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5 out of 5 people found the following review useful

4 years ago
**completed** this course.

I appreciated the structured approach to the course material and the painstaking development of foundational concepts. Dr. Feldman presents the course in an informal, across-the-desk manner. Each lecture feels like you are experiencing an individual tutoring session during office hours. I recommend the course to studen
Read More

I appreciated the structured approach to the course material and the painstaking development of foundational concepts. Dr. Feldman presents the course in an informal, across-the-desk manner. Each lecture feels like you are experiencing an individual tutoring session during office hours. I recommend the course to students who struggle with math or computing anxiety; only mininal calculus is needed to understand and apply the material. Below is a topical overview of the 9-week course.

Lectures:

What is a dynamical system?

General properties - classification / characterization.

Iterated functions, orbit, itinerary; examples.

Differential equations, examples; rule is indirect, involves rate of change of a variable.

Solution methods: analytic, qualitative, numerical / computational / algorithmic.

Initial condition + rule -> existence and uniqueness.

Chaos, examples; deterministic, orbits bounded, aperiodic, sensitive dependence on initial conditions.

The butterfly effect.

Algorithmic randomness, incompressibility.

The logistic equation.

1-D differential equations (chaos not possible) vs 1-D iterated function systems (chaos possible).

Time is continuous vs discrete time intervals; dependent variable is continuous vs discrete values.

Bifurcation diagrams; examples.

Period-doubling route to chaos.

Universality in period doubling, Feigenbaum's constant.

Universality in physical systems; examples.

2-D differential equations (chaos not possible - Poincare-Bendixson theorem); examples.

The phase plane.

Stable and unstable fixed points, orbits can tend to infinity, limit cycles (attracting cyclic behavior) - but no chaos.

3-D differential equations (chaos possible); Lorenz system of equations.

Phase space.

Strange attractors: stable attractors but motion on the attractor is chaotic; examples.

Stretching and folding in chaotic orbits.

Strange attractors combine elements of order and disorder; motion is locally unstable, globally stable.

Pattern formation in dynamical systems; examples.

Reaction-diffusion systems.

Simple, spatially-extended dynamical systems with local rules are capable of producing stable, global patterns and structures.

Interviews:

Stephen Kellert, prof of philosophy at Hamline University.

Chaos theory represents an evolution (vs revolution), a new style of scientific reasoning or doing science.

Represents a conceptual reconfiguration, gets rid of old dichotomies.

You can have conceptual change that's brought about through methodological challenges, not just through grand theoretical structures being changed.

Chaos theory is a part of postmodernism - challenging of strict binaries.

Stephen W. Morris prof of geophysics at Univ. of Toronto.

Pattern formation in nature; examples and demonstrations. "Swimming in the wrong direction of reductionism".

Conceptual - thematic summary

Remarks

Lectures:

What is a dynamical system?

General properties - classification / characterization.

Iterated functions, orbit, itinerary; examples.

Differential equations, examples; rule is indirect, involves rate of change of a variable.

Solution methods: analytic, qualitative, numerical / computational / algorithmic.

Initial condition + rule -> existence and uniqueness.

Chaos, examples; deterministic, orbits bounded, aperiodic, sensitive dependence on initial conditions.

The butterfly effect.

Algorithmic randomness, incompressibility.

The logistic equation.

1-D differential equations (chaos not possible) vs 1-D iterated function systems (chaos possible).

Time is continuous vs discrete time intervals; dependent variable is continuous vs discrete values.

Bifurcation diagrams; examples.

Period-doubling route to chaos.

Universality in period doubling, Feigenbaum's constant.

Universality in physical systems; examples.

2-D differential equations (chaos not possible - Poincare-Bendixson theorem); examples.

The phase plane.

Stable and unstable fixed points, orbits can tend to infinity, limit cycles (attracting cyclic behavior) - but no chaos.

3-D differential equations (chaos possible); Lorenz system of equations.

Phase space.

Strange attractors: stable attractors but motion on the attractor is chaotic; examples.

Stretching and folding in chaotic orbits.

Strange attractors combine elements of order and disorder; motion is locally unstable, globally stable.

Pattern formation in dynamical systems; examples.

Reaction-diffusion systems.

Simple, spatially-extended dynamical systems with local rules are capable of producing stable, global patterns and structures.

Interviews:

Stephen Kellert, prof of philosophy at Hamline University.

Chaos theory represents an evolution (vs revolution), a new style of scientific reasoning or doing science.

Represents a conceptual reconfiguration, gets rid of old dichotomies.

You can have conceptual change that's brought about through methodological challenges, not just through grand theoretical structures being changed.

