Complex Systems


Complex Systems
Admits any term. Contact department for additional information and requirements.
Please use the following information when completing the application.
Code: 00139; Academic Program: Complex Systems; Certificate.


Director of Center for Complex Systems: Charlie Doering

Professors: Doering (Complex Systems, Mathematics, Physics), Newman (Complex Systems, Physics), and Page (Complex Systems, Political Science & Economics)

Associate Professors: Bruch (Complex Systems, Sociology), and Deegan (Complex Systems, Physics)

Adjunct Professors: Romero, Sander, and Simon

Degree Programs

Certificate Program

This interdisciplinary curriculum, leading to a Graduate Certificate in Complex Systems, introduces students to the ideas and methods used in the study of complex, nonlinear and adaptive systems. The specific aim is to allow students from different fields to integrate the rich paradigms and useful analytic and modeling techniques of complex systems into their own research.

The curriculum is designed to be accessible to students in a wide range of disciplines in the physical, biological and social sciences. The program accepts students simultaneously enrolled in a graduate degree program at the University. Applicants who have a graduate degree from another university can apply for the Certificate program but must be U.S. citizens.

Students enrolled in the Certificate Program are encouraged to participate in the research activities of the Center for the Study of Complex Systems (CSCS) including our seminar series, the Complex Systems Advanced Academic Workshop (CSAAW) and other special events.

Careers Related to Complex Systems

Complex systems is a scientific approach that relates to many established fields including medicine, economics, political science, natural resources/environment, business administration, public policy, biology, mathematics, physics, epidemiology and engineering. In recent years, CSCS alumni have found jobs with the University of Illinois, Los Alamos National Laboratory, Facebook, Google, Oakridge National Laboratory, University of Maryland and Duke University, among others. In addition, a growing number of organizations in both the public and private sectors are using complex systems techniques including the Ford Motor Company, Lockheed-Martin, Argonne National Laboratory, the U.S. Air Force and the National Institutes of Health.

Program Objectives

  • To provide scientific training in the emerging field of complex systems.
  • To provide students with an understanding of the complex systems approach to their own and other fields of study.
  • To promote and maintain a sense of community among complex systems students, faculty and researchers.

Program Requirements

  • Students should be familiar with a minimal set of concepts and terms as well as key people, models, and basic "complex systems phenomena."
  • Students must have basic math (through calculus) and computer modeling skills, so that they:
    • understand the uses and limits of these approaches
    • can implement their own simple models
    • can appreciate the CSCS seminars
  • Students should have more advanced skills/knowledge in a relevant field such as dynamical systems, computer modeling, or other approaches to complex systems modeling, perhaps as applied to a particular domain.
  • Additional coursework may be required for students who need to fulfill enforced prerequisites for complex systems (CMPLXSYS) courses.

Students must take five courses, including the Group A course, the Group C course and at least one course from Group D for a total of 15 to 19 credits. It is possible to replace the Group D course with an equivalent advanced dynamical systems course or, in very special circumstances, to replace the Group C course with an equivalent course. The courses in Group B represent the minimal calculus background required for the courses in Groups C and D. They do not count toward the five courses in the certificate program.

Group A

  • CMPLXSYS 501: Basic Readings in Complex Systems (3 credits)

Group B

  • Math 215: Calculus III (4 credits)
  • Math 413/SPP 513: Calculus for Social Science (3 credits)

Group C

  • CMPLXSYS 530: Computer Modeling of Complex Systems (3 credits)

Group D

  • CMPLXSYS 510/Math 550: Introduction to Adaptive Systems (3 credits)
  • CMPLXSYS 541/Phys 413: Physics of Complexity (3 credits)
  • CMPLXSYS 535/Phys 508: Network Theory (3 credits)
  • CMPLXSYS 511: Theory of Complex Systems (3 credits)

Group E

Courses related to Complex Systems and approved for the certificate program by the CSCS Director. The list below represents approved courses offered in previous academic years. Please note this is only a partial list. There may be many other courses related to complex systems offered in any given term. Please contact the CSCS Director for approval if you wish to take a course not on this list.

  • EECS 492: Intro to Artificial Intelligence
  • EECS 547/SI 652: Electronic Commerce
  • EECS 587: Parallel Computing
  • EECS 598: Control of Motion in Animals and Machines
  • EECS 695/Psych 640: Neural Models: Mechanisms of Learning
  • EPID 603: Mathematical Modeling of Epidemiology and Public Health
  • EPID 618: Systems Modeling of Behavior, Social Processes and Chronic Diseases
  • EPID 802: Compartmental Model Analysis of Epidemiologic Processes
  • CMPLXSYS 599: Independent Study of Complex Systems
  • CMPLXSYS 899: Special Topics
  • Math 526: Discrete State Stochastic Processes (Biological Applications)
  • Math 654 Introduction to Mathematical Fluid Dynamic
  • NRE 550/STRATEGY 566: Systems Thinking for Sustainable Development
  • NRE 639: Does Space Matter in Natural Resources Research?
  • Phys 510: Statistical Mechanics I
  • Pol.Sci 793: Complexity Theory in the Social Sciences
  • Psych 643/EECS 643: Theory of Neural Computation
  • Psychology 749: Cognitive Functioning

Application to the Program

Applications are accepted at any time of the year from students already enrolled at the University of Michigan. Please note that CSCS Certificate students are given preferential admission to CMPLXSYS classes so if you are considering taking CMPLXSYS courses that have waitlists, you should consider becoming a CSCS certificate student. All applicants must currently be enrolled in a University of Michigan Master’s or Ph.D. program or have received a Master’s or PhD degree from another university.

