One-Day Sustainability Modules
for Undergraduate Mathematics Classes






Each module targets specific mathematics classes. It introduces a specific planet Earth topic, challenges students to engage in a discussion about the topic, and presents a content-specific mathematical application. Problems, possible projects, and references for further study complete the one page module. A summary of the modules follows:

Module: Measuring the Health of the Earth Using Island Biogeography.
This module is appropriate for Math for Liberal Studies, College Algebra, and Basic Math Modeling courses.

Authors: Jana Eggleston, Farshid Ahrestani, Holly Gaff
Module Summary: This module uses a variety of available data sets to explore methods of calculating biodiversity and measuring landscape as well as the relationship between those. These points are then used to teach logarithms by estimating slopes and intercepts from a log-log plot of the number of species in a given location against a variety of metrics including island size and distance from mainland. Optionally, this could then be adapted to fragmented habitats near a national park or some similar region. Finally, the plots are used to estimate the level of fragmentation that would push the system to a given level of species loss.


Module: Percolation.
This module is appropriate for Discrete Mathematics courses (covers some probability and graph theory).

Supporting excel files with samples:BondPerc.xlsx and SitePercolationExample.xls

Authors: Nathan Shank, Laurie Heyer, Gwen Spencer
Module Summary: This module explores the probabilistic spread of the Emerald Ash Borer (invasive species) through a series of stylized landscapes. The introduction of non-native species can cause imbalance in the environment: if the new species finds a good food source and has no natural predators, its number can explode. There are many examples where this explosion of population causes major problems including driving local species to extinction either through over-consumption or through direct competition for resources.


Module: Carbon Footprint: A Study of Unit and Dimensions.
This module is appropriate for College Algebra and Math for Liberal Studies.

Authors: Laura Foster, Rikki Wagstrom, Jean McGivney-Burelle
Module Summary:
In this module, the context of carbon emission and human consumption are integrated into an introductory lesson on units and estimation.  Background information is provided to familiarize students with the science of carbon emissions as well as greenhouse gas effects on mean global temperatures.

Module: Smart Driving: Reducing Emissions by Choosing "Greenest" Path.
Teacher version Student version
This module is appropriate for Calculus I and II, Discrete Mathematics; additional materials in appendix are suitable for graph theory course and operational research.

Authors: Eugene Fiorini and Benedetto Piccoli
Module Summary:
The impact of pollution produced by vehicular traffic is one of the most important factors affecting public health. According to an article published by R. J. Laumbach and H. M. Kipen in the Annals of the New York Academy of Sciences, epidemiological studies -Y-A4have linked exposure to traffic-related air pollutants to increased respiratory and cardiovascular morbidity and mortality.! The phenomenon is of particular importance in metropolitan areas worldwide. Transportation is also a major consumer of energy. Advances in new technologies for info-mobility provide consistent sources of data on traffic load for most urban areas. It is possible to take advantage of these advances in info-mobility in order to improve the efficiency of energy usage by transportation. This module focuses on choosing the 4least polluting! path when driving from a given starting position A to a given arrival position B. Students may use data available on the web to estimate the pollution effect.


Module: Statistical Exploration of Climate Data
Teacher version Student version
This module is appropriate for introductory statistics classes.

Supporting files:
Module figures for teacher presentation
Data Sets
Fairbanks.dat.txt  getDIMACSdata.sh.txt  McGuireAFB.dat.txt  NewOrleans.dat.txt  Raleigh.dat.txt

Authors: Tamra Carpenter, Robert Vanderbei, Jon Kettenring
Module Summary:
In this module the students will learn some basic concepts in statistical thinking about data, with emphasis on exploratory data analysis. The module will analyze daily temperature data collected over 55 years at a single location. The analysis explores the question, 4Is there any observable temperature trend over this time period at this location?! The challenge is to see a potentially small change within a data set that has both seasonal variability and high daily variability. Basic plots are done to help the students view data in different ways, introduce methods for removing seasonality, and use averaging to reduce day-to-day variability. This module might be viewed as a 4case study! in data analysis. It will give students a taste of what it-F"s like to do -Y4real world! data analysis. Students will work with a large noisy data set and look at it in different ways to try to answer a specific question.


Module: Draft version: Energy Balance Models
This module is appropriate for Calculus and Differential Equations courses.

Authors: Daniel Flath, Hans G. Kaper, Frank Wattenberg, Esther Widiasih
Module Summary: This module introduces the student to the process of mathematical modeling. It shows how the process starts in the 4real world! with a physical system and some observations or an experiment. In a zero-dimensional energy balance model, the Earth's climate system is described in terms of a single variable, namely the temperature of the Earth's surface averaged over the entire globe. In general, this variable varies with time; its time evolution is governed by the amount of energy coming in from the Sun (in the form of ultraviolet radiation) and the amount of energy leaving the Earth (in the form of infrared radiation). The mathematical challenge is to find expressions for the incoming and outgoing energy that are consistent with the observed current state of the climate system, and then use the resulting energy balance model to see whether the climate system admits other equilibrium states and, if so, how a transition from one equilibrium state to another could be triggered. The module includes descriptions of several simple experiments that illustrate various concepts used in the discussion.

Module: How Fuel Efficient Can Cars Possibly Be?
Teacher version      Student version
This would be appropriate for pre-calculus and college algebra courses.

Authors: Darakhshan Mir, Vijay Ravikumar, Aatish Bhatia
Module Summary: Quantifying energy consuption is central to any discussion on sustainability. Students will develop models that explore energy dynamics of cars in order to determine how much energy is necessarily required to power automobile transport independent of future advancements in technology. The models are then studied to explore questions about how behavior could be modified to improvefuel efficiency in ways that support sustainability.

Module: Crop Rotation Scheduling Using Discrete Mathematics
This would be appropriate for discrete mathematics and basic math modeling courses.

Supporting files: CRSpacket.pdf

Authors: Victoria Ferguson-Kramer, Kellen Myers, Yekaterina Voskoboynik
Module Summary: The production of crops is essential to human life. Producing these crops, however, comes with it a cost to the environment. The commonly used agricultural techniques in place in the United States rely on machinery and chemicals in order to keep up with the demand. However, over time, these methods strip the soil of nutrients which in turn require added inputs to produce the crops in the first place. In order to continue to produce crops at current levels of need and, by extension, to increase production, methods to counter these deficiencies must be utilized. One of these methods, used in both organic and 4conventional" agriculture, is that of crop rotation. Crop rotation may be as simple as the current corn/bean rotation in the conventional system, or more elegantly implemented with organic techniques such as intercropping, 4green manure,! and 4catch cropping.! Certain crops have characteristics which lend themselves to rotation. These crops are then rotated with crops which provide income or fodder for animals. However, the creation of a rotational schedule over a plot of subdivided land is a challenge which faces the agriculturist in planning the most efficient use of land so that demand is met, soils are sustained, and economic impact is reduced when leaving land off of a 4production schedule.! The module develops discrete mathematics models that allow for creation of schedules meeting a variety of needs.