Mathematical Background for Complex Systems Science
Teacher
Professor Bernard Manderick
Time and Place
There are no lectures.
Goal
To introduce the students to the mathematical background of the complex dynamics paradigm in artificial intelligence.
Prerequisites
BA computer science or BA mathematics option computer science or equivalent. Linear algebra and calculus are mathematical requirements.
Content
- General introduction to chaos
- Discrete-time dynamics: iterated maps
- Fractals and fractal dimension
- Continuous-time dynamics
- Examples and applications
- Poincaré sections
- Analysis techniques for dynamical systems
- Prediction, modeling, and noise
- Stability
Course Material
Strogatz, Steven H., Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, Perseus Books Group, 2001.
Supplementary Material
- Hilborn, Robert Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers , 2nd Edition, Oxford University Press 2001.
- Wiggins, Stephen Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd Edition, 2003.
Exam
During the course, the students will have to read the course material and write a paper on the subject.
