Readings, etc. - Complex Systems Summer School
Tom Carter

These are some readings, etc., related to the SFI Complex Systems Summer School.

Many of these are things I've developed over the years for CSSS (and other classes I teach), as "lecture notes" for lectures I've given. During many Summer Schools, I was available for discussion of various of these . . .

My home page is here: Tom Carter.

  • These are lecture notes on Information Theory:

        Information theory and entropy.

  • Here are some lecture notes on linear algebra (including a section on eigenvalues / eigenvectors), which in the past have been part of a "Math review" for the Summer School.

        Brief Survey of Linear Algebra

  • Here are some lecture notes on nonlinear systems and chaos -- I use these in a class I teach at my home campus (the notes are "in progress" . . . )

        Nonlinear systems (and chaos . . .)

  • Here are some lecture notes on random walks, with some additional material, including some biological examples

        Random walks

  • Here are some lecture notes on economics, high finance, and Black-Scholes . . .

        High finance (Black-Scholes, etc.)

  • Here is a page linking to several models:

        models (NetLogo and RePast)

  • Here is a pdf of the "What shape is a circle" notes:


  • Here are a powerpoint and a pdf of the "Interdisciplinary" notes:



  • Here are some notes on Computation Theory, which may come in handy for various lectures. These are notes from some lectures I have given during previous Summer Schools:

        Computation theory.

  • and also some notes on quantum computation:

        Quantum computation.

  • Here are some brief notes on "fractional derivatives" -- one way to define them:


  • Here are some notes on "symbolic dynamics"

        Symbolic Dynamics.pdf

  • Here are some notes on "Simpson's Paradox"


  • Here are some notes on assessing risk (and the so-called "doomsday argument")


  • Here are some notes on voting (related to Arrow's Theorem . . .)


  • Here is a short path through some parts of my "entropy" notes focusing on the "economic" (also ideal gas . . .) models, but there is also an additional section on power laws

        A short trip through entropy to power laws

  • Speaking of power laws (and economics), here is some stuff I wrote a while back about "social insurance" of various forms, tax policy, and economic issues . . .

        social insurance

  • Here is a pdf on fractal dimension (including a couple of examples with fractal dimension exactly 1 . . .):


  • This is the current version of the "Theories and Models" material (it's rough -- I'm still working on it . . .):

        Theories and Models (Making sense)

  • Here is MatLab code for some of the Takens' embedding process. This code was written by a CSSS 2003 project group (that included Aaron Clauset) to analyze data from a water wheel experiment. It is largely derived from material in a book by H. Abarbanel ("Analysis of Observed Chaotic Data" -- a very good book, definitely worth looking into if you are analyzing time series or other large data sets), and includes false nearest neighbor / embedding dimension code, etc.

        FNN.m (false nearest neighbor)

        analwheel.m (some other analysis tools)

  • This is Claude Shannon's classic 1948 paper on information, entropy, and communication theory.

        Claude Shannon's paper "A Mathematical Theory of Communication" (and also a site with some background.)

  • A chaos/nonlinear systems explorer - written in java:

        Chaos explorer.

  • I'll also put here links to a couple of books that I have found to be useful resources for exploring/understanding complex systems, with an emphasis on dynamics. Both are fairly technical, but definitely worth exploring . . . :

        Dynamics of Complex Systems by Yaneer Bar Yam.

        Complex and Adaptive Dynamical Systems by Claudius Gros

    Questions or comments may be mailed to:

    tom at