Chaos theory is a part of postmodernism - challenging of strict binaries.

Stephen W. Morris prof of geophysics at Univ. of Toronto.

Pattern formation in nature; examples and demonstrations. "Swimming in the wrong direction of reductionism".

Conceptual - thematic summary

Remarks

a year ago
**completed** this course, spending **2 hours** a week on it and found the course difficulty to be **very easy**.

This course is perfect for beginners who want to get a grasp of the field of chaos with minimal mathematical/numerical material, but yet enough to have a flavor of the underlying world, beyond the bases. Dave Feldman is a great teacher, very dedicated to explaining the ideas in a simple way, accessible to most (if not
Read More

This course is perfect for beginners who want to get a grasp of the field of chaos with minimal mathematical/numerical material, but yet enough to have a flavor of the underlying world, beyond the bases. Dave Feldman is a great teacher, very dedicated to explaining the ideas in a simple way, accessible to most (if not all).

I was already acquainted with chaos, which I had studied at University... 25 years ago. So, I found the course fairly easy and didn't watch all videos. Nevertheless, the material I reviewed was very relevant and interesting: the excellent refresher I was looking for to remind me of the good old days! I took the class parallel to re-reading the book "Chaos", by James Gleick, which Dave Feldman cleverly recommends as a complementary resource. The course and the book complement one another idealy (more historical/people aspects in the book), considering that they follow very similar outlines.

The topic of chaos is coverred very progressively, to introduce the key ideas. Many illustrations are provided and detailed, to clarify the theory by simple computations: the most tricky ones are conducted through programs made availalble by Dave Feldman, so that no mathematical/numerical skill is actually required.

Although the course is clearly aimed at some introductory level, Dave Feldman gives many hints on more difficult issues that would require some more involved approach. In addition, many practice exercises (optional) are proposed at different levels: the most advanced allow those who want to go further than the basic level required for the graded quizzes to tackle more technical problems.

An excellent course that I do recommend to anyone interested in learning about chaos at an introductory level.

I was already acquainted with chaos, which I had studied at University... 25 years ago. So, I found the course fairly easy and didn't watch all videos. Nevertheless, the material I reviewed was very relevant and interesting: the excellent refresher I was looking for to remind me of the good old days! I took the class parallel to re-reading the book "Chaos", by James Gleick, which Dave Feldman cleverly recommends as a complementary resource. The course and the book complement one another idealy (more historical/people aspects in the book), considering that they follow very similar outlines.

The topic of chaos is coverred very progressively, to introduce the key ideas. Many illustrations are provided and detailed, to clarify the theory by simple computations: the most tricky ones are conducted through programs made availalble by Dave Feldman, so that no mathematical/numerical skill is actually required.

Although the course is clearly aimed at some introductory level, Dave Feldman gives many hints on more difficult issues that would require some more involved approach. In addition, many practice exercises (optional) are proposed at different levels: the most advanced allow those who want to go further than the basic level required for the graded quizzes to tackle more technical problems.

An excellent course that I do recommend to anyone interested in learning about chaos at an introductory level.

7 out of 7 people found the following review useful

4 years ago
**completed** this course, spending **2 hours** a week on it and found the course difficulty to be **medium**.

This is a fun class which I would highly recommend. Incredibly accessible course which introduced an interesting branch of mathematics.
If you've done a bit of computer science or programming, this class shows a very interesting result from the simple idea of iteration.
The professor is interesting and makes the mat
Read More

This is a fun class which I would highly recommend. Incredibly accessible course which introduced an interesting branch of mathematics.

If you've done a bit of computer science or programming, this class shows a very interesting result from the simple idea of iteration.

The professor is interesting and makes the material intuitive. Regardless of your level of mathematical comfortability, this class is well paced and provides all the tools you need to proceed through it.

Don't miss this class!!

If you've done a bit of computer science or programming, this class shows a very interesting result from the simple idea of iteration.

The professor is interesting and makes the material intuitive. Regardless of your level of mathematical comfortability, this class is well paced and provides all the tools you need to proceed through it.

Don't miss this class!!

5 out of 5 people found the following review useful

3 years ago
**completed** this course.

