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Santa Fe Institute

Nonlinear Dynamics: Mathematical and Computational Approaches

Santa Fe Institute via Complexity Explorer

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This course covers the principles of nonlinear dynamics using mathematical and computational approaches, teaching students how to analyze and model complex systems. The course aims to help learners understand the behavior of nonlinear systems, develop computational skills for modeling such systems, and apply mathematical tools to analyze their dynamics. The teaching method involves a combination of theoretical lectures, hands-on programming assignments, and practical exercises. This course is designed for students and professionals interested in gaining a deeper understanding of nonlinear dynamics and its applications in various fields such as physics, biology, economics, and engineering.

Taught by

Liz Bradley


4.8 rating, based on 68 Class Central reviews

Start your review of Nonlinear Dynamics: Mathematical and Computational Approaches

  • Anonymous
    I had always dreamed of attending a formal course in Nonlinear Dynamics and Chaos . So in some ways, it was like a dream come true. But i am qualifying the statement because this is a seminal introduction to a broad and rich field and should have much more live interaction (possibly by having some live lectures and live discussions instead of it being completely prepackaged). Of course, the content was great and thanks to the faculty members and their assistants !!!! Ideally, i am looking forward to the day when Santa fe announces a MS / Phd program where one can delve into this fascinatingly rich & complex subject formally, rigorously but at liesure !!!
  • Leo Römers
    I found the course very interesting as it used a rather down-to-earth approach with quite clear explanations of essential concepts and also caveats in practice. Much of the required mathematics is explained in this course focussing on concepts rathe…
  • Stunning course with a high pedagogic motivation and a practical orientation which is very much appreciated. I come from a non-physics background and the maths and programming were challenging at the beginning but ended up wanting MORE videos about how to calculate manifolds in practice and more homework on Lyapunov exponents etc. For me it was just GREAT!
  • Anonymous
    Before reviewing the course, a bit about myself. I am a final semester under-grad student from India, pursuing Maths and Computer Science as my Major Subject. Since I am currently doing my project on the characteristics of Lorenz Attractors, the top…
  • Anonymous
    Actually, I'd place the course at 4,5 out of 5. I think, Liz did a great job at giving an overview of nonlinear-dynamics and it's computation. The difficulty was just right for me - with basic knowledge of Analysis, Linear Algebrac and Programming.…
  • Anonymous
    The course was excellent and I feel fortunate to have had the opportunity. I am working to develop a better understanding of complexity theory while also building foundation knowledge in physics and math. In part, I took the course to understand w…
  • Anonymous
    This course is a great gateway to a difficult subject. Professor Bradley explained the essence of technical concepts without dumbing them down, without ignoring or glossing over their mathematical cores, but also without distractingly excessive de…
  • Anonymous
    A fantastic and engaging introduction to the ideas, implementation, and applications of nonlinear dynamics. The course perfectly mixes the underlying theory and math with practical problems and challenges to implement various standard algorithms. You can either take it as an overview course, or take the opportunities given at every stage to dive into the material, reading the literature and improving on the solutions and algorithms presented in lecture. Prof. Bradley is a clear and entertaining lecturer, and she and her TAs were friendly, responsive, and happy to explain and discuss anything related to the course on the course forum.

    Highly recommended!
  • Anonymous
    I wanted to learn something new in the field of advanced mathematics, something that I never studied in grad school or in real life. I am a retired professor of Mechanical Engineering. I wanted to keep learning something new as just as I did when I was working. This course was excellent. She is an excellent professor and through some correspondence with her a very nice woman. She provided some great examples. I hope she will have more advanced courses in the coming year.
    Professor Jake Trexel
  • Anonymous
    1. Perfect course for first timers who want to learn about the field of Nonlinear Dynamics.

    2. Course offered by a Master Instructor making the course interesting and non-mundane.

    3. Tests, home-works etc., complement the learning beautifully.

    4. Course is not easy-peasy. The videos need to watched, re-watched and contemplated upon for the ideas to sink in.

    5. A good command in mathematical computation (using Mathlab/FreeMat, Python, Mathematica, etc., ) is essential for learning the ideas presented in this course.
  • Tristan Hardy
    Loved the course. Great introduction to the math behind several concepts that were, in turn, hinted at in the Introduction to Complexity course on Complexity Explorer. I agree with other reviewers that are interested in more in-depth courses or tutorials that delve into more examples on how to apply these concepts, rather than simply understand them.
  • Anonymous
    Great introduction and a broad sweep of the field. For its objectives, time commitment, and scope, it works well. Worth taking to get a good perspective on nonlinear dynamics. Would tempt you to dig deeper in at least one area.

    Credit to Liz Bradley for the character of the coverage. The support/Q&A forum was superb.

    Maybe not 5star yet, but better than a 4star. The next iteration should be better.
  • Anonymous
    This course provided a clear and concise introduction to the key concepts of non-linear dynamics and chaos. The ample examples and exercises gave me a hands-on experience of its practical applications.

    Thank you Prof. Bradley (and the TAs) for an amazing experience!
  • Anonymous
    It is a wonderful journey through the mystery of nonlinear dynamics. As a sociological student I am first and foremost fascinated by the complex behaviors of the society, and have been looking at conflict resolution which has extensive application of dynamical system theories and the concepts like attractors. Learning the origin of these concepts and ideas has provided me with more insight into the pattern and above all allow me to understand the little amount of effort that human beings can commit to manipulate society and nature, but there are hope for the better. Liz is such an supportive and wonderful professor, I love listening to her in the videos!
  • Anonymous
    Good introduction to and overview of the NLDS. Sometimes it was hard to grasp some deep technical aspects and connect dots. I would recommend to include more examples and keep on doing analogies and real-world examples.
  • Anonymous
    I come from a System Dynamics background where we utilize the concepts of stocks, flows and feedback loops to understand the dynamics of a system. I was trying to understand concepts like eigenvalues and eigenvectors when I chanced upon information…
  • Anonymous
    The course was excellent and I feel fortunate to have had the opportunity. I am working to develop a better understanding of complexity theory while also building foundation knowledge in physics and math. In part, I took the course to understand w…
  • Profile image for Vishwas V Shankar
    Vishwas V Shankar
    excellent course for those who are getting started in non-linear dynamics and chaos. I am currently on unit 7 and I find this course to be very engaging. the video lectures and the questions for homework and the test are very interesting and leaves you wanting for more, which is also taken care by the supplementary section.
  • Anonymous
    Very well organized course. I though the videos were informative and were for the most part presented at an appropriate level. Occasionally. some of the material went over my head, which may be more of a commentary on my head than on the course ma…
  • Anonymous
    The course is very interesting because besides the basic theoretical aspects of dynamical systems it allows you to undestand the mathematics behind the behavior of such dynamical systems. Also allows you to implement your own programs in order to…

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