Courses Taught

Description: This course provides an introduction to the mathematical and philosophical foundations of the study of complex systems. We study a wide range of mathematical models: continuous-time dynamical systems, iterated maps, random walks and diffusion, Markov models and other stochastic network models, cellular automata and other Bayesian network models, Poisson point processes and other models from probability theory, the Ising model and other models from statistical mechanics, and random matrix theory. We also cover a variety of concepts that are closely related to these models, including limit sets and stability, bifurcations, period-doubling and chaos, conservative and dissipative systems, fractals and fractal dimension, phase transitions and criticality, universality, power laws, stable distributions, energy landscapes, measures of network centrality, coarsening, robustness, information, and Shannon entropy. Interspersed with this, we explore applications in population dynamics, microbiology, evolutionary theory, epidemiology, condensed matter physics, opinion formation, and the environment.

Description: This is the middle course in a three-course honors calculus sequence intended for engineering and science majors. It covers both differential and integral multivariable calculus. Topics include vector fields, line, surface, and volume integrals, Green's theorem, Stokes' theorem, the divergence theorem, and applications (e.g. electromagnetic fields, fluid dynamics).

Description: This is the first course in a three-course sequence designed to provide a standard introduction to the concepts and methods of calculus. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and an introduction to integration.

Description: This is a course in the design, analysis, and implementation of computer and communication networks and systems. Topics include Internet best-effort architecture, data transmission and data encoding, data link control, circuit vs. packet switching, congestion control, shortest path routing, asynchronous transfer mode, local area network technology, protocol design (OSE and IP), network security, and multimedia.