Current University of Michigan Students

If you are currently enrolled at the University of Michigan, please follow these steps:

  1. Fill out the Dual Degree/Program Application which can be found on the Rackham website: Please use the following information when completing the application: Code: 00319; Academic Program: Complex Systems Certificate.
  2. Obtain approval of the Chair of your department. Your Chair must sign page 4 of the application.
  3. Obtain approval of the CSCS Director. The CSCS Director must also sign page 4 of the application.
  4. Submit your application to Rackham.

Non-University of Michigan Students

If you are not currently enrolled at the University of Michigan, you must first apply to a graduate program at the University of Michigan or you must already have a graduate degree, either Master’s level or Ph.D.

If you plan to apply to a University of Michigan graduate program, you can either apply for the Certificate at the same time using the online application form or you can wait until your first term as a graduate student and follow the directions above. The benefit of waiting until your first term is that you will not need to pay two application fees. You will need to pay a separate application fee if you apply for the Certificate along with another graduate program.

If you already have a Master’s degree or Ph.D. degree, you can apply for the Certificate program by filling out an application to the Horace H. Rackham School of Graduate Studies. This can be found on the Rackham website: Click on “Apply for Admission” and use the following information when completing the application: Code: 00139; Academic Program: Complex Systems Certificate. You must fill out a regular application for admission even though the Certificate is not a formal degree program. You can specify on your application that you are applying for the Certificate by using the information above. All applications to Rackham must be filled out and submitted online unless you are past the Rackham deadline. If past the Rackham deadline, please contact our office and we will provide you with a hard-copy application form. Applications to the Certificate program are accepted at any time but the Rackham online application has a deadline. If you are unable to use the Rackham online form you can still apply for the Certificate using a hard-copy form.

International Students

If you are not a U.S. citizen, you must apply to a University of Michigan graduate program in order to enroll in our Certificate. This is due to a U.S. Immigration requirement that international students must be enrolled full-time in order to qualify for a visa. Please follow application guidelines detailed above as well as the guidelines for international students found on the Rackham website. Applications from international students are due by June 1.

For general requirements for the Rackham Certificate Programs, see the Certificate Programs section of the Rackham Graduate School Academic Policies.


Center for the Study of Complex Systems
University of Michigan 321 West Hall
1085 S. University Ave.
Ann Arbor, MI 48109-1107
Phone: (734) 763-3301
Fax: (734) 763-9267
Program Website:


The following courses constitute the range of approved offerings at the time of the assembly of the publication. Not all of the courses listed below are available for registration. Please see the Schedule of Classes on the Office of the Registrar's website for course offerings by term. The final authority for changes in course offerings rests with the academic departments.

Complex Systems (Subject Code: CMPLXSYS)
430/EEB 430.  Modeling Diseases.  Advisory pre-requisite: MATH 115 or 120  (3 credits)

470/PHYSICS 470.  Nonlinear Dynamics.  Required pre-requisite: PHYS125,135or140&MATH115 eq C>  (3 credits)

489.  Adv Topics Cmplx Sys.  Advisory pre-requisite: Advanced standing. Technical prerequisites vary with topic.  (3 credits)

501.  Intro Complex Syst.  Advisory pre-requisite: Graduate standing or permission of instructor.  (3 credits)

510/MATH 550.  Int Adpt Sys.  Advisory pre-requisite: MATH 215, 255, or 285; MATH 217; and MATH 425.  (3 credits)

511.  Theory of CMPLXSYS.  (3 credits)

520/MATH 552/PHYSICS 580.  Nonlin Sys.  Advisory pre-requisite: Graduate standing, Enrollment in Certificate Program, and permission of instructor.  (3 credits)

529.  Prg Agt-Based Models.  (2 credits)

530.  Computer Modeling.  Advisory pre-requisite: Enrollment in certificate program or permission of instructor.  (3 credits)

535/PHYSICS 508.  Network Theory.  Advisory pre-requisite: Calculus and linear algebra; some computer programming experience recommended.  (3 credits)

541/PHYSICS 413.  Int Nonlin.  Required pre-requisite: PHYSICS 401 or Graduate Standing  Advisory pre-requisite: An intermediate mechanics course (such as PHYSICS 401) and/or a course in introductory differential equations  (3 credits)

599.  Ind Study Cmplx Sys.  Advisory pre-requisite: Graduate standing and permission of instructor.  (1 to 3 credits)

899.  Info Diffusion.  Advisory pre-requisite: Graduate standing.  (1 to 3 credits)

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