Very slick! Greg McVerry, a professor, can post all of the readings, assignments, etc. for his EDU522 online course on his own website, and I can indicate that I’ve read the pieces, watched the videos, or post my responses to assignments and other classwork (as well as to fellow classmates’ work and questions) on my own website while sending notifications via Webmention of all of the above to the original posts on their sites.
When I’m done with the course I’ll have my own archive of everything I did for the entire course (as well as copies on the Internet Archive, since I ping it as I go). His class website and my responses there could be used for the purposes of grading.
I can subscribe to his feed of posts for the class (or an aggregated one he’s made–sometimes known as a planet) and use the feed reader of choice to consume the content (and that of my peers’) at my own pace to work my way through the course.
This is a lot closer to what I think online pedagogy or even the use of a Domain of One’s Own in an educational setting could and should be. I hope other educators might follow suit based on our examples. As an added bonus, if you’d like to try it out, Greg’s three week course is, in fact, an open course for using IndieWeb and DoOO technologies for teaching. It’s just started, so I hope more will join us.
He’s focusing primarily on using WordPress as the platform of choice in the course, but one could just as easily use other Webmention enabled CMSes like WithKnown, Grav, Perch, Drupal, et al. to participate.
IndieWeb technology for online pedagogy was originally published on Chris Aldrich
About this course
Already know something about quantum mechanics, quantum bits and quantum logic gates, but want to design new quantum algorithms, and explore multi-party quantum protocols? This is the course for you!
In this advanced graduate physics course on quantum computation and quantum information, we will cover:
- The formalism of quantum errors (density matrices, operator sum representations)
- Quantum error correction codes (stabilizers, graph states)
- Fault-tolerant quantum computation (normalizers, Clifford group operations, the Gottesman-Knill Theorem)
- Models of quantum computation (teleportation, cluster, measurement-based)
- Quantum Fourier transform-based algorithms (factoring, simulation)
- Quantum communication (noiseless and noisy coding)
- Quantum protocols (games, communication complexity)
Research problem ideas are presented along the journey.
What you’ll learn
- Formalisms for describing errors in quantum states and systems
- Quantum error correction theory
- Fault-tolerant quantum procedure constructions
- Models of quantum computation beyond gates
- Structures of exponentially-fast quantum algorithms
- Multi-party quantum communication protocols
Meet the instructor
Isaac Chuang Professor of Electrical Engineering and Computer Science, and Professor of Physics MIT
🔖 Quantum Information Science II was originally published on Chris Aldrich | Boffo Socko
Introduction to Galois Theory
A very beautiful classical theory on field extensions of a certain type (Galois extensions) initiated by Galois in the 19th century. Explains, in particular, why it is not possible to solve an equation of degree 5 or more in the same way as we solve quadratic or cubic equations. You will learn to compute Galois groups and (before that) study the properties of various field extensions.
We first shall survey the basic notions and properties of field extensions: algebraic, transcendental, finite field extensions, degree of an extension, algebraic closure, decomposition field of a polynomial.
Then we shall do a bit of commutative algebra (finite algebras over a field, base change via tensor product) and apply this to study the notion of separability in some detail.
After that we shall discuss Galois extensions and Galois correspondence and give many examples (cyclotomic extensions, finite fields, Kummer extensions, Artin-Schreier extensions, etc.).
We shall address the question of solvability of equations by radicals (Abel theorem). We shall also try to explain the relation to representations and to topological coverings.
Finally, we shall briefly discuss extensions of rings (integral elemets, norms, traces, etc.) and explain how to use the reduction modulo primes to compute Galois groups.
I’ve been watching MOOCs for several years and this is one of the few I’ve come across that covers some more advanced mathematical topics. I’m curious to see how it turns out and what type of interest/results it returns.
It’s being offered by National Research University – Higher School of Economics (HSE) in Russia.
Introduction to Galois Theory | Coursera was originally published on Chris Aldrich | Boffo Socko
Introduction to Dynamical Systems and Chaos (Summer, 2016)
About the Course:
In this course you’ll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.
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:
- Dynamical systems undergo bifurcations, where a small change in a system parameter such as the temperature or the harvest rate in a fishery leads to a large and qualitative change in the system’s
- Deterministic dynamical systems can behave randomly. This property, known as sensitive dependence or the butterfly effect, places strong limits on our ability to predict some phenomena.
- Disordered behavior can be stable. Non-periodic systems with the butterfly effect can have stable average properties. So the average or statistical properties of a system can be predictable, even if its details are not.
- Complex behavior can arise from simple rules. Simple dynamical systems do not necessarily lead to simple results. In particular, we will see that simple rules can produce patterns and structures of surprising complexity.
About the Instructor:
David Feldman is Professor of Physics and Mathematics at College of the Atlantic. From 2004-2009 he was a faculty member in the Santa Fe Institute’s Complex Systems Summer School in Beijing, China. He served as the school’s co-director from 2006-2009. Dave is the author of Chaos and Fractals: An Elementary Introduction (Oxford University Press, 2012), a textbook on chaos and fractals for students with a background in high school algebra. Dave was a U.S. Fulbright Lecturer in Rwanda in 2011-12.
5 Jul 2016 9am PDT to
20 Sep 2016 3pm PDT
A familiarity with basic high school algebra. There will be optional lessons for those with stronger math backgrounds.
- Introduction I: Iterated Functions
- Introduction II: Differential Equations
- Chaos and the Butterfly Effect
- Bifurcations: Part I (Differential Equations)
- Bifurcations: Part II (Logistic Map)
- Phase Space
- Strange Attractors
- Pattern Formation
- Summary and Conclusions
Source: Complexity Explorer
Introduction to Dynamical Systems and Chaos was originally published on Chris Aldrich | Boffo Socko