Nonlinear Dynamics: Mathematical and Computational Approaches

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.

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 topics, covered here, are very interesting as well as quite important to me. I am very much thankful to Prof. Elizabeth Bradley for her crisp and concise course, as well as Mr Joshua Garland for that nice app. The order of the topics are pretty much helpful and I personally love the content and teaching methodology very much.
But, I think, there are a few scopes for improvement for the course.
1. It will be pretty much helpful for the students if there's a GitHub repository for the codes [MATLAB codes to be precise] used.
2. Also, a separate workspace, where students can contribute/moderate their own/existing code [of their favourite languages]. I believe that it might be helpful to get familiar with a different angle of solving a same problem.
3. Sudden voice change during a course is a bit annoying. Rather, it will be better to leave a note at the end of the video. [eg, The graph is discrete. So, please don't join two points on the graph.]
In a nutshell, the course is very helpful and enjoyable to me and I love to thank full Complexity Explorer Team to bring this course.
Thank you.

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. It was not just flipping through the pages, but also not too hard for me to be demotivated. Though the course kept it's focus, it was varied and had a nice rythm of basic theory, maths, programming, demonstration and examples, and applications to it. I feel confirmed to delve further into this topic.

There were some minor rather technical quirks: The discontinuities and noise in the videos and audio were sometimes distracting. It was good to have for a change the voice of Greg - I think that was his name? - in the course, however he sometimes spoke so fast that, for me as a non-native-speaker, it was hard to understand him. A transcript would have been nice, because it sometimes felt rather lengthy to go back and watch a whole section video - which one had already a pretty good understanding of - just to find a very specific answer to one of the multiple choice questions.

Thanks a lot for offering the course, I enjoyed it and took a great deal out of it!

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 what I needed to know. The course fulfilled both objectives. I was quite excited to read various scientific papers with understanding. I am also motivated to focus on getting a better understanding of physics and math. I am not convinced I need to learn programming but I do see that this is an advantage. Liz Bradley is an excellent teacher with her very clear and organized presentation of the concepts. The interviews with the other scientists provided depth and an understanding of applications. I have recommended the course to others and I am confounded by the low completion rate. I have taken several other courses on the Complexity Platform and have found them all to be of the highest standards with teachers who are obviously committed to making the topics understandable. For me, it has been a tremendous resource. I look forward to taking other courses and expanding my horizons. Thank you to all of the people who make the courses possible. Beth Strutzel

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 detail or unexplained technical jargon - all within very bite sized modules. In my experience, this accomplishment is very rare.

I have not completed the course, in fact I don’t think I have taken a single quiz. On the other hand, I have listened to some lectures 5 or more times. Other lectures, I have not gotten to yet - because I don’t feel that I have sufficiently internalized the earlier ones. I’m also referring to Steve Strogatz’s lectures on u tube to fill out a few areas. That slows things a bit.

Bottom line - I will probably not complete this course by December 31, 2017, but I will probably still be listening to some lectures over and over again in 2018. Nevertheless, I find the material valuable and very well done. (Maybe I will try to finish up on time to help your stats).

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 that this course was running its next session which sounded like a great opportunity to enhance my understanding about dynamics of Complex Systems.

The course has helped me better understand differential equations as we use in a system, limitations of eigenvalues in a complex system and the need to understand stable and unstable manifolds, improve my skill in coding to solve homework problems (including performing an RK4 computation!), understand importance of state space, know difference between autonomous and non autonomous systems, have a good understanding of chaos and the concept of delay coordinate embedding.

Now I cannot just observe an eddy in a pool of water or even coffee as it mixes in milk without wondering the possibly chaotic movement of each of those particles as it diffuses.

I am sure these new learning will go a long way in helping me understand Complex Systems and better analyze and understand System Dynamics models.

Thank you Prof. Elizabeth Bradley and Santa Fe Institute for the wonderful course.

Pradeesh

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 what I needed to know. The course fulfilled both objectives. I was quite excited to read various scientific papers with understanding. I am also motivated to focus on getting a better understanding of physics and math. I am not convinced I need to learn programming but I do see that this is an advantage. Liz Bradley is an excellent teacher with her very clear and organized presentation of the concepts. The interviews with the other scientists provided depth and an understanding of applications. I have recommended the course to others and I am confounded by the low completion rate. I have taken several other courses on the Complexity Platform and have found them all to be of the highest standards with teachers who are obviously committed to making the topics understandable. For me, it has been a tremendous resource. I look forward to taking other courses and expanding my horizons. Thank you to all of the people who make the courses possible. Beth Strutzel

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 material. One thing I would have appreciated would have been more pointers toward outside readings that might have helped me fill in some of those blanks. While I appreciate the instructor's desire to keep the videos short and focused, there were times when I think taking more time would have been better. The exercises were very useful, although I wish there would have been programming resources for languages other than MATLAB. Not knowing MATLAB, and struggling to frame problems in a language I am familiar with sometimes made the programming assignments rather time consuming. Despite these minor points, I should say that I thoroughly enjoyed the course and have also found it useful in my own work. I't the third course I taken on Complexity Explorer, and am looking forward to more!

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 calculate and verify some results in a wide variety of scenarios. The quizzes, homeworks and tests helps you to calibrate your undestanding of the topics, I did the programming homeworks using Matlab, but some problems may be resolved by using Excel or another spreadsheet program . The intructor, Prof. Liz Bradley is an excellent teacher, she teach the concepts in a clear manner and give intuitive example(s) that are very useful to graps the ideas. This was my third course finished on the Complexity Explorer platform, I think it was excellent,interesting and a little bit challenging for me but I really enjoyed it.