Other handouts can be fond on this page, http://boole.stanford.edu/cs353/handouts.html Mirrored to my Dropbox at https://www.dropbox.com/s/tn5of68rw375ftg/cs353-handouts.zip?dl=0
I think that’s what a hobby is supposed to feel like: not an obligation, but a state you’re always returning to. It doesn’t have to be expensive, it doesn’t have to be organized, it doesn’t have to depend on other people. It just has to be yours.
Adjunctions as a way to relate two objects (from possibly different categories).
An adjunction is a way to relate two objects a and c, but not directly: C(a,c) Instead, we get two maps, (L)eft and (R)ight, which allow to relate them: C(L(a),c) A(a,R(c)) 1/n The means that there's a pair of arrows, one in each direction, that these two hom-sets are isomorphic. The first example given is currying: a function in two arguments is equivalent to a function of one argument returning another function in the remaining argument. 2/n We can write this like so: C(a✕b,c) C(a,c^b) where L = _✕b, and R = _^b.
Finally, I am concerned about the state of pure mathematics research. More and more, results depend on theorems whose proofs are unpublished or sketchy (or even, in places, incorrect). We rely more and more on unnamed teams of experts who have a sufficiently broad overview of an area to be able to tell us with confidence which papers can be trusted. Fashions change, people desert areas, and I am genuinely scared that we are leaving a mess behind in some areas. There are some theorems whose proofs might be difficult or impossible to reconstruct in 20 years’ time.
This past year has been spent trying to figure out how to stop chasing things endlessly – in work, in accolades, in likes, in what others have that I also want but that maybe I can’t quite explain why I want. To be confident in knowing that whatever comes, will come.
Charlotte de Witte live DJ-set at Studio Brussel in Belgium on November 15th, 2019.
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“Something about that sound and house pulled us back together, giving us a new chapter as friends and collaborators”.
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For them the videos were a grace they didn’t have to earn. I like to tell them the struggle is the more interesting place to be: because a healthy confusion is where the real learning begins. In fact, failing a student CAN be done with grace, so that the student understands their dignity has not been tarnished even though their work has been justly assessed---just as a parent can discipline her child if the child knows her love is unconditional. Grace is precisely what makes hard conversations possible, and productive, between people. But you have to extend the grace first. One of my students said to me, so gently: “Should I be terminally ill later in life, I would want my son to act as you have.”
Creativity is about connection—you must be connected to others in order to be inspired and share your own work—but it is also about disconnection. You must retreat from the world long enough to think, practice your art, and bring forth something worth sharing with others. You must play a little hide-and-seek in order to produce something worth being found.
There’s a lot of talent pooled in Silicon Valley, and it’s hard not to look around at a lot of the companies here and feel that it’s a bit of a shame, a waste of potential. There’s some conflation happening there, of moral value with economic value,
An aspiring research distiller lacks many things that are easy to take for granted: a career path, places to learn, examples and role models. Underlying this is a deeper issue: their work isn’t seen as a real research contribution. We need to fix this. It’s entirely possible to build paths and staircases into these mountains.That is, really outstanding tutorials, reviews, textbooks, and so on. The climb isn’t something to be proud of. The climb isn’t progress: the climb is a mountain of debt.