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\centerline{MONT 104N -- Modeling the Environment}
\centerline{Information on Final Exam}
\centerline{December 1, 2012}
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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 Thursday, December 13, 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 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 through 9
in the Langkamp-Hull textbook).  But I will only ask about topics we have actively discussed in 
class -- for instance, we have not talked about ``chaotic'' solutions
of logistic difference equations (yet!)).   
\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.
\item{$\bullet$}  The exam will also include an essay question 
(worth about 1/3 of the total points) on the set topic 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.
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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 Monday, December 10 or Tuesday, December 11, we 
might start with a class dinner in the Mulledy social 
space.  
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{\it Essay Topic}
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In general terms, what is a mathematical model?  Describe 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.  
Next, {\it why} do we try to build mathematical models of aspects 
of the real world?  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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\noindent
{\it Sample Mathematical Questions}
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\noindent
Answers for all of these are given in the back of our Langkamp-Hull textbook, 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
\item{8)}  Chapter 8/3, 11
\item{9)}  Chapter 9/1a and new part b:  Give a rough hand sketch of what the solution with $p(0) = 30$
would look like, 15.
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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 apart from one simple linear example, we only did those with Excel.)
\bye
