#complexity explorer

Introduction to Dynamical Systems and Chaos (Summer, 2016)

About the Course:

In this course you’ll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.

Topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation. The course will focus on some of the realizations from the study of dynamical systems that are of particular relevance to complex systems:

Dynamical systems undergo bifurcations, where a small change in a system parameter such as the temperature or the harvest rate in a fishery leads to a large and qualitative change in the system’s behavior.

Deterministic dynamical systems can behave randomly. This property, known as sensitive dependence or the butterfly effect, places strong limits on our ability to predict some phenomena.

Disordered behavior can be stable. Non-periodic systems with the butterfly effect can have stable average properties. So the average or statistical properties of a system can be predictable, even if its details are not.

Complex behavior can arise from simple rules. Simple dynamical systems do not necessarily lead to simple results. In particular, we will see that simple rules can produce patterns and structures of surprising complexity.

About the Instructor:

David Feldman is Professor of Physics and Mathematics at College of the Atlantic. From 2004-2009 he was a faculty member in the Santa Fe Institute’s Complex Systems Summer School in Beijing, China. He served as the school’s co-director from 2006-2009. Dave is the author of Chaos and Fractals: An Elementary Introduction (Oxford University Press, 2012), a textbook on chaos and fractals for students with a background in high school algebra. Dave was a U.S. Fulbright Lecturer in Rwanda in 2011-12.

Course dates:

5 Jul 2016 9am PDT to 20 Sep 2016 3pm PDT

Prerequisites:

A familiarity with basic high school algebra. There will be optional lessons for those with stronger math backgrounds.

Syllabus

Introduction I: Iterated Functions

Introduction II: Differential Equations

Chaos and the Butterfly Effect

Bifurcations: Part I (Differential Equations)

Bifurcations: Part II (Logistic Map)

Universality

Phase Space

Strange Attractors

Pattern Formation

Summary and Conclusions

Source: Complexity Explorer

There aren’t a lot of available online lectures on the subject of information theory, but here are the ones I’m currently aware of:

Introductory

Brit Cruise (Khan Academy) Informtion Theory

Seth Lloyd (Complexity Explorer/YouTube) Introduction to Information Theory

Advanced

Thomas Cover (Stanford | YouTube) Information Theory

Raymond Yeung (Chinese University of Hong Kong | Coursera) Information Theory (May require account to see 3 or more archived versions)

David MacKay (University of Cambridge) Information Theory, Inference, and Learning Algorithms

Andrew Eckford (York University | YouTube) Coding and Information Theory

S.N. Merchant (IIT Bombay | NPTEL :: Electronics & Communication Engineering) Introduction to Information Theory and Coding

Fortunately, most are pretty reasonable, though vary in their coverage of topics. The introductory lectures don’t require as much mathematics and can probably be understood by those at the high school level with just a small amount of basic probability theory and an understanding of the logarithm.

The top three in the advanced section (they generally presume a prior undergraduate level class in probability theory and some amount of mathematical sophistication) are from professors who’ve written some of the most commonly used college textbooks on the subject. If I recall a first edition of the Yeung text was available via download through his course interface. MacKay’s text is available for free download from his site as well.

Feel free to post other video lectures or resources you may be aware of in the comments below.

Many readers often ask me for resources for delving into the basics of information theory. I hadn’t posted it before, but the Santa Fe Institute recently had an online course Introduction to Information Theory through their Complexity Explorer, which has some other excellent offerings. It included videos, fora, and other resources and was taught by the esteemed physicist and professor Seth Lloyd.…