The 2001 Fall Quarter home page for this course is located here.
This course is an advanced survey of a range of modern topics in
applied mathematics, theoretical physics, and computer science.
Topics covered may include: chaos, fractals, cellular automata,
boolean networks, random networks and graphs, game theory, agent-based
simulation, and genetic algorithms. Although Calculus is a
prerequisite for this course, most of the topics in this class are not
an extension or application of calculus; this class is designed to
expose students to an array of non calculus-based mathematics.
Students will be encouraged to make interdisciplinary connections
during class discussions, and especially in their final projects.
Evaluation will be based on class participation, bi-weekly problem sets, a few short writing assignments, and a significant final project. Some computer work will be required, but no computer experience is necessary.
Prerequisites: Calculus II (or the equivalent). QR. ES. Lab Fee $15.00. Advanced/Intermediate.
Description from the 1999 course:
This course is a survey of a variety of modern topics in nonlinear dynamics: chaotic finite difference equations, fractals, multifractals, differential equations, boolean networks, and cellular automata. The survey will be conducted at a fairly advanced mathematical level, but the material will be covered with an applied emphasis. Numerical results and applications will be stressed rather than proofs. The text for this course will be Understanding Nonlinear Dynamics, by Daniel Kaplan and Leon Glass. I will likely supplement the text with readings from journal articles and other books.
Evaluation will be based on class participation, weekly problem sets and a final project. Some computer work will be required, but no computer experience is necessary. The final project will provide students an opportunity to examine a particular topic or application in considerable depth. Projects can consist of, but are not limited to: a more rigorous investigation of topics covered in class (i.e., a series of formal proofs); a case study of a particular application; extensive numerical investigation of a model system; a critical investigation of ``chaos theory's'' impact on literature, art, philosophy, or the social sciences; the development of lesson plans or a curricular material for either a high school math course or the introductory course on chaos and fractal taught at COA.
Prerequisites: Calculus II (or the equivalent). Advanced. QR.
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