Two new courses are open for enrolment on Complexity Explorer and if you missed its inaugural course it is currently underway with enough time left for latecomers to catch up.

Complexity Explorer is the web-based repository of educational materials related to complex systems science from the Santa Fe Institute and Portland State University. It offered its first course, Introduction to Complexity, in Spring 2013. 

A class on complex systems science sounded so interesting that, as well as telling I Programmer readers about it, I and another member of the team signed up. We weren't disappointed and discovered that a lot of fascinating material was included in Melanie Mitchell's initial presentation of this course. It brought together a lot of the ideas that we, as programmers, we were already interested in, broadened our knowledge and presented new challenges. 

If you are interested in the topics Dynamics and Chaos, Fractals; Information, Order and Randomness, Genetic Algorithms and Cellular Automata this course explores all of them and more. As well as video lectures, students also have the opportunity to get "hands-on" experience of the ideas using NetLogo, agent-based simulation software based on the stack-oriented language, Logo. 

The course, which underwent extensive revision to eliminate its initial teething troubles, is currently underway as an 11-week course that ends on September 20th. As an introductory course it has no pre-requisites and has a workload of 3 to 6 hours per week depending on how much of the optional homework you want to do.

The two courses that start on September 1st home in on specific aspects of complex systems and both require some math. 

Fractals and Scaling is a 7-week course presented by David Feldman, who previously gave a fascinating course in Chaos and Dynamical Systems on Complexity Explorer. Judging from the following course outline this one is going to be equally interesting and wide ranging:

1. Introduction to fractals. Self-similarity dimension. Review of logarithms and exponents.

2. Box-counting dimension. Further examples of fractals. Stochastic fractals.

3. Power laws and their relation to fractals. Rank-frequency plots. How to estimate power law exponents.

4. Empirical examples of power laws. Other long-tailed distributions: log normals and stretched exponentials. Implications of long tails.

5. Mechanism for generating power laws. Rich-get-richer phenomena. Phase transitions. Other mechanisms.

6. Metabolic scaling. West-Brown-Enquist scaling theory.

7. Urban scaling.

As a taster of what you might encounter at the first part of this course see The Programmer's Guide to Fractals.

High school algebra is all that is required for Fractals and Scaling, but for the other course that starts at the beginning of September,

Elizabeth Bradley's Nonlinear Dynamics: Mathematical and Computational Approaches you need "at least one semester of college-level calculus and physics" plus the ability to program in at least one high-level language with C, Java, Matlab, R, being the ones mentioned. Maps, discrete-time dynamical systems; flows, continuous-time dynamical systems; and non-linear time series analysis are the topics of this course with multiple weeks devoted to each. 

The course description explains:

In each unit of this course, students will begin with paper-and-pencil exercises regarding the corresponding topics, and then write computer programs that operationalize the associated mathematical algorithms.  This will not require expert programming skill, but you should be comfortable translating basic mathematical ideas into code.  Any computer language that supports simple plotting—points on labelled axes—will suffice for these exercises.  We will not ask you to turn in your code, but simply report and analyze the results that your code produces.

Another course coming in Fall 2015 is Agent-Based Modeling in NetLogo but no details of it are yet available. If you want to explore Netlogo prior to its start, see Getting Started With NetLogo by Mike James. 

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