Teaching programming… Without computers.

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Blue vervets are probably one of the most photogenic species of monkey.

At the main maths camp this year, we had five different topic areas that we structured the camp around.  All of them used computers in a big way, except one: Programming.  The justification for this was that we had really nice, user-friendly programs for illustrating ideas in statistics, geometry, and so on, but actually throwing the students into a programming environment would almost certainly be too overwhelming.  A significant number of the students had never touched a computer before, and really taking them into a code environment seemed a bit of a stretch for people still figuring out the idea of a right-click.

That’s not to say that good computer tools don’t exist; just that we haven’t managed to review them yet.  (MIT’s Scratch, for example, looks well worth checking out.)  Furthermore, given the time-scale we were working on, I think there was a lot of value in separating the programming concepts from the physical object of the computer.  This makes the concepts available in a larger context than the computer, which, as a maths camp, we were eager to do.  The idea of setting some basic rules from which we can extrapolate is a basic idea of mathematics.  Getting across the idea of the need for precision was also of key importance.

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A Small Exercise in Categorification

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To celebrate the fact that I’ve finally got latex working on the blog, I’m going to bore you with a post about combinatorics and categories…

As good a picture as any for a post about categorification, right?

After some nice student questions in the Foundations course the other day, David and I were playing around with the number of surjections that exist between finite sets. And somehow this led down the road of writing the number of maps between two finite sets as a sum over the number of pre-image sets. There’s a very nice formula for this, actually. The number of surjections {rm Sur}^n_k from set of n things to a set of k things is given by k!S(n,k), where S(n,k) is the Sterling number of the second kind, which counts the ways of partioning an n-element set into k subsets. (And it’s pretty easy to backwards reason why the number of surjections is this number!) The number of injections {rm Inj}^n_k is the falling factorial, (k)_n=k(k-1)cdots (k-n).

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Because it’s there.

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A tree apparently growing out of a rock, just above the tree line.

Today I climbed up the biggest hill readily visible from Maseno with Aryan, a San Dieagan who’s living at the hospital.  Basic strategy: Pick the largest hill visible from Maseno.  Climb it.  Repeat.  (Well, the repeat will be for another day, but we have some candidates picked out.)  We didn’t really know what to expect in terms of paths; essentially, there’s beautiful hills all around with these giant granite boulders sticking out of them, but we have little idea what the local interaction with them is.  The one we climbed today had farms situated on it, probably to about half way up, including some really steep little plots that we passed through on the way back down. There are cows wandering around everywhere, occasionally exactly where you want to pass by, but that was the most ferocious animal we met.

At the road side we were approached by a guy who was intent on being our guide up the hill; he tried to scare us into taking him on by telling us that the hill was full of vipers and panthers.  This wasn’t terribly persuasive, though: I think we would have been in just as terrible a position if he’d been with us as not.  He didn’t look quite sturdy enough to take on a panther in a fist fight.

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Teaching, teaching, teaching….

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Yesterday I spent five hours in front of a board!  Getting some good honest work in…  Two hours of normal class,doing the Foundations of Pure Math course, two hours of seminar, and an hour making a video lecture for the algebraic structures class.

Here are the videos for the algebraic structures class; it seems like a nice deliverable! It’s for the first section of the notes, which gives an introduction to the definition of a group, along with a bunch of examples.
Group Definition
Integers modulo n
Permutation Group
Dihedral Group
General Linear Group
The videos were shot in David’s house; the clip-on microphone that I picked up last year all but eliminated the terrible echo in the room. On the other hand, there’s a good bit of noise in the audio, which it would be great to figure out how to eliminate.

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Groups, Groups, Groups…

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Group Theory in Probability and Statistics seminar flyer! The image is a couple of my favorite jugglers, Matt ‘Poki’ McCorkle and Brian Thompson.

Lots of teaching things going on right now!  David and I were tasked (with extremely short notice) with developing an online abstract algebra course (entitled ‘algebraic structures’) for second-year undergraduates, and have been hashing out a good direction for the course to take.

One of the main things we realized (in a few hours of back and forth) is that the usual first course in abstract algebra probably isn’t really locally appropriate.  This is largely because we can’t be assured that the later maths classes — which hook abstract algebra into a wide variety of different contexts — will ever be available to the students.  The other big idea we came up with is that it would be great if we got students to the point where they could look at a mathematical problem and find the influence of algebra, and (in a perfect world) craft solutions to the problem appropriately.

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Amagoro Mini-Maths Camps

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Moding High Motto: To Arm the Brain to Conquer.

This weekend we ran four mini-maths camps! These are half-day events held at high schools, which give a sort of introduction to the kinds of things that we do at the main maths camp in August at Maseno.  On this particular trip, we were partnered with the Elewana Project, which works directly with a number of schools in the area; they mainly bring in students from the US during the summer to work with students, though they are beginning to do some two-week camps aimed at improving educational outcomes for secondary students.

The upshot on this particular trip was that the schools we visited had decently-maintained computer labs, thanks to Elewana’s ongoing efforts with the schools.  The schools also have student computer clubs, which allows students to have regular access to their computers.  As such, our program for the camps were focused on:

  1. Getting across the basic idea that mathematics is about understanding and applying a system of rules, and
  2. Getting a little bit of familiarity with the software, so that the students can explore and learn more after we’ve left.

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Akirachix MobileGarage

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A speaker at the MobileGarage event.

Today is the kick-off of the Maseno MobileGarage, a two-day boot-camp hosted by the Akirachix, a group promoting ITC development for women and more generally.  The idea is to give trainings on mobile application development to the local students.  I gave a short 15-minute talk for the kick-off emphasizing the importance of developing open-source tools in addition to focus on winning the lottery in the app store.

With luck, I’ll be able to poach an enterprising undergraduate to help develop an Android version of the photo-uploading script I wrote; I think it would be a great app for getting student work up on a website quickly and easily, which facilitates peer-learning and peer-review of student submissions.

Good times!

Sage for Specht Modules

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Appropos of nothing, these were some cute monkeys playing on the water tank this morning. I actually got a very close look at them, but by the time the camera was out, they were scurrying onto the roof.

As the strike drags on, I’ve had some time to actually do some maths.  In particular, I’m preparing to run a weekly seminar on using representation theory for certain statistical problems.  The plan is to work from some old lecture notes by Persi Diaconis entitled ‘Group Representations in Probability and Statistics.’ These deal with, for example, how long one should apply a random shuffling process before the thing which is being shuffled is well-mixed.  Particular examples include the question of how many times one should shuffle a deck of cards, and how long one should let a random walk on Z_n run before we can be reasonably sure that every point has been reached.  There are numerous real-world applications of the results, and it uses a lot of first-rate representation theory along the way!

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More Strike Down-Time

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The Sizzling Brownie from Laughing Buddha, in Kisumu. It’s a brownie served on a hot plate with a big scoop of ice-cream on top, then drizzled with liquid chocolate which boils when it come into contact with the plate. Mind-bogglingly delicious.

There’s still no foreseeable end to the teacher and lecturer’s strike (in fact, the doctors are joining in, too, now), though I’m assured that there is to be a meeting on Monday to try to negotiate an end.  As such, we’ve been running lots of errands in the downtime…  And in-between work, we’ve been eating healthy amounts of ice-cream and playing a lot of Dominion!

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