Optimization for real-world data. Morse code is a good one; which leads to the entropy of real-world English letters: how probable are the letters A, E, and Z? How probable is the 3-gram of letters 'AEZ'? A well-balanced tree could take this knowledge into account and sparsely add 'nodes' without needing to rebalance as often.
Pairtree with hashes is an interesting real-world problem. Filesystems have a max number of file entries per directory. A good cryptographic hash has equal probabilities of e.g. hexadecimal character occurrence for each digit: each digit character has an equal probability of following any other digit. Shannon used these probabilities for something; I can't remember what it was? One (TED-Ed) YouTube video I found mentioned sorting library books; what's the fastest way? Sorting is not strictly necessary for top-k N-dimensional optimization: tracking high and low points doesn't require sorting the whole (then ordered or partially ordered) set. Here's an example from https://wrdrd.github.io/docs/consulting/data-science# optimization : Optimization⬅ https://en.wikipedia.org/wiki/Mathematical_optimization Find local and global optima (maxima and minima) within an n-dimensional field which may be limited by resource constraints. # Global optima of a 1-dimensional list points = [10, 20, 100, 20, 10] global_max, global_min = max(points), min(points) assert global_max == 100 assert global_min == 10 # Local optima of a 1-dimensional list sample = points[:1] local_max, local_min = max(sample), min(sample) assert local_max == 20 assert local_min == 10 # A 2-dimensional list ... points = [(-0.5, 0), (0, 0.5), (0.5, 0), (0, -0.5)] https://en.wikipedia.org/wiki/Optimization_(disambiguation) https://en.wikipedia.org/wiki/Metaheuristic https://en.wikipedia.org/wiki/Receiver_operating_characteristic http://rayli.net/blog/data/top-10-data-mining-algorithms-in-plain-english/ http://scikit-learn.org/stable/tutorial/machine_learning_map/ https://en.wikipedia.org/wiki/Firefly_algorithm On Thursday, August 16, 2018, Tobias Kohn <ko...@tobiaskohn.ch> wrote: > I couldn't agree more! Such interactive programmes are often so much more > valuable than hours of talking (even though doing interactive programmes > all the time will wear the students out -- as always, there is golden > middle here ^_^). > > Another idea in that direction is to make two or three groups, and then > have a little competition of who can sort a pile of post-its (or whatever) > fastest. And I would recommend to surprise the students. Once they have > learned how to sort numbers, say, give them post-its with picture of > animals, say, or melodies, or whatever you fancy. That forces them to > think outside of the box, and suddenly computer science class becomes so > much more meaningful and memorable! > > Yet another idea: how about sorting Morse code? Usually, we get it sorted > from 'A' to 'Z'. But there are other ways, and before you know it, you are > discussing trees... > > Cheers, > Tobias > > > Quoting kirby urner <kirby.ur...@gmail.com>: > > > I'm glad Tobias took the bull by the horns and didn't eschew a deeper > look into the sorting algorithms. > > As a big fan of animations, my reflex is to scour Youtube for graphical > renderings of the different strategies, but then another thought crops up: > lets get out of our seats and do choreography, Math is an Outdoor Sport! > (PR poster). I should explain. > > The relationships between programming and scripting theater "programmes" > (old spelling) are deep. Give each student a postit with a number and have > them *enact* the sorting algorithm. E.g. starting in a row, turn to person > on your left (if there is one) and swap places if your postit number is > higher... have directors and make a video. Now choreograph (enact, > dance) in a different way. > > Symphonies, plays, musicals, are so multi-track, so parallel, and yet we > fail to exploit those intuitions sometimes. > > Let the Theater Department handle it, in consultation with CS. Could go > under the heading of "Unplugged". Likely the Hobbits are already doing > this in New Zealand (NZ has pioneered unplugged more than most, plus has > Hobbits). > > Seriously, having lived in the Philippines where people routinely learn > group dancing, I'm worried about only acting as teams in three capacities > (a) cheerleader (b) athlete on the field (c) band. Theater is being > eliminated in favor of competitive sports. Perhaps CS could come to the > rescue and say "wait, we need Theater for our simulations". > > More cerebral team-based activities might go a long way towards fighting > the stereotype that computer programmers only live in artificially lit > basements eating pizza. That's a physically damaging lifestyle, nothing to > do with writing code or even doing math. > > === > > Regarding last night's tele-class (real time, zoom.us), I worked through > "cloning a github repo" as the core exercise, a repeat from last week, then > went through the process of updating a notebook live, and pushing the > changes back to the repo. > > The repo was of course the one with yesterday's Jupyter Notebook about > Ordering Polyhedrons by volume. > > https://github.com/4dsolutions/SAISOFT > > I tell them "cloning a github repo" is going to be important for when they > want like a Jake Vanderplas tutorial, i.e. when they want to study a topic > in more depth and the workshop is (A) on Youtube or similar service and (B) > the workshop materials are free via github (a common enough pattern). > > I also reminded them how Google shares TensorFlow in the form of Colab > exercises (Jupyter Notebooks). > > One students asked "R or Python, which is winning in Data Science"? > > My answer: pandas is a relatively recent development and there's already > lots of excellent curriculum based around R, which is likewise free / open > source. The business world is rushing into Python because of DL / ML and so > gains an R-like tool in the process, which enables better town-gown > relations i.e. Harvard can talk to Facebook about Pytorch thanks to already > teaching R in the stats department. > > In other words, it's not either/or, more like two communities forming a > bridge via the common language of data science, which R and Python both > reflect (as do some other languages / ecosystems, not aiming for > comprehensivity here). > > Kirby > > > > On Wed, Aug 15, 2018 at 10:04 AM, Tobias Kohn <ko...@tobiaskohn.ch> wrote: > >> *Hi Jurgis,* >> > > >
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