Math and the environment; these two subjects don’t normally get mentioned in the same sentence. For our purposes here, they will be more specifically the fields of applied mathematics and environmental sustainability. The definition for environmental sustainability is: “policies and strategies that meet society’s present needs without compromising the ability of future generations to meet their own needs.”(What is…), While applied mathematics is “a branch of mathematics that concerns itself with the application of mathematical knowledge to other domains.” (Applied…). There are many applications, here at Ohio University, including statistics, numerical analysis, real and complex analysis, Fourier analysis, linear and nonlinear programming, ordinary and partial differential equations, dynamical systems, algebraic coding theory, bioinformatics, social sciences, and optimization. Most of these have little or nothing to do with the environment, but there are a few that have subtle, yet significant links to how we view our environment. The fields of, differential equations, statistics, and dynamical systems (physics/engineering all encompass some part of environmental sustainability.
The first field of application is in differential equation
s. The primary component that is taught in a differential equations class is that differential equations are just equations with derivatives in them and a derivative is a function in calculus that measures change; very similar to slope. According to Professor Winfried Just, these equations have many uses, one of them being to show the limits of resources for a population with the positive growth model dp/dt = kp(m-p) with “k” being a constant, “p” being the population, “dp” is the derivative or change in “p”, and “m” being the carrying capacity of the environment where the population exists. We can use this model to determine where the system is stable (sustainable) or unstable. The model can also be used to determine the limit to the sustainability of both the population and the resource consumption. The point after this limit is where the system becomes “extinct”, which is rather fitting when dealing with the environment considering that is the term used for a species or resource that runs out in the environment. However, this useful equation would not be possible if there weren’t mathematicians working on the statistics to plug into it.
The field of statistics is the most obvious mathematical contribution to the pursuit of environmental sustainability. According to Webster, Statistics is “a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data”. Not only is stats the most prevalent use of mathematics in the environment, but it is also the most useful. Most people either don’t understand the complexities of the energy systems being created by engineers or how researchers can determine the sustainability level of an ecosystem, but anyone can understand a basic statistic if it is thrown at them. Environmental activist such as Al Gore, use points such as “400,000 miles (roughly the size of Texas) of arctic ice have melted over the past 30 years” (Global…). Another way statisticians can use the average yearly temperature to predict what the temperature will be in the future or they can just note the difference between time periods. According to NASA, the average global surface temperature has increased one degree Fahrenheit, which may not seem like much, but in colder climates, that can mean the difference between ice and water. These statistics can be used for many purposes; including public relations, awareness, and the furthering of more research. 
A great example of how collected data has affected the research towards environmental sustainability is the UN’s Environmental Sustainability Index (ESI). This index is “a composite measure that can summarize environmental performance along multiple axes and that can aid decision makers in choosing the best policies for both the environment and the economy” (The Pilot…). The index is based off of five systems; environmental systems, environmental stresses, human vulnerability to environmental impacts, social & institutional capacity, and global stewardship, which are in turn broken down to a set of 65 variables and 21 factors that need to be put into the system. Some examples are air quality, water quality, and waste production. All these factors end in a score for each country that varies from 0-100, with zero being low sustainability and 100 being highly sustainable with the United States scoring a 53 in 2005 (45th best in the world). One of the most important contributors to this project was reliable data sets and they were analyzed through an understanding of statistics.
One of the most common links between math and other professions is workers’ fundamental understanding of statistics. Another link between math and other professions is in the field of engineering. The core of theoretical physics and engineering is math. It takes a reasonable understanding of a moderate level of mathematics to learn and apply the concepts of those fields. Trace Lydick, a mechanical engineering major here at OU, once stated says “engineering majors should just minor in math because they have to take so many math classes”. Engineers have gone on to make some of the greatest contributions to sustaining our environment. They are coming up with more and more renewable and efficient energy systems with the goal of creating less on an impact on the environment. From wind energy to solar energy, hydrogen cells to tidal currents, engineers are using math along with other skills to help improve how we interact with our environment.
One of the newest and most renewable sources of energy that engineers are working on is tidal energy. This is the process of harnessing the power of both waves and the tides of the oceans to create energy. The UK’s Carbon Trust reasons that "Wave and tidal stream energy has the potential to generate about 15% - 20% of the UK’s electricity.", and this is just using the coastline around the UK. The equation that governs the estimated amount of energy that a wave would produce is ”P=[(pg^2)/(64π)] (Hm0^2)T ≈ (0.5kW/m^3 x s)(Hm0^2)T" with P the wave energy flux per unit of wave-crest length, Hm0 the significant wave height, T the wave period, ρ the water density and g the acceleration of gravity” (Wave…). Because this is a relatively new source of energy has yet to be perfected, but through research and the help of mathematicians using the techniques of optimization, researchers are continuously improving the energy systems used to harness the power of the waves. Some companies such as AETI are now implementing the wind turbine principle and putting it into their wave turbines to increase the energy output of the systems. And with “85% of our energy coming from fossil fuels” (coal, oil, and natural gas), which are a nonrenewable resources, it is very important that we start to use more renewable resources before the fossil fuels run out. 
A wave generator (c-pearce.co.uk )
Even if it is not immediately obvious, there are multiple aspects of math that are used in environmental sustainability and most can be found in the field of applied mathematics. In fact, math is an important part to many things in life, and even though it is often overlooked for its sustainable applications, it is used by people all around the world to help sustain the place that we call home. So no matter how boring or difficult the subject may be, it still remains one of the most important subjects for an individual and for our planet.
“What is Sustainability?”, Basic Info , EPA, 11/17/2010, http://epa.gov/sustainability/basicinfo.htm, 14 Feb 2011
“Applied Mathematics: Definition” , Word IQ, http://www.wordiq.com/definition/Applied_mathematics, 14 Feb 2011
“What is Mathematics- Aplied Track?” OHIO Bachelor of Science in Mathematics—Applied Track, Ohio University , http://www.math.ohiou.edu/programs/undergraduate/Math%20Major%20Applied%20OU.pdf 14 Feb 2011
Notes from Dr. Winfried Just’s Differential Equations class Spring Quarter 2010
“Statistics” Merriam-Webster 2011 http://www.merriam-webster.com/dictionary/statistics 14 Feb 2011 14 Feb 2011
“The Pilot Environmental Sustainability Index”, ENVSTATS, Alex de Sherbinin and Marc A. Levy, Jan 2000, http://unstats.un.org/unsd/ENVIRONMENT/issue8.htm 14 Feb 2011
“Wave and Tidal Energy” , Bio Power Systems, 2011 http://www.biopowersystems.com/market.html Feb 15 2011
“Hydro, Wave, and Tidal” AETI, 2010 http://www.aeti.com/hydro-wave-tidal 15 Feb 2011
“Renewable Energy” Sokol Sota, http://www.greenscreen.org/articles_sr/Energy/Renewable%20Energy/Renewable%20Energy%20-%20Sr.pdf
Feb 15 2011
“Global Warming by the Numbers”, EDF, 2010, http://www.edf.org/article.cfm?contentID=4981 17 Feb 2011
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