A fascinating course, I absolutely loved it! There was a bit of maths involved, but Dave Feldman walked us through it step by step - so slowly that even somebody who has no idea whatsoever of maths should grasp it. Sitting in front of my laptop on the other side of the globe, I felt he deeply cared that you understood
Read More

A fascinating course, I absolutely loved it! There was a bit of maths involved, but Dave Feldman walked us through it step by step - so slowly that even somebody who has no idea whatsoever of maths should grasp it. Sitting in front of my laptop on the other side of the globe, I felt he deeply cared that you understood everything - as somebody said above, it almost felt like a personal tutorial! As I had already done Melanie Mitchell's course (equally excellent!), I was familiar with much of the territory, but Dave's approach helped me to understand some of the more difficult concepts. I think the two courses complement each other very nicely. Highly recommended!

2 out of 2 people found the following review useful

4 years ago
**completed** this course.

This class was just amazing and great. Mr. Feldman knows how to really get you to see the 'big idea' and that's the most import part of any intro class; to get the big picture. Math was light and not terrifying. Deadline is the class day of class. Quizzes were light and the homework was challenging enough if you wanted it to be. I absolutely loved this class.

3 weeks ago

Complexity and Dynamical Systems is a fascinating field of mathematics. There are linear, predictable and well-ordered systems, like simple physical motion. There are non-linear systems, like the weather. What are the latter like? Can they be studied and modeled mathematically?
Professor David Feldman takes a very sy
Read More

Complexity and Dynamical Systems is a fascinating field of mathematics. There are linear, predictable and well-ordered systems, like simple physical motion. There are non-linear systems, like the weather. What are the latter like? Can they be studied and modeled mathematically?

Professor David Feldman takes a very systematic and ordered approach to the subject. He introduces a unit, talks about what he will cover and then take up a simple equation to show how it can lead to either predictable or unpredictable results. He lets us wonder how a deterministic system gives rise to disorder and chaos. Through graphs, charts, step-by-step workouts and illustrations, he gives endless depth to many aspects of dynamical systems.

The quizzes and homework help us do more exercises like these and get the hang of complexity. There are also computer programs that have been developed and are available to explore the parameters of complexity in an exhaustive manner.

I specially liked the paradoxes in complexity. The self-similar replicas of any part of the system that appears chaotic. The co-existence of order and disorder. The sensitivity to initial conditions., and the butterfly effect.

I wonder if fields like quantum mechanics, natural evolution and even past history of the world can be studied as complex dynamical systems.

Professor David Feldman takes a very systematic and ordered approach to the subject. He introduces a unit, talks about what he will cover and then take up a simple equation to show how it can lead to either predictable or unpredictable results. He lets us wonder how a deterministic system gives rise to disorder and chaos. Through graphs, charts, step-by-step workouts and illustrations, he gives endless depth to many aspects of dynamical systems.

The quizzes and homework help us do more exercises like these and get the hang of complexity. There are also computer programs that have been developed and are available to explore the parameters of complexity in an exhaustive manner.

I specially liked the paradoxes in complexity. The self-similar replicas of any part of the system that appears chaotic. The co-existence of order and disorder. The sensitivity to initial conditions., and the butterfly effect.

I wonder if fields like quantum mechanics, natural evolution and even past history of the world can be studied as complex dynamical systems.

2 out of 2 people found the following review useful

3 years ago

I had a great time having this course and Prof. Feldman was so dedicated in diving us into this amazing subject. I think that the course gave us a solid platform in order to go deeper in the study of Dynamical Systems and Complexity.

a year ago
**completed** this course.

I enjoyed the course very much. The teacher is great, he can explain both familiar and new (complicated) matter in a fresh and understandable way. I helped me to understand dynamical systems deeper, as I do dynamical modeling in economics.

4 weeks ago
is taking this course right now.

The effort put into the course becomes clear as soon as you start. A very accessible design of the material without loosing the required depth for a proper understanding of the essence.

a year ago
is taking this course right now.

This was the missing link for me. I had read many popular science books about dynamical systems and chaos, and was eager to gain a more nuanced and technical understanding of the field. The only thing holding me back, of course, was a lack of background in higher mathematics, particularly "differential equations," whic
Read More

This was the missing link for me. I had read many popular science books about dynamical systems and chaos, and was eager to gain a more nuanced and technical understanding of the field. The only thing holding me back, of course, was a lack of background in higher mathematics, particularly "differential equations," which are drawn on heavily in any technical book about the subject. I was starting to get discouraged at the prospect of having to study lots of highly technical math for years and years before being able to advance at all in my understanding of dynamical systems, when I stumbled upon this class. David Feldman's approach is awesome: completely intuitive and broken down into comprehensible chunks. As someone who took calculus in high school and understood practically none of it, I feel very gratified at being able to grasp what differential equations are all about, even if I'm still a bit of a ways from being able to "solve" them mathematically. Taking this class has so filled in the intellectual gaps for me that not only do I want to re-read some of the books I have with the greater understanding, but I'm actually more inspired to learn more higher math so I can study this stuff further. Thanks!

