and Evolution of Infectious Diseases
- MATH 463 / BIOINF 463 / BIOPHYS 463: Mathematical Modeling in Biology
- MATH 466 / EEB 466: Mathematical Ecology
- MATH 550 / CMPLXSYS 510: Introduction to Adaptive Systems (section titled "Introduction to Dynamics for Biocomplexity")
- MATH 559: Selected Topics in Applied Mathematics (section titled "Computation and Neuroscience")
- MICRBIOL 510: Mathematical Modeling for Infectious Diseases

**Theory & Methods**- BIOINF 800: Special Topics (section titled "Computation and Neuroscience")
- CMPLXSYS 501: Basic Readings
- CMPLXSYS 520 / PHYSICS 580 / MATH 552: Empirical Analysis of Nonlinear Systems
- CMPLXSYS 530: Computer Modeling of Complex Systems
- CMPLXSYS 531: Basic Computing Skills for Programming Agent Based Models (ABM)
- EECS 594: Introduction to Adaptive Systems (section titled "Complexity & Emergence")
- HONORS 493: College Honors Seminar (sections titled "Complexity & Emergence" and "Introduction to Networks")
- MATH 425 / STATS 425: Introduction to Probability
- MATH 462: Mathematical Models
- MATH 552 / CMPLXSYS 520 / PHYSICS 580: Empirical Analysis of Nonlinear Systems
- MATH 559: Selected Topics in Applied Mathematics (section titled "Computation and Neuroscience")
- PHYSICS 580 / CMPLXSYS 520 / MATH 552: Empirical Analysis of Nonlinear Systems
- PSYCH 447: Current Topics in Cognition and Perception (section titled "Complexity & Emergence")
- STATS 425 / MATH 425: Introduction to Probability

### Academic Minor in Complex Systems (through Summer 2011) +

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