Chaos and Complexity Courses for Fall 2006, UW-Madison
New Course Offering!
Environmental
Studies 506
Modeling and
Analysis of Environmental Systems
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.
Required Text: DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN
INTRODUCTION TO CHAOS
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
http://www.stat.wisc.edu/~wahba
for more information.