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Santa Fe Institute

Tutorials for Complex Systems

Santa Fe Institute via Complexity Explorer


This course covers several mathematical techniques that are frequently used in complex systems science.   The techniques are covered in independent units, taught by different instructors.  Each unit has its own prerequisites.  Note that this course is meant to introduce students to various important techniques and to provide illustrations of their application in complex systems.  A given unit is not meant to offer complete coverage of its topic or substitute for an entire course on that topic.   

The units included during this offering of the course are:

(1) Introduction to differential equations (David Feldman)

(2) Ordinary differential equations (ODEs) and numerical ODE solvers (Liz Bradley)

(3) Functions and iteration (David Feldman)

(4) Maximum entropy methods  (Simon DeDeo)

(5) Random Walks (Sid Redner)

(6) Vector and matrix algebra (Anthony Rhodes)

(7) Introduction to information theory (Seth Lloyd)

(8) Game Theory I - Static Games (Justin Grana)   (9) Game Theory II - Dynamic Games (Justin Grana)   (10) Introduction to Renormalization (Simon DeDeo)   (11) Fundamentals of Machine Learning (Artemy Kolchinsky)   (12) Introduction to Computation Theory (Josh Grochow)   (13) Fundamentals of NetLogo (Bill Rand)


Other units to be developed over time. 





4.7 rating, based on 25 Class Central reviews

Start your review of Tutorials for Complex Systems

  • Anonymous
    This course begin at a point in the matter which don't know it really are. It's like attending in a class in final stage! Too much math without description. Poor and very summarized definition at the beginning then falling into math without knowing why.
    I was looking for diffusion and random walks to use in social science and i have strong mathematics background but nothing learned about the subject.
    It's just solving some math work without explanation of what is and why is, so i quit.
    I suggest to put in prerequisites, being "Undergraduates of fluid physics" !
  • An excellent tutorial! If you are looking for a quick way to pick up basic working knowledge of information theory you do not have to look any further as this course will get you up and running in a few hours. Moreover, it even does not assume too much of a mathematical knowledge. As long as one is well versed with high school algebra (especially logarithms and basic probability theory) everything discussed in this tutorial should be easy to process and understood.
  • Subhash
    It was a great tutorial! I keep using the Matlab's ode45 solver but didn't know how it works, this ODE tutorial answered it and that too in a light and illustrative fashion. Using the same example throughout has also helped in easy understanding.

    This review pertains to the tutorial by Elizabeth Bradley.
  • Anonymous
    It is a clear and easy to understand introductory course on machine learning for non-experts. The bite-size lecture videos and quiz questions after each video made it easier to understand the concept step by step.
  • Vishnu Reddy
    Excellent and surprising connections. Some references to rigorous treatment and more example problems will be appreciated. Often it is mentioned about non-renormalization of gravity but no further info is provided.
  • Anonymous
    I like the insightful approach. There is no hand-waving but just a few simple and intuitive derivations. Am motivated to read some of the supplementary material.
  • Anonymous
    Very short, complete and well taught tutorials about the tools and mathematical background required for studying, analysing and understanding chaos and complex systems.
  • Anonymous
    Excellent course, fascinating covering updates to an area that I explored many years ago. Thoroughly recommended to anyone who is interested in understanding renormalisation and seeing where it is now. You don't need a very mathematical background to understand the course, though some basic background would probably help. Many helpful supplementary references and exercises. There should be a further course on his current work.
  • Anonymous
    Outstanding introductory tutorial that is supplementing my Stochastic Processes class extremely well. This also clarified classes I took where we simulated Quantum Montecarlo Methods. It provided me a map to work off of for certain understandings I needed. I am working on the supplementary material too. This is a great starting point for self study!
  • This heading is for all tutorials under complexity explorer. I took MaxEntropy tutorial. Wow. Got a very good perspective on curves which are driven from population statistics.

    Note: Not all the tutorials are at the same level, and some are really basic, and some are at an undergraduate level. Therefore you may see a variety of ratings.
  • Anonymous
    The course was a great introduction of Random Walks and I particularly liked the way the Central Limit Theorem is proved using the fourier transform.

    It would have been nice to have something about the specifics of Brownian motion and stochastic processes.
    But great nevertheless
  • Anonymous
    Courses provided by complexity explorer are really useful for strengthening basics, scientific understanding and learning about complex systems. I am looking forward to a network science course in near future. Hopefully, it will be available in complexity explorer soon in coming time.
  • Anonymous
    Fascinating physics methods to be applied on a variety of other disciplines.
    Simon is doing an impressive work in making this knowledge accessible for lay audience and non-physicists.
  • Even though I have only completed the first module I know this is going to be an interesting and useful course. Presentation and course content are great and totally meet my expectations.
  • Anonymous
    I'm surprised because it was what I was looking to start my research project. The explanation of topic by professor Dedeo is simply spectacular.
  • This tutorial is informative and enjoyable, perfect for people new to the subject. Great job! Thanks to Dr. Justin Grana for his time and effort.
  • Anonymous
    An excellent course for the non-specialist. Dummy-Proof. The teacher is excellent and the proposed exercises are very useful. Highly recommended
  • Anonymous
    The content was useful and well presented. The structure was well thought out and presented essential concepts efficiently. Thank you
  • Anonymous
    Very clear and interesting introduction to the fundamentals of machine learning. The structure of the course is well thought. Thanks.
  • Anonymous
    I enjoyed the course and the succinct presentations by Mr Grana. I learned quite a bit and I’m looking forward to Part II.

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