The Center for the Study of Complex Systems (CSCS) and the Horace H. Rackham School of Graduate Studies at the University of Michigan are pleased to offer a Certificate of Graduate Studies in Complex Systems.
This interdisciplinary curriculum, leading to a Graduate Certificate in Complex Systems, will introduce students to the ideas and methods used in the study of complex, nonlinear and adaptive systems. The specific aim of this curriculum 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 as well as a select number of students and professionals from outside the University.
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, reading group and other special events.
Complex systems is a new scientific approach that relates t o 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 wit h the University of Illinois, Los Alamos National Laboratory, Oakridge National Lab oratory, 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 sy stems techniques including the Ford Motor Company, Lockheed-Martin, Argonne National Laboratory , the U.S. Air Force and the National Institutes of Health.
- 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
Students should be familiar with a minimal set of concepts and terms as well as key people, models, and basic "complex systems phenomena."
- Students should have basic math and computer modeling skills, so that they:
- Understand the uses and limits of these approaches
- Can implement their own simple models
- Can understand at some minimal level 90% of 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.
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. Within Group D, students with weaker mathematics backgrounds should take CMPLXSYS 510; students with stronger math backgrounds should take CMPLXSYS 520 or 541. 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 but every student must take at least one of CMPLXSYS 510 or CMPLXSYS 530. The courses in Group B represent the minimal programming and calculus background required for the courses in Groups C and D; we anticipate that most students will not need to take these courses. They do not count toward the five courses in the certificate program.
- Math 413/SPP 513: Calculus for Social Science (3 credits)
CMPLXSYS 530: Computer Modeling of Complex Systems (3 credits)
- CMPLXSYS 510/Math 550: Introduction to Dynamical Systems for Complex Systems and the Life Sciences. (3 credits—revised and lengthened from its previous format to include an introduction to material in CSCS 520 and 541.)
- CMPLXSYS 541/Phys 413: Physics of Complexity (3 credits)
- CMPLXSYS 520/Phys 580: Empirical Analysis of Nonlinear Systems (3 credits)
- CMPLXSYS 535/Phys 508: Network Theory (3 credits)
- CMPLXSYS 511: Theory of Complex Systems (3 credits)
- CMPLXSYS 608: Network Theory of Complex Systems (3 credits)
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 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 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
In order to receive full consideration for enrollment in the Fall term, completed applications should be received by April 30 of that year. 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 CSCS classes so if you are considering taking CSCS courses that have waiting lists, you should consider becoming a CSCS certificate student. All applicants must currently be enrolled in a University of Michigan Master’s or PhD 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:
- Fill out the Dual Degree/Program Application which can be found on the Rackham web site: http://www.rackham.umich.edu/downloads/admissions/forms/DualDegreeProgram.pdf.
Please use the following information when completing the application: Code: 00139; Academic Program: Complex Systems Certificate.
- Obtain approval of the Chair of your department. Your Chair must sign page 4 of the application.
- Obtain approval of the CSCS Director. The CSCS Director must also sign page 4 of the application.
- 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 PhD. 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 PhD 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 web site: www.rackham.umich.edu/policies/forms. 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 accept ed 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.
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.