Hello, my name is David Feldman.
Welcome to the Santa Fe Institute's course "Introduction to Dynamical Systems and Chaos". Thanks for signing up for the class.
The goal of this course is to give you a solid, mathematically grounded introduction to the fields of dynamical systems and chaos.
I've found that with just a little bit of math, basically only using high-school Algebra,
it's possible to get a really solid and grounded understanding of these fields. For example,
in this class you'll learn exactly what the Butterfly Effect is and what it isn't, so you can decide by yourself what it means
and how it applies -or doesn't- to areas of your interest. This course is structured as follows:
In units 1 and 2, I'll begin by introducing the two types of dynamical systems that we'll study throughout the course:
Iterated Functions and Differential Equations.
Units 3 through 7 form the core of the course.
Here, we'll learn about Chaos and the Butterfly Effect, Strange Attractors,
Dynamical Systems, Bifurcations, Universality,
and Pattern-Forming Systems.
Then, in unit 8, I'll take a broader look and we'll consider some of the implications and applications of chaos and dynamics.
As part of this, I'll conduct a series of interviews with other researchers in chaos
to get their opinions on some key questions.
There are a few more things I'd like to mention before we get started.
First, my experience in teaching these topics has been that the first couple of weeks can be a bit of a challenge.
For many of you it will seem too basic, and for others it will seem too hard,
and for some it might seem both too basic and too hard at the same time, which seems impossible,
but my experience says that that's how it seems. It might seem that there's a lot of unfamiliar math
and that we're not moving very quickly or doing very interesting stuff.
However, my experience is that once we get through this introductory material,
we'll kind of end up in the same place, even though we might have different backgrounds
and we will be able to learn about chaos and dynamics, and strange attractors
and it will all work out OK. So I encourage you to stick with it through the first two weeks.
If it seems too easy, don't worry, it will get more complex - if it seems too hard, don't worry, you'll make it.
And, if you have any questions about the course material, please post those questions in the course forum,
which you can find in the Complexity Explorer website. And in general, any questions at all, if you notice that maybe some links aren't working
or something doesn't seem right, let us know on the forum or through e-mail and we'll try to fix it as soon as we can.
So again, welcome to the course.
I'm looking forward to it and I hope you are too!