MATH 4950 

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Spring 2007 courseTopic: FractalsInstructor: Elena Cherkaev Catalog Number: 49501 Credits: 3 Registering requires obtaining the class number from the instructor. Course Outline: This course is part of the REU (Research Experiences for Undergraduates) program, as an important component of the VIGRE grant funded by NSF. The subject varies from one semester to another, in which a faculty member, a graduate assistant, and up to 10 students explore a topic of significant mathematical interest. The students help to present the material or the results of their own investigations, and write a report on their findings. The format of this course is rather flexible, with the class divided into groups, each with 23 students and a particular topic to study over the semester. Fractals are seen everywhere  in shapes of leaves and trees, moutain ranges and coastlines, structure of lungs and porous rocks, and many other physical and biological objects. Fractals are used to design cell phone antennas, describe forest fires, model diffusion of oils and gases, to store data and describe complex systems. The main features characterizing fractals are selfsimilarity, noninteger fractal dimention, and iteration. Billions of fractal shapes can be created using iterated function systems and constructing strange attractors of nonlinear dynamical systems. Prerequisities: We expect backgrounds beyond calculus (such as differential equations, basic complex variables and linear algebra). However, due to the variety of topics available in the class, we do not have a uniform set of requirements. Instead, each prospective student is required to visit the instructor to determine the suitability before registering for the class. Possible topics for the projects are:

