I’m teaching an intro calculus class this year (specifically, ‘Math for Life and Social Science’), and came a while ago to the section on optimization. It’s a really important subject, and yet the optimization problems one finds in Calculus books (even good ones) tend to be contrived examples which I refer to as ‘box factory problems.’ Things along the lines of ‘minimize the surface area of a rectangular box with volume ‘.
These are fine for a problem or two: There’s a useful skill in taking a real-sounding problem and translating it into the mathematics you’re learning. We use the constraints (in this case, on the volume) to reduce the number of dimensions, turn the problem into a one-variable calculus problem, and then solve. All well and good, but these problems somehow completely miss the impact of optimization on society at large. Largely because the optimization problems that occur most commonly in the wild have a slightly different flavour.
Problem: In Boston, we observe that the monthly rent for three one-bedroom apartments are $1300, $1150, and $950. Rent on three two-bedroom apartments were $1500, $1700, and $1200. Assuming that the cost of a 0-bedroom apartment is $500, find the best possible line describing the rent as a function of the number of bedrooms. Continue reading →
This week I’ve been giving lectures at an algebraic geometry workshop in Mombasa. I know what some of you are thinking: ‘But Tom, you’re nothing like an algebraic geometer!’ And that’s true. But often the best way to learn something is by putting yourself in a position where you have to know it, like standing in front of fifty people expecting a clear explanation. In this case, I’ve learned some basics of Grobner bases (mostly from an excellent book by Cox, Little, and Shea) and have been augmenting the lectures and exercise sessions with Sage. I’ve written up some notes on the talks, and I’ll probably convert them into a web-based format with Sage cells and stuff sometime next week…
The workshop has participants attending from Kenya, Tanzania, Uganda, Rwanda, and Zambia. The participants have been super motivated; we’re just finishing up the third and final week of the workshop, and the participants have been staying up late working on final projects. Attendance has stayed high throughout the workshop, to a degree you wouldn’t expect in (say) North America. The chance for exposure to math going on at the international level is a big draw, since it’s still so rare for international mathematicians to come through East Africa. I imagine it’s like if you only got to eat ice cream once every year or three: you’re not going to let anything go to waste.
Back for a day in Nairobi after visiting Paris for FPSAC 2013 and Sage-Days 49. On the whole, it was a really productive visit; I met a number of my primary goals. On the mathematics front, Kenya has been extremely isolating: One of the big goals for the conference, then, was to connect to some new things to work on and figure out what’s been happening in the algebraic combinatorics world in the last year. It was exciting to actually work on math with people: when I arrived in Maseno, it turned out that no new graduate students had come into pure maths in some time, which meant there was no real outlet for doing math with other people. So it’s been kind of a lonely year: I did a lot of work on education, and did some interesting community building around computer science with LakeHub, but often felt like my big area of expertise really wasn’t terribly helpful in Kenya. The institutions weren’t really ready to make use of what I was bringing, since there wasn’t time or space for people to do research. I obviously found lots of great stuff to work on anyway, but it felt a bit funny that I was so unable to engage people on the maths.
LakeHub has been churning steadily along; we had our third event on Saturday, and it was quite successful according to me and everyone else I’ve talked to. We’ve settled on a basic format for the time being, with an event happening every Saturday from 1-5pm. Half of the time these are big group-oriented events with demos and big inclusive activities, and the other half of the time they’re ‘hang-outs’ where people get together to work with other tech-oriented people nearby, and to check in with ongoing study groups.
Consider the KCSE, the national exam taken by hundreds of thousands of Kenyan graduating secondary students each year. It is the sole determinant of whether a student will go to university, which in turn determines whether the student has a chance at a good job and a healthy life. Because of its centrality, the secondary school system in Kenya is almost entirely oriented around trying to cram information from the exam syllabus into student’s heads.
But this approach has two major problems. The first is that no one can force a student to learn. The second is that a single standardized test gives the illusion of a fixed body of knowledge that people need to understand in order to succeed in life. This simply doesn’t reflect the world we live in. The economy of Kenya and the world in general is changing at an incredible rate, and those graduating under the current academic regime simply aren’t getting the skills to compete. And worse, even if the curriculum were to drastically change, it would quickly be obsoleted again. How do we address this?