1 out of 1 people found the following review useful

a year ago
**completed** this course.

Spectacular course. High-level teacher. Can you teach a complex issue for people with little mathematical background. I recommend !! Congratulations to the teacher !!

4 days ago
**completed** this course, spending **10 hours** a week on it and found the course difficulty to be **very easy**.

The standard of this course is so low, that I got bored almost all the time. And I don't feel like I really learned anything from it.

a year ago

This course is a awesome mine of information and knowledge on dynamical systems and chaos. It starts at the very beginning by explaining the mathematical bricks necessary to understand the following units, but it's not a heavy mathematical course.
Quite the opposite. The lead instructor David Feldman is always able to
Read More

This course is a awesome mine of information and knowledge on dynamical systems and chaos. It starts at the very beginning by explaining the mathematical bricks necessary to understand the following units, but it's not a heavy mathematical course.

Quite the opposite. The lead instructor David Feldman is always able to make even the more complex parts of this mooc easy to understand.

David has also developed a well featured web software for visualizing all the course material: equation orbits, Butterfly Effect, bifurcation diagrams and Strange Attractors patterns.

If you're a programmer, you can complete some of the advanced (but optional) exercises using the language of your choice. Here's my version in Python:

https://github.com/madrisan/dynamic-systems-and-chaos

In short this mooc has been a wonderful mathematical trip.

Quite the opposite. The lead instructor David Feldman is always able to make even the more complex parts of this mooc easy to understand.

David has also developed a well featured web software for visualizing all the course material: equation orbits, Butterfly Effect, bifurcation diagrams and Strange Attractors patterns.

If you're a programmer, you can complete some of the advanced (but optional) exercises using the language of your choice. Here's my version in Python:

https://github.com/madrisan/dynamic-systems-and-chaos

In short this mooc has been a wonderful mathematical trip.

6 days ago

I am retired; I've done no mathematics of any significance since the early 70's. This course brought me hours of challenge and joy. Every time I completed homework or unit exams I felt enormous satisfaction.
My deepest thanks to Professor Feldman. He is an extraordinary educator. He communicates clearly and
Read More

I am retired; I've done no mathematics of any significance since the early 70's. This course brought me hours of challenge and joy. Every time I completed homework or unit exams I felt enormous satisfaction.

My deepest thanks to Professor Feldman. He is an extraordinary educator. He communicates clearly and makes the complex understandable. Despite his vast knowledge and expertise, he is still excited about the material he is teaching. Some of my favorite moments were his asides to make sure we appreciated how abstract concepts can be observed in physical systems. The course was well organized and I appreciated that all of the material was accessible for review and replay. The unit summaries were very helpful. I just sorry the course is over.

My deepest thanks to Professor Feldman. He is an extraordinary educator. He communicates clearly and makes the complex understandable. Despite his vast knowledge and expertise, he is still excited about the material he is teaching. Some of my favorite moments were his asides to make sure we appreciated how abstract concepts can be observed in physical systems. The course was well organized and I appreciated that all of the material was accessible for review and replay. The unit summaries were very helpful. I just sorry the course is over.

3 weeks ago

Firstly, the platform is easy to use. It makes focus and moving around content much easier to achieve.
Next, the course itself is riveting not just because of the digestibility of the content, courtesy of the instructor, but also the availability of programs to engage and interact with that enforces the lessons that D
Read More

Firstly, the platform is easy to use. It makes focus and moving around content much easier to achieve.

Next, the course itself is riveting not just because of the digestibility of the content, courtesy of the instructor, but also the availability of programs to engage and interact with that enforces the lessons that David provides.

David is also an engaging instructor and is able to deliver content at a pace and clarity that is oh so important for MOOCs. This is critical in understanding the key lessons or ideas or concepts he wants you to leave with at the tail-end of the course.

And of course, lastly, the subject itself is fascinating and absorbing once you start thinking about the real-world comparisons that David introduces quickly.

Next, the course itself is riveting not just because of the digestibility of the content, courtesy of the instructor, but also the availability of programs to engage and interact with that enforces the lessons that David provides.

David is also an engaging instructor and is able to deliver content at a pace and clarity that is oh so important for MOOCs. This is critical in understanding the key lessons or ideas or concepts he wants you to leave with at the tail-end of the course.

And of course, lastly, the subject itself is fascinating and absorbing once you start thinking about the real-world comparisons that David introduces quickly.

