Course Graphic

Past Classes:

 Topics in Complexity (Winter 2016)

Course description:

The behavior of complex systems will be explored through hands-on experiments and computer simulations. Nonlinearity, fractals, chaos, and self-organization will be studied using double pendulums, flocking models, chaotic video feedback, and social experiments. Emphasis will be placed on experiments and simulations while readings and mathematical derivations will be used to supplement learning. No prerequisites required. Graduate student-led seminar.

 

Complex Systems Applications (BIO 131, Winter 2015)

Instructor(s):  Marshall Kuypers, Aaron Goodman, Jacob Reidhead
Faculty Sponsor:  Marc Feldman

Course description:

Applications of complex systems will be explored in this seminar through lectures, discussions, and a class project. Lecture topics include a discussion of chaos in weather modeling and aircraft turbulence, application of network science to understand Ebola and the ALS ice bucket challenge, and self-organized processes such as crowd dynamics and Wikipedia. The first half of the course will emphasize complex systems applications. Students will apply complex systems analysis techniques to their personal research, a current event, or repeat a classic complex systems experiment. Projects can include topics such as calculating the fractal dimension of a forest, simulating crowd dynamics, studying the degree distribution of social networks, or making a Van der Pol oscillator. Graduate student led seminar. Can be repeated for credit.

Complex Systems Lab (BIO 131, Fall 2013)

Instructor(s):  Marshall Kuypers, Oana Carja, Rebecca Wilbanks and Mark D. Longo
Faculty Sponsor:  Marc Feldman

Fall 2013 Syllabus

Course description:

The behavior of complex systems will be explored through hands-on experiments and computer simulations. Nonlinearity, fractals, chaos, and self-organization will be studied using double pendulums, flocking models, chaotic video feedback, and social experiments. Emphasis will be placed on experiments and simulations while readings and mathematical derivations will be used to supplement learning. No prerequisites required. Graduate student-led seminar.

The Mathematics of Complexity (BIO 131, Fall 2012)

Instructor(s):  Oana Carja, Diamantis Sellis, Joel Thompson and Mark D. Longo
Faculty Sponsor:  Marc Feldman

Fall 2012 Syllabus

Course description:

We’ve all heard the buzzwords – chaos, fractals, networks, power laws.  What do these terms mean in a rigorous, mathematical sense? This 1-2 credit seminar will explore formalisms associated with the study of complex systems. These include non-linear dynamics (and their associated phase space mappings, as well as chaos), graph theory (networks), and fractals (and their associated power laws). Through readings, in-class problem sets, and hands-on computer-based simulations, we will pursue a concrete understanding of these concepts as well as the ability to implement them as mathematical tools. A basic course in calculus and differential equations and some coding experience would be helpful but is not required.

    Videos:

 Note:  This class was largely discussion based.  To get the most from these videos we suggest reviewing the suggested readings listed on the syllabus before viewing.
Lecture 4: Chaos
Lecture 5: Fractals
Lecture 6: Power Laws
Lecture 7: Networks
Lecture 8: Networks II (No Video)

Modeling Complex Systems (MS&E 228, Spring 2012)

Instructor(s):  Robert J. Glass

Course description:

Complex systems are non-linear, non-equilibrium systems that contain interdependent interacting elements and often yield emergent structure (e.g., influence or social networks) and behavior (e.g. cascades such as fads); many (if not most) biological systems and systems that contain humans are inherently complex. This course presents approaches to modeling complex systems for both explanatory and policy related purposes; systems are abstracted and analyzed and ways of influencing them designed. Application spans many fields including management, business, finance, economics, biology, psychology, health, anthropology, sociology, political science, communication and education, all areas where complex systems modeling and design has enormous potential impact. Some familiarity with systems thinking and differential equations is desirable but not required.

We will first investigate a set of canonical abstract models such as the Lotka-Volterra predator prey model that yields bifurcation and chaos, the Bak-Tang-Wiesenfeld sandpile model that yields self-organized criticality, the preferential attachment model that yields scale-free networks, and the opinion dynamics model that yields self-organized group formation. Through these examples, the general conceptual lens for modeling complex systems, where system elements, their behavior and their interactions with other system elements are defined, is illustrated. We will then apply this lens to model a set of real world complex systems for both explanatory and policy related purposes where the system is abstracted and analyzed and ways of influencing the system are designed. Concepts of robustness of policy choice to model uncertainty will be introduced. Throughout the course, students will model and explore the behavior of complex systems (abstract and real world) using a variety of open source (e.g., NetLogo and Repast for agent based, Pajek for networks) and demonstration (e.g., STELLA for systems dynamics provided with one of the course texts) software packages. At the end of the course, each student will complete an independent project where they abstract and model a complex system of their choosing, explore its dynamics and design influence within.

For more information about Dr. Glass or to contact him, please see his Sandia National Labs website.

Topics in Complexity (Bio 131, Fall 2011)

IInstructor(s):  Mark D. Longo, Rebecca Wilbanks, Diamantis Sellis
Faculty Sponsor:  Robert Sapolsky

Fall 2011 Syllabus

Course description:

A survey of the tools, findings, and philosophical and cultural implications associated with the study of complex systems, including self-organization, emergence, networks, nonlinear dynamics, autopoiesis, and others. Classes will include discussions of readings as well as guest lectures by faculty describing aspects of their complex systems of study.