Teaching Networks to High School Students

Yesterday Somerville had its "Study Day", in which high school students from several schools came to Somerville to visit Somerville, meet some students (who gave them tours of both Somerville and, briefly, other parts of Oxford), learn some general things about Somerville with 'global' presentations, and have a 1.5 hour session with one of a few Somerville Tutors who volunteered to help out. I helped out, as did one of our first-year mathematics students, which is essential because the perspectives and insights of our current students are absolutely crucial to any endeavor like this

I was one of the faculty volunteers, and I gave a presentation about the mathematics of networks and then I talked about studying mathematics at Somerville and Oxford (and gave a preview of some of the curriculum changes in applied mathematics that are currently under discussion; these are currently slated to start in Fall 2012, though first we need to decide exactly what they are). I had 17 students in my room, and apparently my mathematics presentation was among the more popular choices of the students who wanted to visit us. (We obviously didn't have room to accommodate everybody who wanted to come.) The abstract that I wrote to be circulated to the selected high schools---and I don't know how they were selected---was the following:

MATHEMATICS: What do Financial Markets and Facebook have in Common?

This session will introduce you to the sheer joy of applied mathematics, and it will also tell you about the mathematics course at Oxford. Changes are brewing in our mathematics course, and here is your early chance to find out what some of them are. If you are considering studying mathematics at university, then this is the session for you! We'll discuss some modern ideas from an area of mathematics called "network science" that can be used to help understand everything from how Facebook works to how financial markets (don't) work. And then we'll talk about possibly mundane but certainly important stuff like the mathematics degrees at Oxford and how you can get involved in research at an early stage. The only requirement for this session is excitement about mathematics and its applications.


This abstract was what was used to advertise mathematics, and I like to think that my experience communicating with the media helped me to write a good abstract.

After the students were chosen, I asked them to read The Physics of Networks by Mark Newman. (I later stressed that the 'physics' of networks and 'mathematics' of networks are, in my view, interchangeable.)

I checked with the students who attended, and they confirmed that Newman's article was at the right level for them, and I think their having read that article as background made the whole presentation easier.

I needed to show lots of fancy, pretty pictures, so I prepared a powerpoint presentation, but I want to stress that this was guidance for our discussion. I asked the students to speak up early and often, because I don't think that my droning on would be the best way to do this. One can't tell this always tell this purely from the posted slides, so I am happy to comment further about that aspect of things. But it is crucial to make sure that one is actually having a discussion with the students, even if one is using slides to facilitate this discussion. One conscious decision I made was not to bother with the references and acknowledgements for results, figures, etc. I am normally a stickler about such things, but I felt in this case that it would be intimidating and actively detract from what I was trying to do---which was to be as accessible as possible and just open the students up to the excitement of the subject and the fact that they could get into it really quickly. (And I hereby apologize to my colleagues for this, but doing the usual thing would in my opinion have massively hindered the students' experience in this case.)

I also wanted to mention that purposely gave an illustration of how networks can be represented in terms of matrices because the students had had some exposure to matrices before. I wanted to relate this active fascinating field to mathematics they have seen in their high school classes. I also wanted to relate it to their personal experiences with social networks such as Facebook. It is this last aspect that makes it easier to explain networks to high school students (and more general lay audiences, for that matter!) than is the case for most active research areas in mathematics.

One thing that I made a point to stress was that undergraduate researchers have been intimately important to my work in this area, that they are really only a couple of years to be able to contribute to such research efforts, and that such opportunities awaited them in Oxford and Somerville. I made a point to show them what one of my current Somerville students is doing and also made a point to show them a really exciting (though admittedly preliminary) result that she showed me just last week. The point of showing the result from last week was to illustrate that mathematics isn't static---knowledge changes, and it can do so very quickly---and also what we want to do to really get somewhere with the preliminary result. I think that this message isn't given even close to often enough. We're not merely teaching or doing research on a body of knowledge that was handed down to us by the luminaries from yesteryear, but we're constantly discovering new things, obtaining more refined understanding and insights on even very old ideas, etc. Sure, there are a lot of mundane subjects to learn that are well-established, but there are lots of new ideas and applications to be found even in traditional subjects like linear algebra.

I spent roughly half the time discussing networks with the students and roughly half the time discussing Oxford and Somerville mathematics with the students. (We occasionally forayed into the differences between the mathematics and physics or engineering degrees, as some students are also deciding not just where they want to apply but also what specific major they would like to have.)

In deciding on one Oxford College versus another, the thing I stressed was that the students should judge the people with whom they would be working (namely, people like me). More than anything else, what Somerville or any other College has to offer is its people. I refuse to toe the company line and say that Somerville is automatically better. That would be stupid and would contradict my true beliefs (as some of you know, there are some things here that are causing me significant displeasure, to put it mildly). Students should decide for themselves whether or not they want to work with me---I hope so, because I think that I'm a damn fine educator and that I have things to offer on both the teaching and research sides that very few others can offer---but the point is that I think that this is the main decision. Prospective Somerville mathematicians should decide for themselves whether they want to work closely with my colleagues and me. The official literature seems to stress the importance of things like our library, and I think that is seriously misguided. The other Colleges have libraries too, and I'm sure that they're all fine libraries. A College's greatest strength is its people---the ones who will frame your College experience more than anything else ever will---and any College that advertises itself differently is doing it wrong. I know that I'm biased, but in mathematics and allied subjects, I think that Somerville has excellent people (including both faculty and students).

Incidentally, the student response seems to have been extremely positive. The students were engaged and they thanked me warmly at the end of the presentation. One student has already e-mailed me for more information about networks. (I gave the students my e-mail address because I figured they'd have more questions later, and I wanted to be able to answer them.) I can't say if Somerville or Oxford will get any additional applications from prospective mathematics students as a result of the presentation and related efforts, but there are 17 high school students who I feel are more excited about mathematics and its applications than they were before I talked to them. And that counts for a lot.

(By the way, this isn't my first time speaking to high school students about my research. When I do this, I always make it a point to show them some of the stuff my undergrads have done and are currently doing. It's really important to show them the research efforts of somebody who was in their position not that long ago.)