Skip to Content

Search: {{$root.lsaSearchQuery.q}}, Page {{$}}

Complex Systems Graduate Certificate

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, 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 who are either:

A) simultaneously enrolled in a graduate degree program at the University of Michigan, or

B) who have a Bachelor's degree or higher from any University AND are 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, sociology, 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 Los Alamos, Oakwood and Argonne National Laboratories; Facebook, Google and the Universities of Duke, Maryland, and Northwestern; to name a few. In addition, a growing number of organizations in both the public and private sectors are using complex systems techniques including the automotive and aeronautics industries; financial services and hedge funds; the U.S. Air Force; the U.S. Army Research Office and the National Institute of Health.

Program Objectives

  • To provide scientific training in the 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 course work may be required for students who need to fulfill enforced pre-requisites for Complex Systems (CMPLXSYS) courses

Students must take five courses, including both Required Core Courses CMPLXSYS 501 and CMPLXSYS 530.  In addition, students must take at least one course from the list of 'Core Electives' below and additional elective courses for a total of 15 to 19 credits.  With permission of the CSCS Director, it is possible to replace the Core Elective course with an equivalent advanced dynamical systems course or, in very special circumstances, to replace CMPLXSYS 530 with an equivalent course. Please note prerequisites for CMPLXSYS 530 include the equivalent of a basic programming course and intermediate-level calculus (Math 216).


  • CMPLXSYS 501: Introduction to Complex Systems (3 credits)
  • CMPLXSYS 530: Computer Modeling of Complex Systems (3 credits) 

CORE ELECTIVES (Choose at least one)

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

  • CMPLXSYS 425: Evolution in Silico
  • CMPLXSYS 435: Ecological Networks
  • CMPLXSYS 489: Entropy & Information
  • CMPLXSYS 599: Independent Study of Complex Systems
  • CMPLXSYS 899: Special Topics
  • EAS 550/STRATEGY 566: Systems Thinking for Sustainable Development
  • 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
  • MATH 526: Discrete State Stochastic Processes (Biological Applications)
  • MATH 654 Introduction to Mathematical Fluid Dynamic
  • PHYSICS 510: Statistical Mechanics I
  • POLSCI 793: Complexity Theory in the Social Sciences
  • PSYCH 643/EECS 643: Theory of Neural Computation
  • PSYCH 749: Cognitive Functioning
  • SI 608: Networks

Application to the Program

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.

Current University of Michigan Students

If you are currently enrolled at the University of Michigan and have completed at least one term of graduate coursework in good academic standing, please follow these steps:

  1. Fill out the Dual Degree/Program Application which can be found on the Rackham web site: Please use the following information when completing the application: Code: 00139; 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 a U.S. citizen not currently enrolled at the University of Michigan - Ann Arbor campus, you must have a Bachelor's degree in order to apply to the Certificate program.

If you plan to apply for another University of Michigan graduate program and also want to concurrently recieve a Complex Systems Graduate Certificate - you must FIRST apply to, and be accepted to the other Graduate program, AND complete at least one term of coursework in good academic standing before requesting admission to another degree or certificate. Students pursuing any combination of master’s degrees/certificates must complete an “Add a Degree or Certificate Application,” and, in accordance with the policy for double-counting credits (section 6.2), submit the appropriate “Dual Degree Course Elections” form.     

If you already have a Bachelor's degree, Master’s degree or PhD degree, and want to pursue the Complex Systems Graduate Certificate as a stand-alone program you can apply by filling out an application to the Horace H. Rackham School of Graduate Studies. This can be found on the Rackham website: 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 full-time  University of Michigan graduate or PhD 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 May 1 for Fall term enrollment.