The Chaos Theory talk this past Wednesday was a lot of fun! Professor Michelle Manes gave us a crash course in elementary discrete dynamical systems, and explained (astonishingly simply and clearly) the math behind “chaos”.
For those of you who attended, here are a list of resources if you are interested in learning more about the subject:
(1) Devaney, “A First Course in Chaotic Dynamical Systems.” This is an undergrad textbook that doesn’t assume much more than a solid background in calculus.
(2) Devaney, “An Introduction to Chaotic Dynamical Systems.” This is a more advance book, designed for graduate students. Requires some real analysis and some complex analysis.
(3) Burger and Starbird, “Coincidences, Chaos, and All That Math Jazz.” This is a book about math for people who don’t really know any of it. One chapter explains some of the intuition behind chaotic behavior, including the connections to real-life dynamical systems, without the mathematical details. The authors try to be funny. You can read it and decide if they succeed.
(4) Gleick, “Chaos: Making a New Science.” This is a book about the history of chaos theory. More mathematical than the Burger & Starbird, but not a textbook like the two by Devaney. Very readable.
(5) Williams, “Chaos Theory Tamed.” Similar to the Gleick book. It includes clear explanations of the mathematics as well as an intuitive approach.
(6) http://math.bu.edu/DYSYS/ Lots of applets and information relating to dynamical systems and fractals. This is run by Bob Devaney, and nicely complements his two texbooks listed above.