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Last Fall, three Stanford classes were “offered online” for free: Andrew Ng’s machine learning class, Sebastian Thrun’s AI class, and Jennifer Widom’s data base class. There had been interest and experiments in online free education for a long time, with the MITx initiative being a particularly significant one, but there were a few innovations in last year’s Stanford classes, and they probably contributed to their runaway success and six-digit enrollment.

One difference was that they did not post videos of the in-class lectures. There was, in fact, no in-class lecture. Instead, they taped short videos, rehearsed and edited, with the content of a standard 90-minute class broken down in 4 ten-minutes video or so. This is about the difference between taping a play and making a movie. Then the videos came with some forms of “interactivity” (quizzes that had to be answered to continue), and they were released at the rate in which the class progressed, so that there was a community of students watching the videos at the same time and able to answer each other’s questions in forums. Finally, the videos were used in the Stanford offerings of the classes: the students were instructed to watch the videos by themselves, and during the lecture time they would solve problems, or have discussions or have guest lectures and so on. (In K-12 education, this is called the “flipped classroom” model, in which students take lectures at home and solve homeworks in class, instead of the traditional other way around.)

In the past few months, there has been a lot of thinking, and a lot of acting, about the success of this experiment. Sebastian Thrun started a company called udacity to offer online courses “branded” by the company itself, and Daphne Koller and Andrew Ng started a company called coursera to provide a platform for universities to put their courses online, and, meanwhile, Harvard and Berkeley joined MIT to create edX.

At a time when the growth of higher education costs in the United States appear unsustainable, particularly in second-tier universities, and when the demand for high-quality higher education is exploding in the developing world, these projects have attracted a lot of interest.

While the discussion has been focused on the “summer blockbusters” of higher education, and what they should be like, who is going to produce them, how to make money from them, and so on, I would like to start a discussion on the “art house” side of things.

In universities all over the world, tens of thousands of my colleagues, after they have “served” their departments teaching a large undergraduate classes and maybe a required graduate class, get to have fun teaching a research-oriented graduate class. Their hard-earned insights into problems about which they are the world’s leading expert, be it a particular organ of the fruit fly or a certain corner of the Langlands program, are distilled into a series of lectures featuring content that cannot be found anywhere else. All for the benefit of half a dozen or a dozen students.

If these research-oriented, hyper-specialized courses were available online, those courses might have an audience of 20 or 30 students, instead of 100,000+, but their aggregate effect on their research communities would be, I believe, very significant.

One could also imagine such courses being co-taught by people at different universities. For example, imagine James Lee and Assaf Naor co-teaching a course on metric embeddings and approximation algorithms: they would devise a lesson plan together, each would produce half of the videos, and then at both NYU and UW the students would watch the videos and meet in class for discussions and working on problems; meanwhile study groups would probably pop up in many theory groups, of students watching the videos and working on the problem sets together.

So someone should put a research-oriented graduate course online, and see what happens. This is all to say that I plan to teach my class on graph partitioning, expander graphs, and random walks online in Winter 2013. Wish me luck!

Despite no popular demand, I have collected all the notes from CS261, the course on algorithms for combinatorial optimization problems that I taught in the past term, in one pdf file, available here, and I have created a new page to collect links to my lecture notes.

For the occasion, I have also posted a single file containing the notes from my Spring 2009 class on the foundations of cryptography. As explained in the foreword to the crypto notes, they use a definition of CCA-security that is wrong, that is, a definition that is weaker than the standard one in a way that actually allows potentially dangerous attacks. The weaker definition, however, is much simpler to define and work with, and I think it is pedagogically justified. I believe that everything else in the notes is consistent with standard definitions. As far as I know, the notes are the only place in which one can find a concrete-security treatment of zero knowledge.

*In which we show how to use expert advice, and introduce the powerful “multiplicative weight” algorithm.*

We study the following online problem. We have “experts” that, at each time step , suggest a strategy about what to do at that time (for example, they might be advising on what technology to use, on what investments to make, they might make predictions on whether something is going to happen, thus requiring certain actions, and so on). Based on the quality of the advice that the experts offered in the past, we decide which advice to follow, or with what fraction of our investment to follow which strategy. Subsequently, we find out which loss or gain was associated to each strategy, and, in particular, what loss or gain we personally incurred with the strategy or mix of strategies that we picked, and we move to step .

We want to come up with an algorithm to use the expert advice such that, at the end, that is, at time , we are about as well off as if we had known in advance which expert was the one that gave the best advice, and we had always followed the strategy suggested by that expert at each step. Note that we make no probabilistic assumption, and our analysis will be a worst-case analysis over all possible sequences of events.

The “multiplicative update” algorithm provides a very good solution to this problem, and the analysis of this algorithm is a model for the several other applications of this algorithm, in rather different contexts.

*In which we introduce online algorithms and discuss the buy-vs-rent problem, the secretary problem, and caching.*

In this lecture and the next we will look at various examples of algorithms that operate under partial information. The input to these algorithms is provided as a “stream,” and, at each point in time, the algorithms need to make certain decisions, based on the part of the input that they have seen so far, but without knowing the rest of the input. If we knew that the input was coming from a simple distribution, then we could “learn” the distribution based on an initial segment of the input, and then proceed based on a probabilistic prediction of what the rest of the input is going to be like. In our analysis, instead, we will mostly take a worst-case point of view in which, at any point in time, the unknown part of the input could be anything. Interestingly, however, algorithms that are motivated by “learn and predict” heuristics often work well also from the point of view of worst-case analysis.

*In which we define a multi-commodity flow problem, and we see that its dual is the relaxation of a useful graph partitioning problem. The relaxation can be rounded to yield an approximate graph partitioning algorithm.*

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