4 weeks ago

Leonardo da Vinci said : "Simplicity is the ultimate sophistication" and professor Feldman with his way of thinking exactly represents Leonardo's thougth.
Only great professors uses scissors, pencils and papers and explain very complicated things with ease .
This course is a very good one, professor Feldman's e
Read More

Leonardo da Vinci said : "Simplicity is the ultimate sophistication" and professor Feldman with his way of thinking exactly represents Leonardo's thougth.

Only great professors uses scissors, pencils and papers and explain very complicated things with ease .

This course is a very good one, professor Feldman's explanations are really clears and complex materials "flows" very well .

Personally have already recommended this course to others and think that I will gladly follow other courses in which professor Feldman will be the teacher considering his high scientific level and his predisposition to teach in a simple way ( where he can ) ...

Simply great !!!

Only great professors uses scissors, pencils and papers and explain very complicated things with ease .

This course is a very good one, professor Feldman's explanations are really clears and complex materials "flows" very well .

Personally have already recommended this course to others and think that I will gladly follow other courses in which professor Feldman will be the teacher considering his high scientific level and his predisposition to teach in a simple way ( where he can ) ...

Simply great !!!

20 hours ago
**completed** this course.

This course is by far one of the best courses I've ever taken. It balances depth and simplicity perfectly. One finishes the course understanding Dynamical Systems and Chaos enough to discuss, question, and apply key concepts to other fields of study. I'm an architect, and I nevertheless understood every topic in the co
Read More

This course is by far one of the best courses I've ever taken. It balances depth and simplicity perfectly. One finishes the course understanding Dynamical Systems and Chaos enough to discuss, question, and apply key concepts to other fields of study. I'm an architect, and I nevertheless understood every topic in the course. Professor David always relates and brings back specific aspects he is teaching to global ideas as to understand the relevance of the topic. I believe this is a great way of teaching as it maintains interest, and allows the student to understand how each piece fits into the general ideas.

a year ago
**completed** this course.

This is a very good introduction to (nonlinear) dynamical systems. Instruction is very good and the provided simulations are very helpful.
I am a math dummy and my background is mostly biology. This class did a so good job in explaining dynamical systems that I realized biological systems are likely to be ( maybe comp
Read More

This is a very good introduction to (nonlinear) dynamical systems. Instruction is very good and the provided simulations are very helpful.

I am a math dummy and my background is mostly biology. This class did a so good job in explaining dynamical systems that I realized biological systems are likely to be ( maybe complex) dynamical systems. However, due to experimental limitations, molecular and cellular biologists hardly can study their systems as a dynamical system. After taking this class, I am decided to try to study biological systems (nervous systems, more specifically) as dynamical systems for my future work.

I am a math dummy and my background is mostly biology. This class did a so good job in explaining dynamical systems that I realized biological systems are likely to be ( maybe complex) dynamical systems. However, due to experimental limitations, molecular and cellular biologists hardly can study their systems as a dynamical system. After taking this class, I am decided to try to study biological systems (nervous systems, more specifically) as dynamical systems for my future work.

4 weeks ago

is taking this course right now, spending
**2 hours** a week on it and found the course difficulty to be **medium**.

Professor Dave Feldman is an excellent teacher. He knows exactly what pace to proceed at, what to repeat more than once, and what thoughts/questions the student must have who is watching. He introduces humour as he goes along which is also great to keep things real almost giving a feeling of being in the room with him.
Read More

Professor Dave Feldman is an excellent teacher. He knows exactly what pace to proceed at, what to repeat more than once, and what thoughts/questions the student must have who is watching. He introduces humour as he goes along which is also great to keep things real almost giving a feeling of being in the room with him. I read the book "Chaos" almost 30 years ago and it was great taking this course now to formalize what I read back then. I am looking forward to doing more courses taught by him and also hope that other courses on the Complexity Explorer site are taught as well as this was.

a year ago
**completed** this course.

This class was great!
What a great journey, from phase lines, through period doubling, all the way through strange attractors. In my opinion it totally succeeded as an introduction, as I was able to build a relationship with the material in advance of staring down the calculus (which I'll be doing next).
I really ap
Read More

This class was great!

What a great journey, from phase lines, through period doubling, all the way through strange attractors. In my opinion it totally succeeded as an introduction, as I was able to build a relationship with the material in advance of staring down the calculus (which I'll be doing next).

I really appreciate professor Feldman's emphasis on visualizations, geometry, and conceptual abstraction. This is the experiential anchor I was looking for to balance my more computational inquiries.

A jolly good frolic through the wonders of dynamical systems!

