Mathematical background for one wishing to study Chaos/Complexity Theory

Question

I don't have a very strong mathematics background. In fact I quite abhorred mathematics during my Middle/High School years. I'm currently applying for PhD programs in the field of literature as that is my expertise. However over the years I have developed an interest in Mathematics. I've audited a few basic mathematics courses at my local university (Finite Math, Intro to Stats, etc). I'm by no means an expert. Over the years I've taken quite an interest in Chaos/Complexity theory. I know it can be applied to areas outside of mathematics such as sociology and economics. However, I'm most interested in its possible application to the humanities (literature, art, etc). I want to research this further but I'm a bit scared of delving in as I don't know how much math I'll actually need to know. Could someone recommend areas of math which are required for an in-depth understanding of Chaos? Perhaps I could combine some course audits with self-teaching in order to better understand the theory.

Sorry if these questions seem painfully obvious.

Answer 1

Here are a few recommendations:

1. You are going to need to have a solid background in calculus, through at least multivariable. If you really understand what's going on there (i.e., what is the definition of a limit), you should be able to grasp the rest.

2. Get Steven Strogatz's book on nonlinear dynamical systems: Strogatz

3. Devaney is good too.

4. List item

5. Also, read Arcadia by Tom Stoppard.

Answer 2

It depends on what you mean by in-depth. I did my senior undergraduate project on chaotic dynamical systems and I can say that the areas I leaned on the most were Calculus and linear algebra. Id you want to get really technical (which I suppose you don't) you can throw in some basic topology and metric spaces.

To understand what chaos is at a high level, I would recommend calculus and linear algebra and maybe some probability. You can make many beautiful images with chaotic systems. For an introduction to this, you could read Barnsley's Fractals Everywhere. It can get technical, but you don't need to understand all the math to get the ideas.

As far as Complexity theory, that's a different beast. For that you will need combinatorics, graph theory and theoretical computer science. There are numerous well known books introducing algorithm analysis.