Applied Mathematics for the Life and Social Sciences PhD

Complex Adaptive Systems Science

Our doctoral students can choose to pursue the Complex Adaptive Systems Science concentration, which is designed to train the next generation of scientists in advanced concepts and methods needed for approaching diverse phenomena in the social and life sciences. Students’ career opportunities will be enhanced by combining fluency in the common language of complexity with a solid foundation in the domain knowledge of existing academic disciplines. There is a growing need for scientists to be able to work and collaborate in an increasingly interdisciplinary context.

The concentration is integrated with diverse university-wide research and emphasizes the value of a complex adaptive systems perspective when seeking solutions to critical societal issues. Complex adaptive systems science is the study of interactive and dynamic systems that learn and change over time.

Complex system behaviors are often said to be emergent and subject to self-organization, which makes them more difficult to predict. Such examples can include studying the long-term changes in epidemics, land degradation, urban growth, and natural disasters and their resulting impacts.

Learning Outcomes

Complex adaptive system concepts and tools can serve as bridges between disciplines, providing a common language, and thereby promoting the interdisciplinary collaborations needed to come to grips with the intellectual and societal challenges of the 21st century. Students will be fluent in the language of complexity while also ensuring they receive a solid foundation in the domain knowledge of existing academic disciplines.

By broadly embedding an understanding of complex adaptive system-relevant approaches into the practice of normal science, students will gain the ability to transform science. The CASS program promotes the development and testing of more robust theory and sophisticated methods in a wider array of research settings. This is needed to develop a deeper understanding of the nature and dynamics of complex adaptive systems, grounded in concrete examples and applications. 


A minimum of 15 credits is required for a PhD concentration in Complex Adaptive Systems Science. The required core courses will bring students together in an integrated learning environment to form a cadre of diverse backgrounds. The core courses are designed to provide students with methods and theory appropriate to the study of complex adaptive system science. They will explore the link between concepts of sustainability and systems approaches to knowledge, and will develop the integrative methods needed to work on sustainability problems.

Choose one from the following foundational courses (3 credits):

  • ASM/BIO/SOS 570 Fundamentals of Complex Adaptive Systems Science (Fall)
  • SES 494/591 Fundamentals of Complexity (Spring) 

Choose one from the following mathematics courses (3 credits):

  • AML 591 Probability Theory 
  • AML 610 Topics in Applied Mathematics for the Life and Social Sciences
  • APM 598 Mathematical Methods for Complex Adaptive Systems (Spring)
  • ASM 591 Dynamic Modeling in Social and Ecological Systems

Choose one from the following modeling courses (3 credits):

  • ABS 560 Ecological Modeling (Spring)
  • AML 520 Agent Based Modeling
  • AML 591 Modeling in Game Theory (Spring)
  • AML 612 Applied Mathematics for the Life and Social Sciences Modeling Seminar (Spring)
  • ASM 591 Dynamic Modeling in Social and Ecological Systems
  • CSE 561 Modeling and Simulation Theory & Application (Spring)
  • GIS 598 Local Statistical Modeling (Fall)
  • PAF 591 Introduction to Policy Informatics
  • PUP 598 Modeling and Simulating Urban Environments
  • SOS 591 Agent-Based Modeling for Sustainability (Fall)
  • SOS 591/AML 591/BIO 591 Ecological Modeling

One course in applying CASS approaches as approved by committee (3 credits)
For example:

  • ANB 602 Current Issues in Animal Behavior (Spring)
  • ASM 591/BIO591 Readings in Complexity (Spring)
  • BIO 522 Populations: Evolutionary Ecology
  • BIO 545 Populations: Evolutionary Genetics
  • BIO 591 Topics in Mathematics for Life and Sustainability Science
  • GLG 495/598 Environmental Systems Biology (Spring)
  • PAF 591 Complexity in Public Policy & Management (Spring)
  • PAF 691 Social Dynamics and Policy Informatics (Fall)
  • PSY 576 Dynamics in Psychology
  • PSY 598 Dynamics in Perception, Action and Cognition (Spring)
  • SES 494/591 Fundamentals of Complexity (Spring) 
  • SES 591 The Origins of Life (Spring)
  • SES 598 Environmental Systems Biology
  • SES 598 Fundamentals of Complexity (Spring)
  • SOS 591 Adaptation Resilience Transformation
  • SOS 591 Applied Robustness Analysis in Social-Ecological Systems
  • SOS 598 Social Network Analysis 

Research or reading and conference with a CASS faculty member (3 credits)