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\centerline{MONT 100N -- Modeling the Environment}
\centerline{Information on Final Exam}
\centerline{November 29, 2017}
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\noindent
{\it General Information and Groundrules}
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As announced in the course syllabus, the
final exam for our Montserrat seminar  will be given
at the announced time for MWF 9:00am classes:
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\centerline{\it Friday, December 15, 8:00am to 10:30am} 
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The exam will be held in O'Neil 123, {\it not our regular
class room}.
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\item{$\bullet$} This will be an individual exam.  No sharing of information 
in any form will be permitted during the exam.
\item{$\bullet$} You may use (and should use) a calculator during the exam,
but no other electronic devices.  {\it Know how to compute logarithm and 
exponential values} using your calculator in addition to basic arithmetic.  
\item{$\bullet$}  If you are well-prepared and work 
steadily, I expect the exam will take about 1 1/2 hours
(90 minutes) to complete.  However, you will have the
full 2 1/2 hour period (150 minutes) to work if you 
need that much time. 
\item{$\bullet$}  This will be a {\it comprehensive} exam.  The 
exam questions may cover concepts
and techniques from any section of the course (Chapters 1,2,3,4,5,7,8
in the Modeling the World textbook -- we did not cover the topics in
Chapter 6 yet).  But I will only ask about topics we have actively discussed in 
class, the problem sets, or the projects.   
\item{$\bullet$} There will be four or five mathematical
problems (each possibly with a few separate parts).  These
questions will be similar to things you have seen on the
problem sets or the group projects.
Some sample exam questions are given later in this document.
I will post solutions for those in a few days -- my recommendation
is to try working out solutions first on your own, then use
the solutions to check your work.  
\item{$\bullet$}  The exam will also include an essay question 
(worth about 1/3 of the total points) on one of the set topics below.  It should
take you between 30 and 45 minutes to produce a good, detailed
answer for that question.  So it will be necessary to spend
a sufficient portion of your preparation time on deciding what you want 
to say.
\item{$\bullet$} I will be available during the reading period
at the following times for ``last minute'' questions:
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\item{$\bullet$} Monday, December 11, 3:00pm - 4:45pm
\item{$\bullet$} Tuesday, December 12, 8:00am - 12:00noon
\item{$\bullet$} Thursday, December 14, 8:00am - 10:00am
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{\it Essay Topics -- You will have the choice of answering either one of the
following prompts -- I will include both in the exam sheets; you choose
which one you want to address.}
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\item{\it Topic A} 
In general terms, what is a mathematical model?  
Describe in general terms what they are, 
how they are constructed, and how they are used.  Give examples of two 
different types of mathematical models we have studied in this course.  
Even if mathematical models don't capture every feature of a real world
situation, why is it still important to develop them and understand the
information we get from them?  As an example, why is it important to understand 
how radioactive substances decay?  What types of models that we discussed would 
apply to describe that process?  What are three of the main issues discussed 
in the film {\it Containment} that we saw with the rest of the Natural World Cluster?
How do those issues connect with other topics we discussed semester like the
properties of different sources of energy used in the U.S. and their 
effects on the environment?  How are mathematical models important in
understanding our choices of which energy sources to use?
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\item{\it Topic B} 
What does Jared Diamond mean by a ``collapse'' in his book with
that name?  Discuss the five-point framework for understanding
causes of collapses that Diamond lays out in the Prologue.  
Which of those factors does he say are {\it always} present?  
Discuss how the framework applies to {\it either} the collapse 
of the Easter Island civilization or the Classic Maya civilization
in Central America.  ``The past is a foreign country; they do things 
differently there,'' is the famous opening line of a novel called 
{\it The Go-Between} by L. P. Hartley.  How does Diamond's point of view 
in {\it Collapse} relate to that attitude about the past?  For instance, 
would he say the past is not really that foreign after all,
or would he argue that there is some key difference that sets us apart 
from previous civilizations and lessens the causes for concern about
our ultimate fate?  What do {\it you} think about this question, after having
read several sections of {\it Collapse}?
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\noindent
{\it Sample Mathematical Questions}
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\noindent
Full solutions for all of these will be posted later so you can check your
work.
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\item{1)} Chapter 1/5, 11, 14  (Note: the conversion factors you need
are given in the text. I will supply any information like that you would need
for questions like these ones.)
\item{2)} Chapter 2/2, 7
\item{3)} Chapter 4/6, 8, 9  
\item{4)} Chapter 5/2, 4, 6, 7, 8, 9
\item{5)}  Chapter 7/1, 4 (know the general solution for affine first-order
difference equations and how to determine equilibrium solutions algebraically; 
I will not give you that formula), 13 -- sketch
the solutions by hand in rough, qualitative terms for (ii)
\item{6)}  Chapter 8/6, 8 (only parts (a) and (b) would be suitable
for an exam question, though!), 11
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{\it Note:}  I could also ask you ``qualitative'' 
questions relative to the process of fitting a linear or exponential
model to data like one of the questions from the midterm, including
questions about the process of transforming the data via logarithms
for the exponential cases.
I {\it can't really} ask you to compute a regression equation
for fitting a linear or exponential model to data,
of course, since apart from one simple linear example, we only did 
those computations with Excel.)  I could give you the equation of
a regression line, though, and ask you to give a model prediction
for an $x$-value not occurring in the data.  
\bye
