MATH 033: Mathematics for Sustainability is a course designed by the late Dr. John Roe, Russ deForest, and Dr. Sara Jamshidi of Penn State University. The course invites students to observe the role that mathematics plays in sustainability. I have had the pleasure to teach and contribute to this course throughout my time as a graduate student, and I have developed this landing page to describe the course in detail.

Content Description

The description you will find on the University Bulletin explains MATH 033 as follows:

The course provides students with the mathematical background and quantitative reasoning skills necessary to engage as informed citizens in discussions of sustainability related to climate change, resources, pollution, recycling, economic change, and similar matters of public interest. Students apply these skills through writing projects that require quantitative evidence to support an argument. The mathematical content of the course spans six key areas: measuring (representing information by numbers, problems of measurement, units, estimation skills); flowing (building and analyzing stock-flow models, calculations using units of energy and power, dynamic equilibria in stock-flow systems, the energy balance of the earth-sun system and the greenhouse effect); connecting (networks, the bystander effect, feedbacks in stock-flow models); changing (out-of-equilibrium stock-flow systems, exponential models, stability of equilibria in stock-flow systems, sensitivity of equilibria to changes in a parameter, tipping points in stock-flow models); risking (probability, expectation, bayesian inference, risk vs uncertainty; and deciding (discounting, uses and limitations of cost-benefit analysis, introduction to game theory and the tragedy of the commons, market-based mechanisms for pollution abatement, ethical considerations).

In the Syllabus, students will also find the following introduction to the course:

You are coming of age in a world full of promise and possibilities—and also a world that faces large scale problems. Many of these problems center on sustainability questions like “can this (key part of our social or economic system) last?” or to put it in a way that has a little more math in it, “how long can this last?” For example, modern society is a profligate consumer of energy, most of which is supplied by fossil fuels: coal, oil, and natural gas. Fossil fuel supplies, though of vast and unknown size, are limited. How long can they last? What’s more, there is a strong scientific consensus that the carbon dioxide gas (also known as CO2) released by burning fossil fuels is affecting Earth’s climate, making it more unstable. How much more CO2 can we emit before climate instability becomes dangerous? These are big problems. Bright possibilities for addressing them include renewable energy sources like wind and solar. No doubt you have heard all of these things before—as well as many other news stories about “sustainability,” both positive and negative. The “Mathematics for Sustainability” course is built on three main ideas:

  1. Many of the key choices that humans face in the twenty-first century are rooted in sustainability questions. These include choices that we must make together, as citizens, as well as choices related to individual lifestyles.
  2. In a democracy, as many people as possible need to participate in well-informed discussion of these sustainability questions. They are too important to be left to “experts” alone.
  3. We may engage with sustainability questions from a wide variety of perspectives, including scientific, technological, political, artistic, ethical, and religious. For many of these discussions, we need some knowledge of mathematics in order to participate in a well-informed way.

Our primary goal as instructors of MATH 033 is to provide an environment where students gain the mathematical competency and confidence to apply to issues related to sustainable development (in the sense of the United Nations Sustainable Development Goals). We encourage students to see themselves as actors in a larger effort towards achieving various sustainable development goals, equipped with unique skills, experiences, and interests from which to approach these goals. As a dialogical course, MATH 033 challenges students to critically consider existing opinions from “experts” and attempt to answer questions on their own with careful mathematical reasoning, forming their own educated opinions. We admit as an instruction staff that we do not have all of the answers, and that it is our collective duty to develop solutions together.

Course content (coming from the course textbook) is sectioned into six themes: measure, flow, connectivity, change, risk, and decision-making. From a mathematical perspective, the course content is self-contained and ordered as to culminate on more controversial or uncertain topics which call for stronger mathematical and ethical competencies.

The following hyperlink contains Sample Problems from the course.

Course Format

The course currently runs as a “2 + 1 hybrid”, meaning 2 credits are designated as in-person instruction, while the remaining 1 credit is asynchronous online instruction. Online instruction consists of watching short, pre-recorded lecture videos and submitting short, accompanying quizzes.

The following hyperlink contains a Sample Syllabus from Fall 2023.

Students are randomly assigned groups of roughly 5 people which they maintain for the entirety of the semester. Groups work together on in-class activities, as well as on in-class tests. Students are graded individually for their work on these assessments.

We use our course blog for submitting longer forms of writing such as reflections on articles, research projects on sustainability, or any extra credit posts involving reflecting on an event or piece of media related to the course.

In particular, the weekly format for MATH 033 looks as follows:

  1. Pre-Recorded Video Lectures & Pre-Class Readings: For most in-person classes there will be 10-15 minutes of pre-recorded lectures and a reading to complete prior to the class session. Video lectures will introduce course content and present relevant examples. Readings will provide background for in-class discussion.
  2. Pre-Lecture Assignments (PLAs): Beginning in Week 2 there will be a PLA due by the morning of the class day. Each PLA is a short Canvas quiz on content from the video lectures and readings. These PLAs are part of the preparation for each in-class session.
  3. In-Class Activities: Class time will be a combination of working in groups on problems, mini-lectures introducing new concepts and reviewing examples, and group discussions on related topics. Active in-class participation determines part of your grade for the course.
  4. Weekly Writing Assignment: Most Writing Assignments involve reflective writing about a related reading. Some Writing Assignments will involve learning how to typeset mathematics on the blog, making quantitative estimates of energy use or greenhouse gas emissions, or learning to use a spreadsheet to make calculations and analyze data sets.

