COS 323 Fall 2007 Computing for the Physical and Social Sciences Ken Steiglitz COS 323 Fall 2007 Computing for the Physical and Social Sciences Ken Steiglitz

Mechanics and course structure See course web page:  course info See course web page:  course info Syllabus, lecture outlines, slides (many courtesy of Prof. Szymon Rusinkiewicz) Syllabus, lecture outlines, slides (many courtesy of Prof. Szymon Rusinkiewicz) Master list of references in pdf, some on reserve in library Master list of references in pdf, some on reserve in library

Goal of course: learn numerical computing through applications 5 assignments: population genetics, finance, chaos, image processing, simulation of nonlinear systems 5 assignments: population genetics, finance, chaos, image processing, simulation of nonlinear systems Term paper Term paper

Stanisław Ulam with MANIC I --- about 10 4 ops/sec

Reading, background Optional text: Numerical Recipes in C [PTVF92]. Really a reference available on web Optional text: Numerical Recipes in C [PTVF92]. Really a reference available on webhttp:// Master reference list Master reference list COS 126 is entirely adequate, don't get too fancy --- We're after the algorithmic and numerical issues COS 126 is entirely adequate, don't get too fancy --- We're after the algorithmic and numerical issues MAT 104 is entirely adequate MAT 104 is entirely adequate Referencing all sources: Do it! Referencing all sources: Do it!

Modeling in general Purposes: quantitative prediction, qualitative prediction, development of intuition, theory formation, theory testing Purposes: quantitative prediction, qualitative prediction, development of intuition, theory formation, theory testing Independent and dependent variables, space, time Independent and dependent variables, space, time Discrete vs. continuous choices for space, time, dependent variables Discrete vs. continuous choices for space, time, dependent variables Philosophy: painting vs. photography Philosophy: painting vs. photography

Examples Discrete-time/discrete-space Discrete-time/discrete-space spatial epidemic models spatial epidemic models Sugarscape Sugarscape seashells seashells lattice gasses lattice gasses cellular autimata in general cellular autimata in general

Examples, con’t Difference equations Difference equations population growth population growth population genetics population genetics digital signal processing, digital signal processing, digital filters, FFT, etc. digital filters, FFT, etc.

Examples, con’t Event-driven simulation Event-driven simulation market dynamics market dynamics population genetics population genetics network traffic network traffic

Examples, con’t Ordinary differential equations Ordinary differential equations market dynamics market dynamics epidemics epidemics seashells seashells insulin-glucose regulation insulin-glucose regulation immune system immune system predator-prey system predator-prey system n-body problem, solar system, n-body problem, solar system, formation of galaxy formation of galaxy

Examples, con’t Partial differential equations Partial differential equations heat diffusion heat diffusion population dispersion population dispersion wave motion in water, ether, earth, … wave motion in water, ether, earth, … spread of genes in population spread of genes in population classical mechanics classical mechanics quantum mechanics quantum mechanics

Examples, con’t Combinatorial optimization Combinatorial optimization scheduling scheduling routing, traffic routing, traffic oil refining oil refining layout layout partition … and many more partition … and many more

Spatial Epidemic Models [Dur95] R. Durrett, "Spatial Epidemic Models," in Epidemic Models: Their Structure and Relation to Data, D. Mollison (ed.), Cambridge University Press, Cambridge, U.K., [Dur95] R. Durrett, "Spatial Epidemic Models," in Epidemic Models: Their Structure and Relation to Data, D. Mollison (ed.), Cambridge University Press, Cambridge, U.K., Discrete-time, discrete-space, discrete- state Discrete-time, discrete-space, discrete- state Simulation, ODEs, PDEs Simulation, ODEs, PDEs