DIMACS Center, CoRE Building, Rutgers University, Piscataway, NJ

**Organizers:****Midge Cozzens**, DIMACS, midgec at dimacs.rutgers.edu**Eugene Fiorini**, DIMACS, gfiorini at dimacs.rutgers.edu**Fred Roberts**, DIMACS, froberts at dimacs.rutgers.edu**Mary Lou Zeeman**, Bowdoin College and the Mathematics and Climate Research Network (MCRN)

If you are interested in beta-testing any of the modules described below, please contact Eugene Fiorini (gfiorini at dimacs.rutgers.edu) at DIMACS.

**Title**: Carbon Footprint: A Study of Unit and Dimensions

**Authors**: Laura Foster, Rikki Wagstrom, Jean McGivney-Burelle

**Module Summary**: This module integrates the context of carbon emission and human consumption 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.

**Target Audience**: Precalculus courses including algebra

**Prerequisite Math**: Scientific notation, metric system

**Applications**: Environmental Awareness, Climate Science

**Title**: Measuring the Health of the Earth Using the Theory of Island Biogeography

**Authors**: Jana Eggleston, Farshid Ahrestani, Holly Gaff

**Module Summary**: Biodiversity has been shown to be a good measure of the health of the planet system (McGrady-Steed et al. 1997). The more species and genetic diversity, the more stable the ecosystem (Butchart et al. 2010). Sustainability of the planet needs this diversity to withstand stresses from changing weather patterns, disease and human population growth (Heller and Zavaleta 2009). Island biogeography is the study of the factors affecting species diversity of natural communities. As our natural landscape is becoming more and more fragmented, it resembles a series of islands. This module uses a variety of available datasets 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 the like. Finally, the plots are used to estimate the level of fragmentation that would push the system to a given level of species loss.

**Target Audience**: Math for Liberal Studies, College Algebra, Math Modeling Courses
Introductory Biology, Earth Science, Oceanography, and Geophysical Laboratories

**Prerequisite Math**: Basic plotting skills, slope-intercept line formula, and summation notation

**Applications**: This module addresses the factors affecting species diversity of resultant communities.

**Title**: Percolation of the Emerald Ash Borer

**Authors**: Nate Shank, Laurie Heyer, Gwen Spencer

**Module Summary**: This module explores the probabilistic spread of the Emerald Ash Borer (an invasive species) through a series of stylized landscapes.

**Target Audience**: The ecological motivation, description of percolation and subsequent proofs would be an appropriate lesson for an advanced undergrad probability class. The ecological motivation, description of basic math background, description of percolation, and simulation component would be an appropriate lesson for an earlier course, or for a general course on quantitative methods in ecology

**Prerequisite Math**:

**Applications**: Invasive species threaten local ecology as well as renewable economic resources systems (in this case, the timber industry). Local species may be over-consumed or out-competed for food sources: extinctions result in gaps that destabilize greater ecological processes.

**Title**: Exploring Corn Land Use for U.S. Ethanol Production/Consumption

**Authors**: Guadalupe Lozano,

**Module Summary**: This module studies historical trends in the use of corn land for ethanol production/consumption by constructing and interpreting functions built from datasets. Linear and exponential functions and their relationships are explored in terms of predicting future land use for the production of ethanol.

**Target Audience**: Precalculus courses including algebra

**Prerequisite Math**: Basic function properties and plotting skills

**Applications**: Environmental Awareness

**Title**: Smart Driving

**Authors**: Benedetto Piccoli, Eugene Fiorini

**Module Summary**: The impact of pollution produced by vehicular traffic is one of the most important factors affecting public health. The phenomenon is of particular importance on metropolis of most countries worldwide. According to the 2009 Annual Energy Review of the U.S. Energy Information Administration the share of energy used to transportation amounts to 27%. On the other side, new technologies for info-mobility provide consistent sources of data on traffic load for most urban areas. The module focuses on choosing the "least 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.

**Target Audience**: Math students following calculus, a discrete math, optimization or even computer science. For advanced part optimization, operational research or graph theory course.

**Prerequisite Math**: Precalculus. For the advanced part optimal paths over graphs.

**Applications**: The results of the module will be ways of computing "greenest" paths. If applied on large scales this would substantially contribute to reduction of pollution due to transportation.

**Title**: Sex Change (Intersex) Modified by a Herbicide (Atrazine)

**Authors**: Kimberly Hunter, Steve Greenfield, Renee Moore

**Module Summary**: Atrazine is a herbicide that has been widely used in the United States for over 50 years. Laboratory studies have shown that atrazine may cause sex change in male frogs and fishes. This module examines the relationship between atrazine levels in the blood of largemouth bass fish and the percentage of bass with intersex (combination of male and female reproductive structures). Secondly, the module examines whether atrazine load (amount of atrazine applied per unit area) is associated with detectable levels of atrazine in the water.

**Target Audience**: Introductory statistics (no calculus necessary)

**Prerequisite Math**: High School Algebra

**Applications**: Biology, Environmental Studies, Ecology

**Title**: Earth's Energy Balance

**Authors**: Hans Kaper, Dan Flath, Esther Widiasih

**Module Summary**: The Earth's climate system is a complex system. It has many components ? the atmosphere, oceans, lakes and other bodies of water, snow and ice, land surface, all living things, and so on. The components interact and influence each other in ways that we don't always understand, so it is difficult to see how the system as a whole evolves, let alone why it evolves the way it does. Sometimes we can build a physical model of the system ? for example, an aquarium to study the behavior of a school of fish, or a social network to study human behavior. In climate this is not possible; we have only one Earth, and we cannot perform a real-life experiment. (Remember that climate refers to large regions and long time spans.) But we can study the climate system using mathematical models. This module develops models that are used to explore the effects of greenhouse gases on earth's climate, including comparisons with different planets.

**Target Audience**: Precalculus

**Prerequisite Math**: A thorough understanding of functions and their properties

**Applications**: Climate Analysis

Additional modules are under construction and their summaries will be posted soon:

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Document last modified on January 5, 2012.