Mathematics

Prerequisite: Consent of the graduate advisor. This course provides essential mathematical tools for the study of complex systems. Topics include vector calculus, linear algebra and aspects of differential equations and partial differential equations.

Prerequisite: Consent of the graduate advisor. This course introduces physical approaches to dealing with complex, many-body systems. Two distinct and complementary frameworks are presented: analytical mechanics and statistical physics. Core concepts include Lagrangian and Hamiltonian formulations of mechanics, phase space, nonlinear dynamics, chaos, fractals, free energy, entropy, partition functions and statistical ensembles.

Prerequisite: Consent of the graduate advisor. The first part of the course will cover nonlinear chemical kinetics, control of chemical reactions, self-assembly at microscopic and macroscopic levels, and development of new techniques for materials synthesis. In the second part, quantum chemical models for describing large systems and their interaction with the surroundings will be introduced.

Prerequisite: Consent of the graduate advisor. The course will explore how to analyze biology from a systems-level point of view. Students will explore design principles in biology, including plasticity, exploratory behavior, weak-linkage, constraints that deconstrain, robustness, (non)optimality and evolvability.

Prerequisite: Consent of the graduate advisor. Overview of computer science topics relevant to complex systems, including software development, design of algorithms, computer simulation, computer and sensor networks, social networks and agent-based systems.

Prerequisite: Consent of the graduate advisor. This course introduces the principles and methods of complex systems engineering. The course is organized as a progression through the systems engineering processes of analysis, design, implementation and deployment with consideration of verification and validation throughout. Case studies and guest lectures in each phase present best practice in the field …

Prerequisites: Passing preliminary examination and graduate advisor consent. This course provides an overview of complex systems and describes theoretical, numerical and computational approaches to defining, analyzing and solving applied problems in complex systems.

Prerequisites: CPLX 710A, passing preliminary examination and graduate advisor consent. Hands-on activities on complex systems topics. Examples of course project topics include complex networked systems (sensor networks and social networks) and agent-based modeling (genetic programming and evolutionary strategies).

Prerequisites: Passing preliminary examination and graduate advisor consent. Advanced studies in various subjects related to complex systems through special seminars, informal group studies of special problems, or group research on complete problems for analysis and experimentation.