“Emergent property” has been an increasingly prominent buzzword in recent decades, as researchers attempt to understand how a living cell can be fashioned from molecules, none of which is alive; how a brain can remember a face, even while no neuron has an image of the face, and yet the brain consists of nothing but neurons; how an epidemic can have recognizable patterns of growth and dissipation, though the infected individuals are always new. The course will explore how the mathematical theories of dynamical systems, stochastic processes, and thermodynamics have been variously brought together in recent years to model the behavior of complex systems.
 

Dynamic Syllabus

Week	Topic	Problem sets
1	Introduction
2	Fundamentals of thermodynamics
3	Dynamical systems	Problem set 1 (Solution)
4	Evolutionary thermodynamics
5 -- 7	Population models	Problem set 2
8 -- 9	Higher-dimensional dynamical systems
10 -- 11	Interacting partical systems
12 -- 13	Neural networks
14	Student presentations

Prerequisites

A moderate level of comfort with linear algebra, calculus, and probability theory will be supposed. This is primarily a course in mathematical models and methods. Theorems will be proved! On the other hand, many mathematical tools will be built up from the middle, leaving it to the students to decide for themselves how much technical detail they wish to explore in the privacy of their closet.

Last updated January 29, 2002

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