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PMath 370 Chaos and Fractals
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Fall 2006
This course is designed to introduce a wide range of students to the mathematical foundations of chaos, fractals, and discrete dynamical systems. Many students are intrigued by the scientific, visual, and computing aspects of chaos and fractals, but do not have much idea of the mathematics involved. This mathematics can be introduced to a student who has a background of calculus and linear algebra.
Instructor
Infinite Binary Fractal Trees
Text
AUTHOR: Gulick, Denny.
TITLE: Encounters with chaos
CALL NUMBER: Q172.5.C45G85 1992 [on 1 day reserve]
IMPRINT: McGraw-Hill, c1992.
The book is out-of-print, but copies made by UW Courseware Solutions will be available from PIXEL PLANET MC 2018.
Course Outline
- Periodic Points - iterates of functions, fixed points, basins
of attraction, periodic points, attracting/repelling points, bifurcations,
Sharkovsky order.
- Chaos - Transitivity, strong chaos, conjugacy, linear functions,
nonlinear maps.
- Fractals - Dimensions, Julia sets, Mandelbrot sets, iterated function
systems.
- Anything else I happen to think is interesting at the time.
Course Mark
The mark in the course will be computed as follows.
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Six Assignments
[Due Sep 22, Oct 6, 20, Nov 3, 17, Dec 1] - 25% (or 15%)
- Review of book, paper, web pages, or video
[Due Oct 13] - 10%
- Midterm test
[on Fri Oct 27 in class] - 15%
- Project or essay [Due on Monday Dec 4] - 20%
- Final exam
[December 9th, 9:00 am - 11:30 am, RCH 308] - 30% (or 40%)
Chaos and Fractal Resources
Books, articles, videos, web links, and programs on chaos and fractals.
Further Course Information
This page was last updated on
by K. G. Hare