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Introduction

Hi everyone,

This is John Roe. I'm a midcareer mathematician and have just (last month) finished a stint as department head. Hooray! For a couple of years it has been growing on me that I want to engage more directly with sustainability issues, as I've come to understand the astonishing rate at which our species seems to be spending down our planetary inheritance. I've been planning to join the Azimuth group since I heard about it, but felt that I should wait until my departmental duties were over.

The theme of my mathematical work has been generalizations of the Atiyah-Singer index theorem, especially to non-compact manifolds. In thinking about this stuff, I stumbled upon the fact that what's relevant for index theory is the large scale or "coarse" geometry of a non-compact manifold. This subject has lots of relationships with networks and spectral graph theory in particular, which I know is a topic of interest here. That's one thing I'd like to explore. (To read a little bit more about my stuff, take a look at my Notices article or this book.)

One topic that interests me a lot at present is education for sustainability through college math classes. One the one hand, most college students (here in the US) have to take some kind of "quantification" or "general education" class in math. On the other hand, much "sustainability awareness" just involves exactly the kind of basic quantitative literacy that these classes should be teaching. How to bring these together? Marty Walter's class at Boulder is one example, but is it scalable?

I have been writing about sustainability from a less technical and more theological perspective over at my blog Points of Inflection for a year or so now. I've been coding since the early 1970s, in various languages, and am presently trying to learn Haskell.

Comments

  • 1.
    edited July 2012

    Hi, John! Since I've spent a bunch of time at MIT where everyone is gung-ho about the Atiyah-Singer theorem and its generalizations, I was wondering if you were indeed 'the' John Roe. You are! That's great.

    When I return to U.C. Riverside in the fall, I'm going to add more material on sustainability, ecology, climate change and the like to many of the math classes I teach. Easy example: when teaching very easy first-order ODE, include not just the equation describing exponential growth and the logistic equation describing limited growth, but also the equation

    $$ \frac{d P}{d t} = \alpha P - \beta $$ that describes a simplified model of 'fishing', where fish are extracted at a constant rate $\beta$. This shows how overfishing can drive fish extinct. Of course it's oversimplified, since it's hard to extract fish at a constant rate when there are almost no fish left, but I'll say that.

    I haven't taught 'general education' math classes, but they'd be a really great opportunity to increase statistical literacy and teach them about sustainability and... well, impose all sorts of views on the students. (So there's a danger here, too.)

    I'll need to check out Mary Walter's class.

    Comment Source:Hi, John! Since I've spent a bunch of time at MIT where everyone is gung-ho about the Atiyah-Singer theorem and its generalizations, I was wondering if you were indeed 'the' John Roe. You are! That's great. When I return to U.C. Riverside in the fall, I'm going to add more material on sustainability, ecology, climate change and the like to many of the math classes I teach. Easy example: when teaching very easy first-order ODE, include not just the equation describing exponential growth and the logistic equation describing limited growth, but also the equation $$ \frac{d P}{d t} = \alpha P - \beta $$ that describes a simplified model of 'fishing', where fish are extracted at a constant rate $\beta$. This shows how overfishing can drive fish extinct. Of course it's *over*simplified, since it's hard to extract fish at a constant rate when there are almost no fish left, but I'll say that. I haven't taught 'general education' math classes, but they'd be a really great opportunity to increase statistical literacy and teach them about sustainability and... well, impose all sorts of views on the students. (So there's a danger here, too.) I'll need to check out Mary Walter's class.
  • 2.

    Hi John. I took your algebraic topology course at Penn State back in 1999, where I completed a Ph.D. in physics, and, later, a postdoc in geosciences. I am also interested in the idea of introducing sustainability and environmental issues into basic service courses. I hadn't seen Walter's class / text. It looks interesting. I've often thought that one way to approach the problem is to supplement the mathematics with interactive computer simulations, such as the box models being studied here at Azimuth (and in Walter's class). That could make interesting quantitative system dynamics more accessible to students who don't have the math background to, for example, solve systems of nonlinear differential equations.

    By the way, since you mention theological perspectives, you may be interested in the book A Climate for Change: Global Warming Facts for Faith-Based Decisions. Probably nothing new to you, but written by a scientist-and-pastor wife-and-husband team to present an evangelical perspective on sustainability.

    Comment Source:Hi John. I took your algebraic topology course at Penn State back in 1999, where I completed a Ph.D. in physics, and, later, a postdoc in geosciences. I am also interested in the idea of introducing sustainability and environmental issues into basic service courses. I hadn't seen Walter's class / text. It looks interesting. I've often thought that one way to approach the problem is to supplement the mathematics with interactive computer simulations, such as the box models being studied here at Azimuth (and in Walter's class). That could make interesting quantitative system dynamics more accessible to students who don't have the math background to, for example, solve systems of nonlinear differential equations. By the way, since you mention theological perspectives, you may be interested in the book [A Climate for Change: Global Warming Facts for Faith-Based Decisions](http://climateforchangethebook.com/). Probably nothing new to you, but written by a scientist-and-pastor wife-and-husband team to present an evangelical perspective on sustainability.
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