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\centerline{MONT 108N -- Mathematics Through Time}
\centerline{Information for Midterm Exam}
\centerline{October 13, 2010}
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{\it General Information}
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The first midterm exam will be given in class on Friday, October    
29 (this is a week later than originally announced).  
It will cover the mathematical and historical material we have studied
since the start of the semester (starting {\it after} the discussions of 
{\it The Immortal Life of Henrietta Lacks}).  
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This means in particular:
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\item{1.}  The ``finished products'' of high school level algebra
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\itemitem{a.} Base 2, 8, 10, 60, etc. positional number systems
\itemitem{b.} Solving quadratic equations by factoring and the quadratic formula
\itemitem{c.} Know the derivation of the quadratic formula via completing
the square
\itemitem{d.} Solving other forms of equations
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\item{2.} Egyptian mathematics 
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\itemitem{a.}  Know the approximate historical period represented by
our primary Egyptian mathematical sources (the Rhind and Moscow mathematical
papyri).
\itemitem{b.}  Know the basic idea of their number system and
the number symbols for 1's, 10's, 100's, 1000's (see page 40 in {\it The Babylonian Theorem})
\itemitem{c.}  ``Egyptian multiplication and division'' by repeated doubling
\itemitem{d.}  Egyptian computations with unit fractions via tables of 
representations like the one from the Rhind papyrus on page 44 of {\it The Babylonian Theorem});
also know that there are many different representations for fractions as sums of unit fractions.
\itemitem{e.}  Be prepared for problems like the ones on Problem Set 2.
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\item{3.}  Old Babylonian mathematics
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\itemitem{a.}  Know the approximate historical period represented by the 
Old Babylonian mathematical texts.  
\itemitem{b.}  Know their base-60 number system and number symbols and be
able to read our simplified form and ``the real thing'' 
\itemitem{c.}  The role of addition, multiplication, reciprocal, $n^3 + n$, ... tables 
in Babylonian arithmetic
\itemitem{d.}  Know the different interpretations of the Babylonian ``quadratic algebra''
problem texts like YBC 6967 given by Otto Neugebauer, Jens Hoyrup, and Peter Rudman.  
\itemitem{e.}  Know what is on the ``Plimpton 322'' tablet and why this provides
evidence for Rudman's interpretation of the ``quadratic algebra'' problem texts.  
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{\it Format}
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Approximately 60\% of the exam will consist of two or three short mathematical
problems similar in format and content to the ones you have seen on the problem sets.  
The remaining approximately 40\% will be distributed, in a way
to be determined, among a few multiple choice questions, short answer 
questions, and a short essay.  This 40\% will concentrate on aspects of 
the history.    
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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)}  ``The distinguishing feature of Babylonian mathematics is
its algebraic character.'' Of the historians we have mentioned, who
would agree with this claim, and who would disagree?  
Explain using the the interpretations your historians would give 
for the YBC 6967 problem of solving the equation $x = 60/x + 7$.  
\item{2)}  How are the Egyptian and Old Babylonian ways of dealing
with fractions different from each other, and different from what
we do today?  Which of these three systems has the capability of dealing
with more fractions {\it in exact, finite terms} (that is, without
resorting infinite repeating expressions)?  Explain.  
\item{3)}  Getting on his soapbox, Rudman states that ``high school mathematics
education today, with its emphasis on creating high scores on standardized
tests, all too often neglects the derivations where mathematics is learned
and emphasizes memorizing the equations that provide quick solutions in
the standardized tests but that are then rapidly forgotten ... .''   Is today's
approach really all that different, though, from the Egyptian and Old Babylonian
problem texts we have seen, where solutions of the problems posed are given
as series of ``do this, then do that'' steps for solving the problems?  
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{\it Miscellaneous Groundrules}
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No use of cell phones, pagers, I-pods, or any other electronic devices
beyond a calculator will be allowed during the exam -- turn them off
and stow them in your backpack.
\bye
