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\centerline{MONT 102N -- Modeling the Environment}
\centerline{Information on Final Exam}
\centerline{December 1, 2011}
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{\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 Wednesday, December 14, 8:00am to 10:30am} 
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I will see about obtaining the small classroom SW 330 (the 
room where we did the midterm) for our use that day.    
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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 a calculator during the exam,
but no other electronic devices.
\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 more time.  
\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, and may cover concepts
and techniques from any section of the course.  In other 
words, this will be a {\it comprehensive} exam.  
Some sample exam questions are given later in this document.
\item{$\bullet$}  The exam will also include an essay question 
(worth about 1/3 of the total points) on a set topic chosen
from the topics listed below.  It should
take you between 30 and 45 minutes to produce a good, detailed
answer for one of these questions.  So it will be necessary to spend
a sufficient portion of your preparation time on deciding what you want 
to say for each topic.
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\noindent
{\it Review Session}
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If there is interest, I would be happy to run a review
session for the final.  If we do it in the evening
either Sunday, December 11 or Monday, December 12, we 
might start with a class dinner in the Mulledy social 
space.  
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\noindent
{\it Possible Essay Topics}
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\item{1.}    What are the major reservoirs of carbon in the Earth's
short-term carbon cycle?  What are the major flows (``fluxes'') 
of carbon between those reservoirs?  Describe them in 
words and via a diagram.  In our final group project, we
looked at a simple model of this system.  
What features of the real world carbon cycle did that model 
include?  What are three possibly important features of the 
real world carbon cycle that were left out?    
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\item{2.}   Why do we try to build mathematical models of aspects 
of the real world at all?  Can {\it any} mathematical model be a 
completely accurate representation of some aspect of the natural world?  
As an example, why do scientists think it is important to 
understand how much $CO_2$ is present in the atmosphere?  What
tends to happen when $CO_2$ levels rise?  
Describe a key piece of evidence that suggests human activities might 
have changed atmospheric $CO_2$ levels over the past 50-200 years. 
Explain the case for saying the evidence points to that conclusion,
and relate your answer to the results of modeling 
exercises we did in this class.  
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\item{3.}   Suppose someone expresses the following 
opinion:  ``Atmospheric $CO_2$ levels were much higher at some points in 
the distant past and we're here now, aren't we?  What is there to worry 
about?   Even if our fossil fuel burning does put $CO_2$ into the 
atmosphere, the Earth will adapt to it.  And besides, we need to use
fossil fuels to maintain our economic growth.''  First, is what this
person is saying in the first sentence factually correct?  How do
we know?  Second, do you agree with the ``what is there to worry 
about?'' part?  If you don't agree, explain -- are there  
important things that this person is leaving out or overlooking?   
Try to relate your answer to results of modeling exercises we did 
in this class.  If do agree, also explain making reference to topics we
discussed in class.    
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{\it Sample Mathematical Questions}
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\noindent
Answers for all of these are given in the back of the book, so
you can check your work:
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\item{1)} Chapter 1/17, 19 (Note: the conversion factor you need for 
19 is given on page 329(!) I will supply any information you would need
for qeustions like these ones.)
\item{2)} Chapter 2/5,7,19,25 (Note: in 5, ``normalized'' means compute the 
$CO_2$ output per $10^{12}$ BTU produced)
\item{3)} Chapter 3/3,9,17,19 (Note: for 17, see example on pages 58 and 59)
\item{4)} Chapter 4/5, 15 
\item{5)}  Chapter 5/3,7,11abcf
\item{6)}  Chapter 6/5a, 7
\item{7)}  Chapter 7/7, 9
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{\it Note:}  I could also ask you ``qualitative'' 
questions relative to the process of fitting a linear, exponential,
or power law model like some of the questions from the midterm, including
questions about the process of transforming the data via logarithms
for the exponential and power law cases.
I {\it can't} ask you to compute a regression equation
for linear, exponential, or power law model fitting
of course, since we only did those with Excel.)
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