Since the tapes are sold for $39.00 each, purchasing the set yields a saving of $13.00!
Description
This set is frequently used by the instructor of a college or high school class in Dynamical Systems. The students can obtain copies of the book for $35.00 and the entire class can view the videos in segments during the course.
Review
The Satellite Scholar, January 1994
The CHAOS SET by Robert L. Devaney includes the video Chaos, Fractals and Dynamics a book also entitled Chaos, Fractals and Dynamics and a second video, Transition to Chaos. Suitable for high school and beyond, the distributor offers each film of this set separately but recommends purchase of both tapes and the book together at a reduced price.
The videotape Chaos, Fractals and Dynamics has received excellent reviews and has been said to "make the notion of chaos come alive," in the words of James Mason in the Mathematics Teacher. This tape offers a basic explanation of dynamical systems and how they are modeled by iterating the quadratic function and trigonometric functions.
The first half of the film, Chaos, Fractals and Dynamics, offers a basic explanation of dynamical systems then focuses at length on iterated function systems on the real line using the quadratic function.
The film's second half examines iterated function systems on the complex plane, detailing stable and chaotic orbits and dynamics of the Julia Set.
Devaney's pace is brisk, but the mathematics are thoroughly explained with the use of may examples, variously repeated on the theme. Excellent use if made of computer-generated graphics, especially motion-tracking of the different images. Students who are not familiar with dynamical systems math, may need to take this material in smaller segments, but even a newcomer will profit and will problably have his/her curiouslity informatively piqued.
The companion film, Transition to Chaos, restates the meaning of iteration along with its diverse day-to-day applications. Then Devaney probes the orbit diagram nad the Mandelbrot set. He shows how these images are constructed and explains the relationship between the images in terms of the mathematics of chaos theory.
These two films and the accompanying book make a fine addition to the math libraries of any high school.