\documentclass[11pt]{article}
\def\Z{\mathbb{Z}}
\def\Q{\mathbb{Q}}
\def\R{\mathbb{R}}
\def\C{\mathbb{C}}
\usepackage{latexsym,amsmath,amssymb}
\usepackage[all]{xy}
\newenvironment{packed_enum}{
\begin{enumerate}
  \setlength{\itemsep}{1pt}
  \setlength{\parskip}{0pt}
  \setlength{\parsep}{0pt}
}{\end{enumerate}}
\newenvironment{packed_item}{
\begin{itemize}
  \setlength{\itemsep}{1pt}
  \setlength{\parskip}{0pt}
  \setlength{\parsep}{0pt}
}{\end{itemize}}
\setlength{\textwidth}{6.5in}
\setlength{\oddsidemargin}{0in}
\setlength{\textheight}{9.0in}
\setlength{\topmargin}{-0.5in}
\begin{document}
\centerline{Montserrat 101N -- Analyzing Environmental Data}
\centerline{Information on Midterm Projects}
\centerline{January 16, 2018}
\vskip 10pt
\noindent
{\it General Information}
\vskip 10pt
One of the larger assignments for our seminar this semester will be 
a group project leading to 
\begin{packed_item}
\item an \emph{oral presentation} to the assembled Natural World Cluster
(to be given the evening of Monday, March 12 in Rehm Library), and
\item a \emph{follow-up paper}, due Friday, March 23.
\end{packed_item}
Students in all of the Montserrat seminars will be doing oral presentations 
this spring.  The faculty teaching the other Natural World
seminars this year have expressed a strong interest in hearing, and 
having their students hear, what our seminar
has been doing this year.  As you might know from talking
to students in the other seminars, we are all approaching the 
natural world from very different directions and from the points of view
of different areas of human knowledge.  So as our seminar's assignment
of this type, we will be working on putting together
a program of presentations around the general theme of \emph{mathematical
modeling}, with examples showing the sorts of insights the quantitative, ``systems,'' 
and other mathematical techniques we have been studying can give into various questions.  
\vskip 10pt
\noindent
{\it The Oral Presentations}
\vskip 10pt
\begin{packed_item}
\item There will be 5 groups (two with 4 members and three with 3)
We will discuss the process of forming the groups and choosing the 
topics for the presentations (see below) in class.  \emph{All groups
must be determined and topics chosen by Friday, February 2, at
the latest.}
\item Each group will be responsible for about 10 - 12 minutes of
the program.  Each member of each group will give roughly equal parts 
of the group's presentation (about 3 minutes) and part of your grade will reflect how 
well-prepared you are and how successfully you communicate the ideas
in your presentation.\footnote{If you believe you have a disability
that prevents you from participating in this sort of presentation,
you should contact the Disability Services Office, have them verify
this and contact me as soon as possible so that we can work out an
alternate way to meet this course requirement.}
\item The groups will want to use PowerPoint to prepare slides
for the presentations and we will prepare carefully in class so
that you are comfortable presenting somewhat technical material to 
a large audience.  
\item Make no mistake -- this is going to be challenging.  You
will need to focus on just the right information to convey to
get the points you want to make across in a (very) limited amount 
of time.  It's going to take a lot of preliminary work and practice
for this not to seem a bit terrifying(!)  But being comfortable with
speaking in public this way is a very valuable skill to have 
in many different walks of life and that is part of the reason
for this assignment and the Montserrat focus on this skill this year!
\end{packed_item}
\vskip 10pt
\noindent
{\it Possible Topics for the Oral Presentations and Papers}
\vskip 10pt
\begin{packed_enum}
\item[(1)] {\it Mathematical modeling in general, exponential models, an
important application} -- In the presentation, you would start with
a general discussion of the questions: Just what is a \emph{mathematical model} and
how are they developed? Illustrate this with an exponential model for radioactive decay
and discuss \emph{radiocarbon dating} using the isotope $C^{14}$ (Carbon-14).  
For the paper, you would then go into much more detail about how this idea was developed,
how it is used in practice, what variants and related methods people use to estimate
the ages of organic and non-organic materials, and so forth.  
\item[(2)] {\it The ``systems'' perspective} -- For the presentation, you would 
begin by introducing the concept of balancing and reinforcing feedback loops
in systems along the lines suggested by Donella Matthews in Chapter 1 of \emph{Thinking in Systems}.
Give some everyday examples like the ones discussed there, then formulate 
quantitative versions as difference equations and discuss their properties.  
For the paper, you would go into more detail about these models and the 
effect of \emph{delays}.  Develop models that exhibit
the sorts of oscillations Matthews describes in her Chapter 2.  
\item[(3)] {\it Exponential and logistic population models} -- In the presentation, 
you would introduce exponential and logistic population models as difference equations
for the population function $Q(n)$, with $n$ the discrete time.  For the paper, you 
would go on to discuss other discrete time population models such as the \emph{Gompertz}
models, that do not have some of the problematic aspects of the logistic model from 
the biological point of view.  
\item[(4)] {\it Systems of difference equations and epidemic models} -- In the 
presentation, you would introduce the SIR model we studied last semester and 
indicate how it describes a certain class of infectious disease outbreaks.  For the 
paper, you would then go on and study how the SIR model can be modified to take
other aspects of infectious diseases and public health interventions into account.  For instance,
how can models like this help plan public health measures such as vaccination campaigns,
quarantines, etc.?
\item[(5)] {\it Modeling extraction of nonrenewable resources} -- For this
presentation (which is more challenging because it's one of the less 
familiar ones for us as of the start of the semester), 
you would discuss the models for the economic systems
governing extraction of non-renewable resources like coal or oil -- see
the discussion on pages 60 - 66 of \emph{Thinking in Systems}.   Formulate
the models using the ideas for difference equations that we have discussed
and discuss the behavior of the solutions.  The paper would then be devoted
to a more detailed discussion of these topics.  
\item[(6)] {\it Modeling harvesting of renewable resources} -- In the Chapter
7 project from last semester, we discussed the effect of various 
harvesting strategies on natural resources such as fisheries.  We were essentially
looking at this ``from the fishes' point of view'' without taking into account
the economic factors that would drive people to change their harvesting 
strategies over time.  For this project presentation (which is also more challenging 
because it's one of the less familiar ones for us as of the start of the semester), 
you would discuss the models for the economic systems
governing harvesting of renewable resources -- see
the discussion on pages 66 - 72 of \emph{Thinking in Systems}.   Formulate
the models using the ideas for difference equations that we have discussed
and discuss the behavior of the solutions.  The paper would then be devoted
to a more detailed discussion of these topics.  
\item[(7)]  {\it A topic of your own} -- I am also open to considering a topic
that your group would specify and carry out with my guidance.  If you want
to try this, you will need to present a proposal and get my approval for 
your topic \emph{no later than Friday, February 2}.
\end{packed_enum}
\end{document}
