Tag Archives: reasoning

Regression to the mean

One topic we will address in Unit 3.3 is “regression to the mean”.  That is the statistical fact that if one member of a random series is extreme, the next is most likely going to be closer to the average.

The article below gives an interesting take on this in looking at the chances that the children of successful politicians have to grow up as successful politicians themselves.



Thoughts about blog posts

So we are more than halfway through the first blog assessment period.  The TAs and I have read through everything that you all have posted.  There are a lot of interesting ideas out there, ideas that, with a bit of thought, could be developed into excellent posts.  (And remember, you can go back and edit your post, until the end of the blogging period, if you want to improve it; the final grade will be based on the final version of your post.) But fewer of the posts are excellent right now.  Here are some suggestions for the future.

  1. You cannot get points for posting if you don’t post.  As of right now, 8 class members have not made any posts at all, and a further 16 have not posted anything beyond the introduction that was required in week 1.  Yes, I know that according to the grading rules, you can in theory make things up in the second or the third blogging period, but it will take practice – practice which might as well start now.
  2. Posts should contain numbers, but should also set those numbers in context.  Too many posts suffer from the “gee whiz” use of numbers (this is a problem with a lot of environmental writing generally, I find): “if we all did this simple thing we could save 3000 barrels of oil a year”.  All well and good, but how does 3000 barrels a year compare to the total amount of oil that “we” are responsible for consuming?  Is it huge in relation to our total consumption, or insignificant? If insignificant, is it worth the time to do the simple thing (whatever it is)? What are the costs of doing the “simple thing”? etc.
  3. Posts should also contain calculations: it’s not a math post just because you quote a lot of numbers from some web site or other. This post for instance tries to do that by expressing energy consumption of different countries in terms of the number of people who consume one MToe/year.
  4. I’d like to see a clearer awareness of the distinction between environmental benefits (accruing to society at large) and financial benefits (maybe to the individual consumer) – I’m thinking of some of the posts about hybrid cars here, for example.  Related, though not the same point, is to make some effort to quantify trade-offs: if putting solar panels on my roof costs me x dollars right now, and saves me y dollars per year using net metering, how many years will it take to pay back my investment?  (This particular example requires some financial math, about the present value of an annuity, that we will cover in the next chapter.)

Okay, that’s enough suggestions for one post!   Remember that I or the TAs are happy to talk about your blogging during office hours or at any other time by appointment…


This is the home page for MATH 033 – Mathematics for Sustainability.  This is a new course at Penn State which I expect to teach for the first time in the Fall Semester of 2014.

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 PSU), 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.