The math group in Bahir Dar was incredibly hospitable, and, as mentioned in the previous post, has some really interesting outreach projects going on. They have a couple-few research groups getting started, one working on fluid dynamics, and one working on lattice theory (as in posets, not -modules). One of the really inspiring things about the visit was that, in addition to having an awesome and enthusiastic staff, they are also receiving quite reasonable support from the University (and by extension, the government) for advancing their research and outreach projects. People involved in project work can apply to have reduced teaching loads, giving them equal pay but plenty of time to advance the projects. Meanwhile, the university is hiring more lecturers to make up the extra time; presumably this will end up looking like a much more flexible version of the research universities in the US, which have a two-tiered system of research professors and lecturers. This allows them to reward people with good ideas and plans with extra time, rather than making the decision at-or-before hiring time; it’s an interesting idea, and probably much more appropriate to the local context than the US system. It reaffirms my feeling that until African countries will continue to lag in science until the governments get serious about funding the universities for research: Here we have an example of awesome university support which is fuelling great projects. Another positive development is that Bahir Dar sounds like it’s starting to put caps on the number of courses people can teach; this keeps people from taking on unrealistic teaching loads in order to get a bigger pay-check, a real problem in Kenya. Of course, such a move also needs to be paired with decent pay for lecturers!
One of thing I heard repeatedly at Bahir Dar was that the research programs need more mentorship. They are about to start offering a PhD program in math, and only have a few PhD holders to start from. This means that there is a danger of the research programs being a bit too over-specialized, especially when combined with the fact that it’s very difficult for people to get out for conferences to share ideas. As a result there’s a real need for interaction with vagabond mathematicians like myself. I think the next time I have a few months free, I’m going to strongly consider going and giving some research-oriented course(s) for the department there. If you’re a vagabond mathematician, I think it would be really cool for you to do so, too! Ethiopia’s really lovely, and it would be an excellent way to get involved in an exciting environment.
I’m currently visiting Bahir Dar University, in Ethiopia. It was a natural place to visit while Kenya is out-of-session for their elections. Abebe Regassa, a lecturer here, came to Maseno last August for the maths camp, and will be co-facilitating the first Ethiopian maths camp this July with Berie Getie.
The math department here is very exciting to be in contact with. The department is large (now at about 50 staff), has a mandate to get research groups going, and has given Abebe and Berie reduced teaching loads to coordinate outreach activities. They’re actually already doing a fantastic job, by the accounts I’ve heard thus far.
One outreach project is the Outreach Program for Talented Students. This project has run for two years, funded thus far by the Gelfand Family Charitable Trust, though it will be moving to Univesity funding soon. The project puts on a science-and-technology camp for 450 elite students. This year, there will be 300 students from schools around Bahir Dar, and 150 from all over the country. The camp runs for 40 days(!) and uses a team-teaching model (one university lecturer, one secondary teacher, and a lab assistant for each class of 30 students). After 15 days of common curriculum, the camp is split into two streams, one focused on general science topics, and the other focused on ICT and electronics. At the end, 45 students are selected from the 450 to continue working with the Bahir Dar university staff on interesting projects. (There’s a 62-page report on the program here.)
Like many people, I’ve been fairly shocked at the suicide of Aaron Swartz a couple days ago. Here’s some background, if you haven’t read anything about it: Cory Doctorow’s obit post, and Lawrence Lessig’s Prosecutor as Bully.
I have two trains of thought on all this: On the first, I think back to being in high school and coming up against systems that just carried on, not bothering to question their relationship to their underlying purpose. Like an ‘American literature’ class which involved almost no actual reading, instead focusing entirely on grammar exercises. Or an ‘independent study’ art class which led, by a strange run of events, to a suspension from school after the Columbine shooting, as the school administration cast about to get rid of any student who reminded them too much of the tragedy in Colorado. The thing I had been working on was a comic book about the incredible tedium and irrational boundaries of life in an American suburb. Through my time in school I developed this sense that the vision of the people running the show was too narrow to understand what was possible: the admins were so interested in maintaining a status quo that there was no possibility of examining underlying assumptions, or addressing the contradictions in a school that treats its students like prisoners.
And then I moved on, and life got better.
Aaron Swartz was constantly running up against the contradictions between the old world and the new digital society, and taking concrete actions that exposed those contradictions and forced the conversation forward.