### Program Requirements

Students are required to elect **15 credits (5 courses)** including two core courses and three electives from the following areas of focus: (1) Social Sciences, (2) Biological Science, (3) Physical Science and Engineering or (4) Complex Systems Theory and Methods. Two of the electives are to be from one area and one from another.

### A. Core Courses (Take 2 of 4)

**CMPLXSYS 270**/Intro to Agent-Based Modeling (ABM)**CMPLXSYS 391**/Poli Sci 391 Intro to Modeling**CMPLXSYS 501**Basic Readings in Complex Systems**CMPLXSYS 511**Theory of Complex Systems

**Elective Courses**

Students must take two (2) courses from one section and one (1) course from another section. An elective course can be from this list or a course not on this list as long as it is approved by the CSCS Director.

### Section I: Physical Science & Engineering

CMPLXSYS 535/PHYSICS 508 | Network Theory |

CMPLXSYS 541/PHYSICS 541 | Nonlinear Dynamical Systems |

EECS 492 |
Introduction to Artificial Intelligence |

EECS 587 |
Prallel Computing |

EECS 598 |
Algorithms for Robotics |

ENGR 371/Math 371 |
Numerical Methods for Engineers & Scientists |

MATH 176 |
Explorations in Topology and Analysis (Nonlinear Systems and Chaos) |

MATH 463/BIOPHYS 463 |
Mathematical Modeling in Biology |

MATH 471 |
Introduction to Numerical Methods |

### Section II: Social Science

CMPLXSYS 250 |
Social Systems & Energy |

CMPLXSYS 260/SOC 260 |
Tipping Points, Bandwagons and Cascades: From Individual Behavior to Social Dynamics |

CMPLXSYS 489/POLISCI 489 |
Collective Intelligence |

EECS 594 |
Introduction to Adaptive Systems: Complexity & Emergence |

MATH 217 |
Linear Algebra |

MATH 425/STATS 425 |
Introduction to Probability |

NRE 550/STRATEGY 566 |
Systems Thinking for Sustainable Development |

POLISCI 598 |
Mathematics for Political Science |

PSYCH 447 |
Current Topics in Cognition and Perception: Complexity & Emergence |

PUBPOL 513 |
Calculus for Social Scientists |

SI 301 |
Models of Social Information Processes |

### Section III: Biological Science

BIOPHYS 463/MATH 463 |
Mathematical Modeling in Biology |

CMPLXSYS 425 |
Evolution In Silico |

CMPLXSYS 510/Math 550 |
Introduction to Adaptive Systems |

EEB 315/ENVIRON 315 |
Ecology & Evolution of Infectious Disease |

EEB 401 |
Advanced Topics in Biology: Interrogating Data With Models |

EEB 466/MATH 466 |
Mathematical Ecology |

ENVIRON 401 |
Modeling Coupled Human-Natural Systems |

MATH 559 |
Selected Topics in Applied Mathematics: Computation and Neuroscience |

MICRBIOL 510 |
Mathematical Modeling for Infectious Diseases |

PHYSIOL 520 |
Computational Systems Biology Physiology |

### Section IV: Theory & Methods

CMPLXSYS 489 |
Advanced Topics in Complex Systems |

CMPLXSYS 501 |
Intro. to Complex Systems: Basic Readings |

CMPLXSYS 520/PHYSICS 580/MATH 552 |
Empirical Analysis of Nonlinear Systems |

CMPLXSYS 530 |
Computer Modeling of Complex Systems |

EECS 594 |
Introduction to Adaptive Systems |

HONORS 493 |
College Honors Seminar: Complexity & Emergence and Introduction to Networks |

MATH 425/STATS 425 |
Introduction to Probability |

MATH 462 |
Mathematical Models |

MATH 559 |
Selected Topics in Mathematics: Computation and Neuroscience |

### Advising

The CSCS Director and core faculty will serve as advisors to students. The CSCS Chief Administrator, Mita Gibson, (msgibson@umich.edu) will be the initial point of contact. Students who wish to enroll in the minor must first declare their major and then contact the CSCS office.

## Prerequisites

No formal prerequisites (beyond those required for specific courses) but it is strongly recommended that students have experience with at least one and preferably two calculus courses.

## Additional Information

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 minor requires foundational courses in complex systems theory and modeling. Students are encouraged to attend research seminars and workshops hosted by **CSCS**. This will provide an opportunity for undergraduates to engage intellectually with students and faculty from a range of fields.