What a great journey, from phase lines, through period doubling, all the way through strange attractors. In my opinion it totally succeeded as an introduction, as I was able to build a relationship with the material in advance of staring down the calculus (which I'll be doing next).

I really appreciate professor Feldman's emphasis on visualizations, geometry, and conceptual abstraction. This is the experiential anchor I was looking for to balance my more computational inquiries.

A jolly good frolic through the wonders of dynamical systems!

a year ago
**completed** this course.

The presentation by the professor of the complicated material was very clear in terms of the verbal explanation of the concepts and the visual presentations. The homework and the exams were closely tied to the presentations which facilitated comprehension. The focus was on the conceptual but, also, there were exerci
Read More

The presentation by the professor of the complicated material was very clear in terms of the verbal explanation of the concepts and the visual presentations. The homework and the exams were closely tied to the presentations which facilitated comprehension. The focus was on the conceptual but, also, there were exercises for those students with more technical expertise. I thoroughly enjoyed the course. Now I have a background to explore the topics in greater depth which I think is one of the best outcomes from such a course.

a year ago
is taking this course right now.

Prior to this course I had read popular expositions such as James Gleick's "Chaos", but had never had access to a basic formal exposition of complex behaviour. This course offers a fascinating introduction to chaos theory. I had plenty of "aha" moments, and David Feldman's excursion into the philosophical consequence
Read More

Prior to this course I had read popular expositions such as James Gleick's "Chaos", but had never had access to a basic formal exposition of complex behaviour. This course offers a fascinating introduction to chaos theory. I had plenty of "aha" moments, and David Feldman's excursion into the philosophical consequences of determinism producing unpredictability was also an eye-opener.

This a fun and accessible course, and I find myself eagerly awaiting release of the next Unit each week. Thoroughly recommended

This a fun and accessible course, and I find myself eagerly awaiting release of the next Unit each week. Thoroughly recommended

a year ago
**completed** this course.

The course is comprehensible by illuminating most important concepts in deterministic chaos. I believe that it is essential for those who use these concepts (eg: Butterfly Effect, Innitial conditions, Order and Chaorder) etensively to justify applications and emergent methodologies.
Thanks to David Feldman and his te
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The course is comprehensible by illuminating most important concepts in deterministic chaos. I believe that it is essential for those who use these concepts (eg: Butterfly Effect, Innitial conditions, Order and Chaorder) etensively to justify applications and emergent methodologies.

Thanks to David Feldman and his team for the clarity.

Because the importance of this course (MOOC) in spreading significant knowledge and making it accessible to everybody, I encourage donatations to keep the flame burning.

Judy Tal

Thanks to David Feldman and his team for the clarity.

Because the importance of this course (MOOC) in spreading significant knowledge and making it accessible to everybody, I encourage donatations to keep the flame burning.

Judy Tal

3 days ago
**completed** this course.

Whether you've taken higher mathematics or not, Dr. Feldman's course on dynamical systems and chaos is brilliantly accessible, and you're sure to walk away with a bird's eye view of this fascinating field of research as well as enough foundation to explore it deeper on your own. Dr. Feldman is a brilliant, intuitive in
Read More

Whether you've taken higher mathematics or not, Dr. Feldman's course on dynamical systems and chaos is brilliantly accessible, and you're sure to walk away with a bird's eye view of this fascinating field of research as well as enough foundation to explore it deeper on your own. Dr. Feldman is a brilliant, intuitive instructor who has distilled a rich and complex field down to its essence. Truly a gift. Highly recommend!

4 weeks ago
**completed** this course.

Excellent course ... the best online course I have taken so far. The subject is difficult, but the instructor is EXCELLENT and CRYSTAL CLEAR. The very fact that he makes things simple is the sure sign that Prof Feldman knows what he teaches. Make sure that you do the assignments and you will not regret the effort you put into taking the course. Highly recommended!

4 weeks ago
is taking this course right now.

Prof David is simply the best. He takes such care with his explanations, and he really works to help his students make sense of complexity theory. The lectures are clear and the tests reflect the material accurately such that if you understand everything, you'll definitely be able to understand and answer all of the questions. Thank you for making this course :)

13 hours ago
**completed** this course.

Complexity and chaos is something I've been intrigued about for many years but the thought of the mathematics involved preventing me from checking it out further (even though I did college level differential equations and the like many years ago). This course was therefore ideal in that it summarized the basics without higher maths.

a year ago
**completed** this course.

Very clear explanations and interesting topics. The best way to start learning about some a rich and deep subject in a theoretical way, for a more mathematical way, it gives a good base and sets important foundations and, possibly, even a deeper non-analytical understanding of dynamical and chaotic processes and phenomena.

