## Mathematics for Sustainability (Part 1)

guest post by John Roe

This year, I want to develop a new math course. Nothing surprising in that—it is what math professors do all the time! But usually, when we dream of new courses, we are thinking of small classes of eager graduate students to whom we can explain the latest research ideas. Here, I’m after something a bit different.

The goal will be through a General Education Mathematics course, to enable students to develop the quantitative and qualitative skills needed to reason effectively about environmental and economic sustainability. That’s a lot of long words! Let me unpack a bit:

General Education Mathematics At most universities (including Penn State University, where I teach), every student, whatever their major, has to take one or two “quantitative” courses – this is called the “general education” requirement. I want to reach out to students who are not planning to be mathematicians or scientists, students for whom this may be the last math course they ever take.

quantitative and qualitative skills I want students to be able to work with numbers (“quantitative”)—to be able to get a feeling for scale and size, whether we’re talking about gigatonnes of carbon dioxide, kilowatts of domestic power, or picograms of radioisotopes. But I also want them to get an intuition for the behavior of systems (qualitative), so that the ideas of growth, feedback, oscillation, overshoot and so on become part of their conceptual vocabulary.

to reason effectively A transition to a more sustainable society won’t come about without robust public debate—I want to help students engage effectively in this debate. Shamelessly stealing ideas from Andrew Read’s Science in Our World course, I hope to do this by using an online platform for student presentations. Engaging with this process (which includes commenting on other people’s presentations as well as devising your own) will count seriously in the grading scheme.

environmental and economic sustainability I’d like students to get the idea that there are lots of scales on which one can ask the sustainability question – both time scales (how many years is “sustainable”) and spatial scales. We’ll think about global-scale questions (carbon dioxide emissions being an obvious example) but we’ll try to look at as many examples as possible on a local scale (a single building, the Penn State campus, local agriculture) so that we can engage more directly.

I have been thinking about this plan for a year or more but now it’s time to put it into action. I’ve been in touch with my department head and got a green light to offer this for the first time in Spring 2014. In future posts I will share some more about the structure of the course as it develops. Meanwhile, if anyone has some good suggestions, let me know!

### 10 Responses to Mathematics for Sustainability (Part 1)

1. John Baez says:

In case you’re curious: John Roe is a math professor at Penn State University who works on index theory (roughly the relation between the topology of manifolds and solutions of linear partial differential equations on these manifolds) and coarse geometry (roughly the study of geometrical properties of spaces that are visible at arbitrarily large distance scales). He also likes rock-climbing, theology, guitar, ecology and economics. And he’s a member of the Azimuth Project!

I think it’s great for mathematicians to develop courses for undergraduates that help them develop the skills needed to reason clearly about economic and ecological issues. I want to do it myself! So, when he told us he was writing about this over on his blog, I asked if I could crosspost it here, and he agreed.

I hope all of you can come up with good suggestions to help him develop his course. I probably need those suggestions even more than him!

2. Peter Best says:

Great idea, the whole area of sustainability and climate adaptation needs some stronger analytical support.

The great news now is the easy availability of reanalysis data sets on which to base some practical assignments, the amazing variety of R software (e.g. Revolution Analytics platforms) and the active groups such as those of Richard Katz and Richard Smith in the USA and Leonard Smith in the UK on the statistics side of sustainability applications.

I would be keen to help. My partner and I used to teach Maths/physics at university level before setting up our own consultancy company in environmental and forecasting aspects of indusrty planning.

I am interested in the applied risk side of sustainability, especially innovative insurance options for agricultural planning under climate variability and change. A recent talk to a group of CEOs in Brisbane can be found at:

Peter Best Adjunct Prof at QUT and USQ, Queensland

3. enthuse says:

I feel sad that now you and many others have given up on quantum gravity. maybe there is no progress possible in that field.

4. Eitan Angel says:

Well, you are probably already be familiar with it, but just in case you are not let me give a quick plug to Marty Walter’s recently published textbook Mathematics for the Environment as well as the (outdated) web page for the course he developed at the University of Colorado. Marty has been working on this for a while so he would certainly be a good resource.

• John Baez says:

Thanks, that looks very helpful! Maybe John Roe knew about it, but I didn’t.

• John Roe says:

Eitan – Thanks. Yes, I have Marty’s book, and I have talked with him about his course as well. Here’s a review I wrote.

5. John Roe says:

Here are links to the next parts of my blog series:

Part 2

Part 3

• Dan says:

It sounds like a very interesting (and useful) course. I look forward to seeing how your thinking on it progresses. On the off-chance that you haven’t heard of them already, you might want to look at the books Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin by Weinstein and Adam and Consider a Spherical Cow: A Course in Environmental Problem Solving by John Harte. Both are basically worked examples followed by related problems. Guesstimation seems to cover a lot of the ground that you’re calling “Measuring” and Consider a Spherical Cow has a lot of stock-flow problems that might go well with what you’re calling “Changing.” While Guesstimation is meant for the general reader, Consider a Spherical Cow is meant for upper level students in environmental sciences, so you probably wouldn’t want students in a Gen Ed course to try reading it. But some of the problems might be adaptable to your course.

• John Roe says:

Thanks, Dan. I had seen “Guesstimation” before and was struggling to remember the title…so your message really helped!