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Complexity Explorer: Nonlinear Dynamics: Mathematical and Computational Approaches

 with  Liz Bradley
This course provides a broad introduction to the field of nonlinear dynamics, focusing both on the mathematics and the computational tools that are so important in the study of chaotic systems. The course is aimed at students who have had at least one semester of college-level calculus and physics, and who can program in at least one high-level language.

After a quick overview of the field and its history, we review the basic background that students need in order to succeed in this course. We then dig deeper into the dynamics of maps—discrete-time dynamical systems—encountering and unpacking the notions of state space, trajectories, attractors and basins of attraction, stability and instability, bifurcations, and the Feigenbaum number. We then move to the study of flows, where we revisit many of the same notions in the context of continuous-time dynamical systems. Since chaotic systems cannot, by definition, be solved in closed form, we spend several weeks thinking about how to solve them numerically and what challenges arise in that process. We finish by learning about techniques and tools for applying all of this theory to real-world data.
17 Student
reviews
Cost Free Online Course
Subject Calculus
Institution Santa Fe Institute
Language English
Certificates Certificate Available
Calendar 10 weeks long
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FAQ View All
What are MOOCs?
MOOCs stand for Massive Open Online Courses. These are free online courses from universities around the world (eg. Stanford Harvard MIT) offered to anyone with an internet connection.
How do I register?
To register for a course, click on "Go to Class" button on the course page. This will take you to the providers website where you can register for the course.
How do these MOOCs or free online courses work?
MOOCs are designed for an online audience, teaching primarily through short (5-20 min.) pre recorded video lectures, that you watch on weekly schedule when convenient for you.  They also have student discussion forums, homework/assignments, and online quizzes or exams.

17 reviews for Complexity Explorer's Nonlinear Dynamics: Mathematical and Computational Approaches

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5 out of 5 people found the following review useful
3 years ago
Leo Römers completed this course, spending 2 hours a week on it and found the course difficulty to be medium.
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 rather than all technical details. Personally I would have preferred the mat Read More
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 rather than all technical details. Personally I would have preferred the mathematics to be a prerequisite (to avoid spending time to listen to familiar material) or subject of e.g. separate preparatory lessons. Both quizzes and tests help to clarify concepts covered in video lectures. I didn't do the "homework" that requires some basic programming skills, but used Excel in some cases as a quick bypass. This has been my third Complexity Explorer course of the Santa Fe Institute and I am generally very pleased with them.
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1 out of 1 people found the following review useful
10 months ago
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Anonymous completed this course.
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 g Read More
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!
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1 out of 1 people found the following review useful
2 years ago
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Anonymous partially completed this course.
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 profe Read More
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.

Sincerely

Professor Jake Trexel

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3 out of 3 people found the following review useful
3 years ago
Juan Cabrera García-olmedo completed this course.
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!
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a year ago
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Anonymous completed this course.
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. Read More
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.

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2 out of 2 people found the following review useful
2 years ago
Tristan Hardy completed this course, spending 2 hours a week on it and found the course difficulty to be easy.
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.
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2 months ago
James Paul Chibole completed this course.
The relationship between concepts is well built starting from the basics to higher one. Once the instructor introduces a concepts, then in final stage she explains the limitations of the concept. the next chapter's concept is therefore an effort to address the shortcomings of the previous concepts, and so on and so on. Read More
The relationship between concepts is well built starting from the basics to higher one. Once the instructor introduces a concepts, then in final stage she explains the limitations of the concept. the next chapter's concept is therefore an effort to address the shortcomings of the previous concepts, and so on and so on. In other words, a concept is just not introduced from the blues. There are also aside mathematical notes in the so called supplementary materials to understand the concepts deeper making the course highly effective.
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3 years ago
Flavio Massimo Saldicco completed this course.
Exceptionally well taught, well organized, very good balance between theory and practice. The programming assignments were fun and motivating. It would be nice to have in the future a second, "advanced", session.
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10 months ago
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Anonymous completed this course.
An Interesting introduction to chaos and its application to real world. 10 weeks of both understaing theory and doing some programming exercises.
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3 years ago
Bob Brown completed this course, spending 6 hours a week on it and found the course difficulty to be hard.
Very good and well taught. The quizs are informative as well. Many examples were given to make learning easier. I highly recommend.

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0 out of 2 people found the following review useful
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0 out of 2 people found the following review useful
2 years ago
Gaetano Pagani completed this course.
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a year ago
Nicholas Jackson completed this course.
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0 out of 1 people found the following review useful
2 years ago
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Anonymous partially completed this course.
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0 out of 1 people found the following review useful
2 years ago
Mauro Lacy completed this course.
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a year ago
Simon Crase completed this course.
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0 out of 3 people found the following review useful
3 years ago
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Anonymous completed this course.
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