3 weeks ago
**completed** this course.

A fine course dealing with difficult and complex topics. The instructor knows his stuff and manages to explain in clearly and in detail the concepts using little more than pencil, paper, and the occasional online resource necessary for the complex mappings required to visualize the subject.

This is teaching at its finest.

This is teaching at its finest.

2 weeks ago

A new topic, was handled in a very fun and interesting manner by the Instructor.

Everything was explained in a manner that made it easy to u derstamd, including the mathematical equations. I look forward to continuing this complexity journey.

Thank you for the introduction and lighting the path.

Everything was explained in a manner that made it easy to u derstamd, including the mathematical equations. I look forward to continuing this complexity journey.

Thank you for the introduction and lighting the path.

a year ago
**completed** this course.

Great course taught by a fun and knowledgable instructor Dave Feldman. Dr. Feldman is at once smart, thorough, and funny. The course lays in foundational material and then thoughtfully explores the topic of dynamical systems, including "chaos" theory. Highly recommended.

9 months ago
**audited** this course.

The course gives an interesting outline of dynamical systems. However if you are already experience in math you might find it too vague. I would recommend then just to watch the summaries of each week (which are very good). Other than that, the course is really good.

3 weeks ago
**completed** this course.

Explained very clear the concept of randomness and chaos.

There were excellent programs on which to explore the idea of deterministic chaos, Henon equations, Lorenz equation and so on.

I learnt a lot while enjoying the lessons and doing the quizzes.

Highly recommended.

There were excellent programs on which to explore the idea of deterministic chaos, Henon equations, Lorenz equation and so on.

I learnt a lot while enjoying the lessons and doing the quizzes.

Highly recommended.

a year ago
**completed** this course.

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

a year ago
**completed** this course.

This is one of the best lectures I have ever taken. Prof. Feldman exactly knows what the students need, and teaches in a very kind manner. I surely recommend this course to everybody who wants to step into the world of complexity but does not have much background.

This is one of the best lectures I have ever taken. Prof. Feldman exactly knows what the students need, and teaches in a very kind manner. I surely recommend this course to everybody who wants to step into the world of complexity but does not have much background.

a year ago
is taking this course right now.

The course was spectacular. One of the teachers with the best teaching I have had the opportunity to be a student. You can teach difficult content to people as little mathematical background like me. Congratulations!! I recommend everyone to do the course.

a year ago
**completed** this course.

David ROCKS in leading this class. Clear and concise! The math part is just fine . . . but it could benefit from a bit more philosophical grounding so I understand WHY I should study this topic. Despite that, it is just plain interesting material.

a year ago
**partially completed** this course.

I took previously the fractals entire course, and Davide Feldman the instructor of bouth courses is !!!!!THE BEST!!!!! teacher i ever had, is absolutly friendly and his explanations of the materia is very clear. Thanks a lot David your the best!!

2 weeks ago
**completed** this course.

Extremely invaluable for those starting out in this field. David was excellent at integrating the highly-interesting aspects of this topic with appropriate levels of mathematics so a to maximize understanding.

Thanks for your efforts David.

Thanks for your efforts David.

17 hours ago
is taking this course right now.

Great instructor, does a good job of explaining complicated concepts to the uninitiated. Definitely created a passion in me for the subject and I will be back to take any other courses offered with David and/or through Complexity Explorer.

a year ago
**completed** this course.

Super interesting, well paced, fun and useful! I specifically appreciated the thorough examples, and the tools that let you play around with numbers, attractors and strange attractors yourself. Thank you complexity explorer!

a year ago
**completed** this course.

Very helpful entry point to dynamical systems, with an almost peerless genius teacher. You won't regret taking this well designed, very interesting course. Advanced maths background is not required so dive right in.

a year ago
**completed** this course.

The course is excellent. I highly recommend this one to the broad audience. It is interesting and self-consistent. If you are not the expert in the field it's still a good idea to watch couple of lectures .

3 days ago
**completed** this course.

Great course to start and introduce into a new perspective of dynamical systems: social, natural, physics, economics, etc. I took very interesting principles to develop in ecology and nuclear desintegration.

a year ago
is taking this course right now.

t h a n k y o u a 1000 times for enlarging my small horizon

it is truly a pleasure and I will never forget how this course enlightened me about a certain part from psychoanalysis that seemed to remain inaccesible.

it is truly a pleasure and I will never forget how this course enlightened me about a certain part from psychoanalysis that seemed to remain inaccesible.

yesterday
**completed** this course.

