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Online Course

Introduction to Renormalization

Santa Fe Institute via Complexity Explorer


What does a JPEG have to do with economics and quantum gravity? All of them are about what happens when you simplify world-descriptions. A JPEG compresses an image by throwing out fine structure in ways a casual glance won't detect. Economists produce theories of human behavior that gloss over the details of individual psychology. Meanwhile, even our most sophisticated physics experiments can't show us the most fundamental building-blocks of matter, and so our theories have to make do with descriptions that blur out the smallest scales. The study of how theories change as we move to more or less detailed descriptions is known as renormalization. 

This tutorial provides a modern introduction to renormalization from a complex systems point of view. Simon DeDeo will take students from basic concepts in information theory and image processing to some of the most important concepts in complexity, including emergence, coarse-graining, and effective theories. Only basic comfort with the use of probabilities is required for the majority of the material; some more advanced modules rely on more sophisticated algebra and basic calculus, but can be skipped. Solution sets include Python and Mathematica code to give more advanced learners hands-on experience with both mathematics and applications to data.

We'll introduce, in an elementary fashion, explicit examples of model-building including Markov Chains and Cellular Automata. We'll cover some new ideas for the description of complex systems including the Krohn-Rhodes theorem and State-Space Compression. And we'll show the connections between classic problems in physics, including the Ising model and plasma physics, and cutting-edge questions in machine learning and artificial intelligence.



  1. Introduction to Renormalization
  2. Markov Chains
  3. Cellular Automata
  4. Ising Model
  5. Krohn-Rhodes Theorem
  6. A Classical Analogy for Renormalization in Quantum Electrodynamics
  7. Conclusion: The Future of Renormalization & Rate Distortion Theory
  8. Homework


Taught by

Simon DeDeo

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4.5 rating, based on 13 reviews

Start your review of Introduction to Renormalization

  • Ka Lok Kam

    Ka Lok Kam completed this course.

    I love the course. The lecturer is passionate and funny. He gives us the idea of Renormalization in depth. But the topic of Renormalization is very broad, so he can only give us a little taste of that. I did hope there is a course opened in complexity in the future, which is suitable for senior undergraduate students. Thank you.
  • Anonymous

    Anonymous completed this course.

    Very relevant to some problems I am working on at present. Actually I started it, put it it on hold as I was busy, then got hold of a new problem that looked as if renormalization would help and was inspired to complete tutorial. Simon DeDeo has also provided a really nice reading list.
  • Peter Dzwig

    Peter Dzwig completed this course.

    Excellent. I wanted to refresh something that I learnt many years ago, but it would suit most people with a modest background in maths. Like any course it could have been improved in parts. Thoroughly recommended.
  • Anonymous

    Anonymous is taking this course right now.

    I am constantly being inspired by the concepts introduced in this course. Dr. Simon DeDeo explains everything so well. The course is really fun and informative. We need more courses like this for modelers!
  • Alejandro Puga Candelas completed this course.

    Excelente professor! It's incredible to find this course is for free! A great opportunity to learn new topic from a new perspective
  • Johann Hamel-Akré completed this course, spending 4 hours a week on it and found the course difficulty to be medium.

    A very good course by a very knowledgeable professor who does a good job at explaining the rather complex concept of renormalization. I found the content of the course very interesting, engaging and thought provoking, although I don't see when I would apply what I learned in a project. It's not meant to say that learning about renormalization is useless, but it's a pretty advanced technique that requires a clear incentive to be needed beyond pure intellectual interest.
  • Anonymous

    Anonymous completed this course.

    Very nice tutorial, gets you thinking about renormalization in a unique way, combining seemingly disparate fields such as (semi)group theory, Markov chains, cellular automata, statistical mechanics and QED. Only basic mathematics are needed, and the emphasis is on the conceptual side; however it's still interesting for more advanced learners because of the unique perspective being offered.
  • Anonymous

    Anonymous is taking this course right now.

    This course is uniquely excellent in its presentation of both relevant and fresh ideas and literature on the topic of RG. In contrast to the traditional approach on the topic, it manages to give the full picture that it becomes clear that the arbitrariness involved in the RG analysis is because the RG idea is important for a larger landscape of compressed data representations beyond physics.
  • Anonymous

    Anonymous completed this course.

    I found this short tutorial very influential on the maturation of some of my ideas about perception, even though that was mentioned only at the very end, and I'm grateful for that. The teaching is clear, concise, and enthusiastic. Considering how abstract but pervasive these concepts are, this is highly recommended.
  • Anonymous

    Anonymous completed this course.

    This was a very good introductory course, it seems very short, since you enjoy it in every step of the way. The professor is very charming and the topics at hand are very interesting. My only complaint is that it could be a bit longer.
  • Anonymous

    Anonymous completed this course.

    Promised a lot but turned out to be the typical traditional textbook course. I wish I could say more but it fell quite short even if there is interesting content but nothing you cannot find in other MOOCs.
  • Anonymous

    Anonymous is taking this course right now.

    A very short course that didn't delivered much, even though the lectures were carefully crafted, but I would not have expected otherwise given that this was such a short tutorial on a very specific topic.
  • Profile image for Ces Alonso Lobo
    Ces Alonso Lobo

    Ces Alonso Lobo completed this course, spending 3 hours a week on it and found the course difficulty to be easy.

    Another amazing math course imparted by this crack. Messi cleans the boots of this mathematician . Magical, is the best definition he deserves

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