A new graduate course for Spring 2001 at the Massachusetts Institute for Technology...

18.325: Topics in Random Walks and Diffusion

Martin Z. Bazant


Interdisciplinary registration is encouraged for this Topics in Applied Mathematics course. Various mathematical aspects of random walks and diffusion will be developed in the context of real applications from a wide variety of scientific disciplines. A basic understanding of probability, partial differential equations, transforms, complex variables, asymptotic analysis, and computer programming would be very helpful, but there are no formal pre-requisites.

Mathematical Topics: random walks, limit theorems, asymptotics, Levy flights, random waiting times, renormalization groups, percolation.

Applications: financial derivatives pricing and hedging, bacterial motion, heat transfer, porous media, polymers, electrodeposition.

Micrograph of a lithium battery. (H. Feil, Philips Research, Eindhoven)

Diffusion-Limited Aggregation. (L. M. Sander)

Trading of Microsoft stock & the NASDAQ index. (BigCharts.com)

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