Very well structured and interactive course. Great presentation of the subject; easy to comprehend even without solid mathematical background. The Complexity Explorer platform is very user friendly.

a year ago
**completed** this course.

Fantastic course. David takes you along nice and easily through the subject but still manages to cover a lot of stuff to give a really good grounding in the area. Liked his sense of humour too :)

10 months ago
**completed** this course.

Thanks a lot for such nice and interesting course.

Thanks a lot for such nice and interesting course.

Thanks a lot for such nice and interesting course.

Thanks a lot for such nice and interesting course.

Thanks a lot for such nice and interesting course.

Thanks a lot for such nice and interesting course.

Thanks a lot for such nice and interesting course.

a year ago

Introductory concepts, light on math.

Is unfortunate this kind of materials is not included in high school education globally. Fundamental concepts to understand how complex systems behave and fail.

Is unfortunate this kind of materials is not included in high school education globally. Fundamental concepts to understand how complex systems behave and fail.

a week ago
**completed** this course.

Excellent course with well-built and interesting lectures. The supplementary materials are interesting, the needed software tools work well. The tutor is very good, easily understandable and funny.

a year ago
is taking this course right now.

Interesting and complex ideas explained using high school maths (with some optional homework that contain a little bit more advanced exercises). Very easy to follow the instructor. 5 stars!

a year ago
**completed** this course.

El curso me pareció de una intensidad y profundidad acorde con lo propuesto -nivel de matemática medio- si la tercera lectura fue muy larga, ed dos partes sería más fácil de comprender

a year ago
is taking this course right now.

This is an excellent introduction to a complex set of ideas. Well worth the time! I thoroughly recommend this course to anyone interested in learning more about complexity and dynamical systems.

a year ago
**completed** this course.

Great introductory course in Dynamical Systems and Chaos. There aren't many prerequisites. Physics or Math students may find it relatively easy, but it is supposed to be an introduction.

a year ago
**completed** this course.

A great introduction to the field of Nonlinear Dynamics. The subject is tackled from many different perspectives. The course offers both qualitative and quantitative insights into the subject.

yesterday
**completed** this course.

Compliments! Well structured course. Interesting and motivating.

Take this course, read Gleicks Book and watch Strogatz lecture and you got your own personal route to chaos....

Take this course, read Gleicks Book and watch Strogatz lecture and you got your own personal route to chaos....

a year ago
**completed** this course.

A really useful and good course. All topics are covered in a very clear and understandable way. Course will add something for people from all different backgrounds.

a week ago
**completed** this course.

Great way to understand the basics of dynamical systems and chaos. Dave is great, capable of delivering complex concepts in a very simple and easily understandable way.

a year ago
**completed** this course.

The course is very pleasant to follow. The teacher introduces concepts slowly and explains things very clearly. This is a fascinating subject. Thanks for the great work.

a year ago
**completed** this course and found the course difficulty to be **easy**.

Perfect course for beginner. Chaos and dynamical systems were really confusing to me before I started this course but know everything is becoming clearer.

a year ago
**completed** this course.

Smooth introduction to the subject. Easy but not too simple, it helps built a solid ground and supplmentary material will help those who want to go deeper.

a year ago

The course is easy to follow even with a high school math background. the teacher makes sure to rephrase every concepts so they are easy to grasp.

3 weeks ago
**completed** this course.

Easy but very interesting introduction to chaos and complexity. First step on the stair of complexity. Very clear and to the point. Loved it.

a year ago
is taking this course right now.

Very clear explanations. I really undesrtood the concepts of every lesson and was able to do the exercises. I enjoyed the course very much.

a year ago
is taking this course right now.

Great introductory course. Professor Feldman does a great job in delivering the content clearly and in an interesting manner. Two thumbs up.

a year ago
**completed** this course.

I found the course a thought provoking and enjoyable introduction to the subject and am now interested in further studies in this area.

a year ago
is taking this course right now.

I'm really enjoying the course. The website is laid out well so it's easy to flip between videos and find the course materials you want.

a year ago
**completed** this course.

Very good an interesting course, well organized, great materials. Very good introduction to an extremely interesting and useful scientific area.

a year ago
**completed** this course.

Great course. Very interesting yet no too complicated (but homeworks have an advanced level if you want to be more challenged).

a year ago
**audited** this course.

It was an excellet course. The clss materiales were veryI very well organized and very useful. I really enjoyed it.

a year ago
**completed** this course.

Great! Learned a lot and was somehow always motivated to go on . I will try out the other Complexity Explorer Courses ;)

0 out of 1 people found the following review useful

0 out of 1 people found the following review useful