Chaos and Complexity Courses for Fall 2006, UW-Madison

New Course Offering!

Environmental Studies 506
Modeling and Analysis of Environmental Systems

Prof. Jon Foley (
Center for Sustainability and the Global Environment
Nelson Institute for Environmental Studies

Fall 2006

Lectures:  WF 1:20-2:10
Lab 301:  W 2:30-4:30
Lab 302:  F  2:30-4:30

Room 272, 1710 University (the old "Enzyme Institute" on campus maps)

Level:  introductory graduate, or advanced undergraduate

Prerequisites:  undergraduate science background, working knowledge of calculus; consent of instructor

Description:  This course will focus on system dynamics and the use of modeling techniques to solve complex environmental problems.  Fundamental mathematical approaches, plus the use of computer simulation techniques, will be emphasized.  This course is intended to be a graduate-level introduction to environmental systems modeling, with applications in ecology, hydrology, climatology, biogeochemistry and broader environmental science / earth system science fields.

Modeling projects will be based in Stella (a visual computer language used by many system dynamics experts), which can handle fairly sophisticated projects.  Students will also do a term modeling project on their own, where they can develop their model in other software packages (i.e., C++, Matlab, Fortran, IDL, Vensim) if they like.  Previous programming experience is not required.

Lab assignments will focus on key problems in environmental and earth system science fields, such as population dynamics and species interactions, terrestrial ecosystem processes within natural and managed landscapes, hydrological processes and water resources,  biogeochemical cycles, climate air quality, dynamics and global change.  A strong connection to human dimensions issues (e.g., land use / land cover change, water consumption, atmospheric emissions) will also be included.

Note:  Credit will not be given to students who have also taken Environmental Studies 461 (Environmental Systems Concepts).  Envir. St. 461 (offered every spring) is strongly recommended for most undergraduates (especially those earning the Environmental Studies Certificate) and beginning graduate students with non-science backgrounds.

########## MATH 415 ############

Course Information for Math 415 (Fall 2006)
Van Vleck B325, 02:30 PM - 03:45 PM, TR
Prerequisites: Calculus and Linear Algebra, or instructor's consent for graduate students and advanced undergraduate students from outside mathematics.

Authors: Morris W. Hirsch, Stephen Smale, Robert Devaney
Publisher: Academic Press
ISBN: 0123497035

Recommended Text: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Paperback)
Steven H. Strogatz
Publisher: Perseus Books Group
ISBN: 0738204536

NOTES. Grad students and advanced undergrads have a choice of doing a term project in lieu of the final exam and other requirements in the course. There will be a take-home final or an oral exam whichever the students prefer in case a project is not the option.

The course will review the relevant linear algebra and occasional review of topics from multi-variable calculus to refresh memory.

The students are welcome (and encouraged) to bring research projects from their labs, thesis or an advanced course from outside Mathematics, and to apply modeling methods as part of class homework to gain a practical understanding of the subject. I will provide examples of applications to social networks, behavioral sciences, brain and biology, ecology, economics … depending on the audience.

Statistics 840 Statistical Model Building and Learning
(with Reproducing Kernels, Splines and Related Objects) will be given this fall TuTh 4:00. Pls see Grace Wahba's
home page for more information.