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\chapter*{Preface}

As we near the end of the second decade of the 21st century, humans are grappling
with a number of tough decisions concerning our place in the natural world
and the consequences of how we have used various resources and impacted our
environment.  For instance,  we have continued to use fossil fuels to generate 
energy for our industries and transportation, with inevitable effects  
from the pollution they generate.  In particular, it is growing 
increasingly clear that human activity is causing 
long-term changes in the Earth's climate.  Are there realistic alternatives 
to those fuels that would sustainably provide for human society's
energy needs and have fewer harmful effects?  How do we decide
what alternatives make more sense?   

As a mathematically-literate
and thinking human being, I firmly believe that our ability to develop answers to 
such questions and to understand the political, economic and social issues involved 
depends on being able to deal in an informed way with
\emph{quantitative information}.  Mathematical models--equations of various 
sorts capturing relationships between variables involved in a complex situation--are 
fundamental for understanding the potential consequences of choices we make.  In 
the mathematical component of this course covered in these
notes, we will introduce a number of basic techniques for constructing models 
and see ways they can be applied to study environmental issues. 

More specifically, we will study the following topics:
\begin{enumerate}
\item  Basic techniques of measurement, data analysis, and presentation of 
data in numerical and graphical forms
\item  Functions and modeling -- we will see how to use 
linear, exponential, and power functions to describe different situations 
and how to select an appropriate model for a given situation
\item  Difference equations and modeling -- we will see how to set up
and solve difference equations that describe how systems evolve
over time (treating time in discrete units).  
\end{enumerate}
We will not make use of any calculus or mathematics more advanced 
than ideas about functions, graphs, algebra, some geometry, etc.
So everyone should have seen all the mathematical prerequisites and
some of the basic ideas behind material we study may be familiar 
from mathematics courses you took in high school.  What will probably
be different, though, is the consistently applied and environmental
focus of everything we do.

However, as you surely know, understanding the predictions of even the most
accurate and realistic mathematical models is \emph{not the whole story}, not 
by a long shot! 

Andrew Revkin made the following insightful and prescient observations 
in a 2011 blog post:  
\begin{quotation} 
There is not one climate dispute. 
There are two, and the solutions are not the same.  First, we need to separate 
the two. The science debate does not work in politics. If you study the conservative 
approach to climate change policy long enough, the implication that they are trying 
to participate in a scientific conversation starts to fade away\footnote{This is 
true even though they phrase their arguments as attempts to sow doubt in the 
minds of ordinary people about the overwhelming consensus that scientists have achieved 
using scientific language, ``alternative facts,'' and competing ``experts'' 
to muddy the waters.} and you realize the underlying logic they are using actually starts from the conclusion 
that regulation and government intervention are bad\footnote{For example, this was essentially
President Trump's argument for pulling the U.S. out of the Paris climate accords in June 
2017 because he claimed that the accords would lead to a loss of jobs in the U.S. economy
and a loss of independence for the U.S. in its decision-making on environmental
issues.} ... . This allows them to make big, bold, statements about their identity and 
character and values rather than wallowing around in overly-precise, overly-pedantic 
language and data.

The center-left in the U.S. has a persistent problem with this dynamic because they see 
every situation where they have a factual advantage as proof of their superiority and 
then they proceed to hammer people with logic while ignoring the repeated lessons 
of political strategy.  The debate needs to start with values! Science has no values. 
Science only describes the physical world.

To win the scientific debate about climate change, we just ... oh wait, we already did. 
But to win the political debate, we need to spend less time on the details of the scientific 
debate and much more on the underlying values--the costs to humanity, society, and the 
economy of extreme weather, local floods, local droughts, freshwater scarcity, infectious 
disease, food security, coastline loss, biodiversity loss, etc., etc. It sounds backwards 
since the political challengers are denying the possibility of those dangers, one might 
think we need to respond to their challenge.

We do not. That’s what science is for.
\end{quotation}

Some of these questions have been at the center of the political
polarization in the U.S. that has become more and more pronounced over
the last 20 years.   Check your views on science and policy, then ask yourself:  are you a 
communitarian or an individualist?  Are you a liberal, a conservative, or perhaps a 
libertarian?  While I have my own views about these questions (and you will
no doubt see what they are as we discuss them), \emph{I will never try to 
impose those views on you as students, or punish you, by means of grades,
or comments in class, or in any other way, for holding opinions
that go against mine.}  The goal of this class and these notes will be to help you 
examine your views, whatever they are, and see if they hold up to that
scrutiny.  If they do, you should also be able to give an account of 
your thinking and defend it with evidence and with eloquence.  

\aufm{John B. Little}

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