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\centerline{MONT 109N -- Mathematics Across Cultures}
\centerline{Information for Midterm Exam}
\centerline{March 16, 2011}
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{\it General Information}
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The first midterm exam will be given in class on Friday, March
25 (this is a week later than originally announced).  
It will cover the mathematical and cultural/historical material we have studied
since the start of the semester.  There will probably be some questions dealing
with aspects of the material we discussed from {\it Collapse}.  
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This means in particular
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\item{1.}  ``Modular arithmetic'' and applications to questions about calendrical cycles 
(as in Problem Set 2).
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\item{2.}  The Classic Mayan number and calendar systems (see Problem Sets 1 and 2).
Note:  For questions about computations within the Sacred Round and Vague Year
calendars, I would give you the lists of ``month'' names in order to use.
There is no need to memorize them.  
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\item{3.}  Ideas about maps, models, ways of representing information (Marshall Islands
``stick charts'' as a key example).
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\item{4.}  How societies can choose to succeed or fail ({\it Collapse}); the
examples of the Easter Islanders; Mangareva, Pitcairn and Henderson Islands;
the Classic Maya.
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\item{5.}  The {\it kalah} form of the {\it mancala} game family (see Problem Set 3)
(know the basic rules and how to analyze what happens with particular moves).
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\item{6.}  {\it Symmetry} the definition of a group, the classification
of the 17 ``wallpaper groups'' applications to Escher's regular subdivision
drawings, Islamic art.   (A possible question here would be to try to 
identify the type of a plane pattern in our classification, {\it given a table
of the different types} like the one from a class handout.  As in the case
of the Mayan calendar, it will {\it not} be necessary to memorize the 17 types.)
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{\it Format}
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Approximately 40\% of the exam will consist of one or two short mathematical
problems similar in format and content to things you have seen on the problem sets.  
The remaining approximately 60\% will be divided, in a way
to be determined, between multiple choice questions, short answer 
questions, and a short essay.  This 60\% will concentrate on aspects of 
the history and ideas from {\it Collapse}.    
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{\it Essay}
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The essay question will be one of the following:
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\item{1)}  Describe the Sacred Round, the Vague Year, and the Long Count
used by the Classic Maya in their calendar system.  The date March 25, 2011 
would be given in the full Mayan system by 12.19.18.4.3, 4 Akbal, 16 Cumku.  
Explain what each of these means and which part of the system it refers 
to.  After the collapse of the Classic Maya civilization about
900 C.E., Long Count dates were no longer used, although the Sacred
Round and the Vague Year remained in use.  Given what we know about
the situation of the Classic Maya collapse, why do you suppose
that was true?  
\item{2)}  What is the mathematical meaning of {\it symmetry}?  What
examples of symmetry transformations have we used in discussing 
examples from visual art in this course?  What is the mathematical
concept of a {\it group} and why is it important for the study of
symmetries?  Describe how symmetry groups can be used to classify
plane periodic patterns.  In what sense are two patterns of
the same type similar?  In what ways can they be different? 
\item{3)}  How important are leaders in determining the success 
or failure of a civilization?  To what extent did bad leadership 
contribute to or cause the collapses described by Jared Diamond 
that we talked about in our discussions of {\it Collapse}?  
Can wise leadership avert or minimize the effects of situations
that might tend toward societal collapse?
What do you think about the current performance
of leaders in the contemporary world?
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{\it Miscellaneous Groundrules}
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No use of cell phones, pagers, I-pods, I-pads, e-readers, or any other 
electronic devices beyond a calculator will be allowed during the exam -- turn 
them off and stow them in your backpack if you must carry them with you.
\bye