In addition to the above weekly components, there are other, less frequent forms of assessment:

  1. Chapter Tests: throughout the semester there will be 5 Chapter Tests reviewing material from the identified chapters of the textbook. The Chapter Tests are completed in-class. You are able to discuss problems and work with the other members of your group and you may use handouts from previous in-class activities.
  2. Final Writing Project: There is a Final Writing Project, due on Monday of the last week of classes. This assignment has several components spread over the second half of the semester (beginning in Week 7). You will propose and then write on a topic related to one of the Sustainable Development Goals (SDGs).

Course Materials

If you are an educator interested in seeing specific course material, please contact Russ deForest for access.

Course Sites

Students of the course use the following sites throughout the semester:

  • Most class resources and out-of-class assignments are posted on Canvas.
  • Many of the writing assignments will involve the course blog.
  • As a work-in-progress, we have been migrating many of the course’s lecture videos, quizzes, and other quantitative assignments to MyOpenMath. (Note: It is easy to port any content hosted on MyOpenMath to Canvas, meaning students do not have to leave Canvas in order to take such quizzes or watch the lecture videos).

Textbook

The (only) required course textbook is Mathematics for Sustainability, by J. Roe, R. deForest and S. Jamshidi.

  1. One may find a free electronic copy of the book through the Penn State Library (which requires authentication via Penn State WebAccess).
  2. To purchase a physical textbook is optional. Copies are available through the Penn State bookstore, from the publisher, and from other online retailers.

External Resources

  • Our course adopts an intersectional view of sustainability known as sustainable development. This sense of sustainability is exhibited famously by the United Nations Sustainable Development Goals, a list of 17 global goals towards achieving a more just, sustainable, and resilient world by the year 2030.
  • The MATH 033 teaching team likes to stress the importance of using credible sources. One of the best resources for a course about mathematics and sustainability is Our World in Data, a hub of data whose goal is to make existing knowledge on global problems accessible and understandable. This site is particularly great for analyzing progress on the United Nations Sustainable Development Goals.
  • As we practice conversions, re-expressing quantities in “human terms,” and understanding energy and emissions, we also steer students towards the EPA Greenhouse Gas Equivalencies Calculator. This site allows one to convert emissions or energy data to the equivalent amount of carbon dioxide (CO2) emissions from using that amount, with a good amount of flexibility for inputs and outputs.

My Contribution

I began my involvement with the MATH 033 course at Penn State in Spring 2020 as a first-year Graduate Teaching Assistant. Russ deForest served as my mentor as I observed his classes throughout the semester. I helped teach a few lectures and served as a Teaching Assistant during in-class activities. Amidst the ensuing pandemic and need to digitize the course, Russ and I worked together to record all lectures and post them as videos in the style of Khan Academy, broken-up by topic. We also were dissatisfied with the course’s level of engagement with ethical decision-making at the time. We had the idea to incorporate weekly case studies and reflections known as Writing Assignments. These assignments also bolstered the course’s commitment to writing and scientific communication. I designed the majority of the prompts, focusing on issues such as Geo-Engineering, Climate Refugeeism, and modern technological advancements in Transit and Policing.

We constantly update the course contents to be relevant and tailored to the backgrounds and interests of the students. My personal goal is to connect all of our lectures/mathematical concepts to recent news, and I aim to identify a human element with everything we do. I have procured a long list of “beginning-of-lecture topics” that I use to introduce new mathematical or ethical concepts. Previous examples include Celebrity Private-Jet Use, how Startups and Non-profits affect Sustainability, the recent Inflation Reduction Act, and more.

In total, I have taught MATH 033 as the principal instructor during Fall 2020 (one section), Fall 2021 (two sections), Fall 2022 (one section), and Fall 2023 (two sections), as well as mentored with Russ deForest’s section during Spring 2020.

I presented at the 2023 JMM Conference on Mathematics for Sustainability in January 2023 in a talk entitled: Quantitative and Ethical Reasoning in General Education Mathematics. Follow the hyperlinked text to find a portion of the presentation I gave on Tipping Points (mathematically: a value for a parameter to a system at which one or more possible equilibrium states of the system make discontinuous jumps in response to a small change in the parameter). Tipping Points are a growing worry for scientists as the world’s “parameters” rapidly change: might some of Earth’s systems respond with dramatic (i.e., discontinuous) changes to their equilibria? Might reversing these changes be harder than we realize? My talk illustrates an example of the weird logic of Tipping Points. 

I am very grateful for all of the opportunities teaching this course has brought me, and I appreciate all of the kind feedback given to me by previous students.

Bulletin Information

MATH 033: Mathematics for Sustainability is a 3-credit, undergraduate-level, General Education (GQ) course offered at Penn State University Park that satisfies multiple GenEd Learning Objectives: Effective Communication, Crit and Analytical Think, Key Literacies, and Soc Resp and Ethic Reason, as well as the Quantification requisite for a Bachelor of Arts. A composition course at the level of ENGL 15 is recommended but not required as a prerequisite, while High School Algebra or MATH 004 is also a prerequisite to MATH 033. However, MATH 033 does not serve as a prerequisite to any mathematics course, and thus should be treated as a terminal course.