Afonso mentioned the release of lectures notes of a course he gave this past fall on on his twitter and on his blog. I liked the notes very much and giggled at that part:
It is known that 43 $<$ R(5) $<$ 49. There is a famous quote in Joel Spencer's book [Spe94] that conveys the di fficulty of computing Ramsey numbers:
\Erd}os asks us to imagine an alien force, vastly more powerful than us, landing on Earth and demanding the value of R(5) or they will destroy our planet. In that case, he claims, we should marshal all our computers and all our mathematicians and attempt to find the value. But suppose, instead, that they ask for R(6). In that case, he believes, we should attempt to destroy the aliens."
Preface
These are notes from a course I gave at MIT on the Fall of 2015 entitled: \18.S096: Topics in Mathematics of Data Science". These notes are not in nal form and will be continuously edited and/or corrected (as I am sure they contain many typos). Please use at your own risk and do let me know if you nd any typo/mistake. Part of the content of this course is greatly inspired by a course I took from Amit Singer while a graduate student at Princeton. Amit's course was inspiring and in uential on my research interests. I can only hope that these notes may one day inspire someone's research in the same way that Amit's course inspired mine. These notes also include a total of forty-two open problems (now 41, as in meanwhile Open Problem 1.3 has been solved [MS15]!). This list of problems does not necessarily contain the most important problems in the eld (although some will be rather important). I have tried to select a mix of important, perhaps approachable, and fun problems. Hopefully you will enjoy thinking about these problems as much as I do! I would like to thank all the students who took my course, it was a great and interactive audience! I would also like to thank Nicolas Boumal, Ludwig Schmidt, and Jonathan Weed for letting me know of several typos. Thank you also to Nicolas Boumal, Dustin G. Mixon, Bernat Guillen Pegueroles, Philippe Rigollet, and Francisco Unda for suggesting open problems.
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