\magnification=\magstep1
\noindent
\noindent
{\it Muhammad Javaid -- Looking Further into Plimpton 322}
\bigskip
What you say about Robson's reinterpretation of 
Plimpton 322 and her ideas about the correct approach
to the study of ancient mathematics is generally excellent.  
You have understood her main points well
and summarized them clearly.  This paper also seems 
more carefully written than the second paper for
our course was -- it reads much more smoothly, so good work!

However, I would say that the paper does not go quite far enough
in some cases.   Since we discussed some of
this in quite a bit of detail in class, it would 
have been good to say more.  First, you need to be 
careful with the ``reciprocal pair'' terminology since
the way the actual numbers on Plimpton 322 are derived
is {\it not just} the listing of $x, 1/x$ pairs as on the 
MLC 1670 tablet that Robson reproduces in her Figure 9.  It
would be more accurate to say that the numbers
on Plimpton 322 are {\it derived from} reciprocal pairs
by the same sort of formulas we saw in the analysis of 
YBC 6967:  from the pair $x,1/x$, the numbers
$$\eqalign{c &= (x + 1/x)/2\cr
           a & = 1\cr
           b & = (x - 1/x)/2\cr}$$
are formed and then $c^2 = a^2 + b^2$. It is essentially 
the numbers $c$ and $b$ (possibly scaled) that occur on Plimpton 322.
The goal of a problem text like YBC 6967 is then to derive 
the $x$ and $1/x$ from knowledge of $c$ and $b$.   
It would have been good to say something
about Rudman's alternative explanation for the genesis of
Plimpton 322 -- see page 97 in his book.
Second, since you mention the $p,q$ in the 
generating formulas for Pythagorean triples in the course
of discussing Robson's thoughts about Neugebauer's
interpretation, it would have been good to say more
there too.  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  See above -- it would be more accurate to 
say that these scholars see Plimpton 322 as a list of information
{\it derived from} reciprocal pairs -- the numbers on
the tablet are not the numbers $x,1/x$ in the reciprocal
pair themselves.  
\item{2.}  Technical comment -- In a paper like this, when you draw on a statement 
in a source for one of the things you are claiming, even if you are
only giving a paraphrase (a rewording in your own words), you need
to provide a reference to the place in the source (for instance a page
number) you are referring to.  Although you identified the source
by name, you did not provide that.  You should get into the habit 
of doing this as a matter of course for research papers in all of your classes.
I am only lowering you score in the ``cites quotations
properly'' category a bit for this.  {\it But be careful about this point
in the future.}  
\item{3.}  This is an accurate and well-written summary of Robson's argument for
rejecting the trigonometry table idea.  However, I think it is 
important to realize that there are possible objections to what
she is saying too.  For instance, when she says that the the Babylonians
did not have a notion of measuring angles and did not visualize circles
as being traced out by a radius making a varying angle with the 
positive $x$-axis, she is certainly correct.  But after that she seems 
to be {\it almost} doing the same sort of anachronistic reasoning from modern-day
mathematical ideas for which she criticizes the others when she
is claiming that there could not be any connection with what we
would call trigonometry.  It 
is certainly within the Babylonian scheme of things
to think of describing the {\it shape} of triangles or rectangles by 
using {\it ratios of the lengths of their sides} (or the square of 
such a ratio).  This effectively leads
to the same sorts of quantities we call trigonometric functions of the 
angle.  It also gives another possible explanation for the left-hand column
of the remaining part of Plimpton 322 that would make sense in the 
Babylonian context.  Whether you call the tablet a trigonometric table
or not based on this is a matter of terminology, I would say.  But I think
that it easily 
could have been a table of quantities related to differently shaped rectangles 
or triangles to the Babylonian scribe who wrote it.  
\item{4.}  And by the way, this would also give a way
to reconcile the idea that Plimpton 322 deals with rudimentary
forms of things that later became formalized in trigonometry 
with Robson's ideas about the table format.  Suppose the 
relevant number to the Babylonians
was the ratio $c^2/b^2$ -- a sort of ``shape parameter'' --
(not the $p$ or $q$ from Neugebauer's generating formulas for 
Pythagorean triples).  Then the remaining part of the table would
fit the ``formatting rules'' Robson infers.  
\item{5.}  See the general comments above about reciprocal pairs
and their relation to the numbers on Plimpton 322.
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately and completely presents facts and viewpoints of sources -- 15
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 10
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas --10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented  -- 10 
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 18
\item{2.}  (10) Is free of misspellings -- 9
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 9
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 9
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 14
\item{8.}  (10) Cites quotations and/or references correctly -- 7
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 95; Style and English Usage -- 91.
\vfill\eject
\noindent
{\it Peter Zona -- The Final Word on Plimpton 322}
\bigskip
What you say about Robson's reinterpretation of 
Plimpton 322 and her ideas about the correct approach
to the study of ancient mathematics is generally excellent and
well written.  You have understood her main points well
and summarized them clearly.  

However, I would say that the paper does not go quite far enough
in some cases.   Since we discussed some of
this in quite a bit of detail in class, it would 
have been good to say more.  First, you need to be 
careful with the ``reciprocal pair'' terminology since
the way the actual numbers on Plimpton 322 are derived
is {\it not} just the listing of $x, 1/x$ pairs as on the 
MLC 1670 tablet that Robson reproduces in her Figure 9.  The numbers
on Plimpton 322 are really {\it derived from} reciprocal pairs
by the same sort of formulas we saw in the analysis of 
YBC 6967:  from the pair $x,1/x$, the numbers
$$\eqalign{c &= (x + 1/x)/2\cr
           a & = 1\cr
           b & = (x - 1/x)/2\cr}$$
are formed and then $c^2 = a^2 + b^2$. It is essentially 
the numbers $c$ and $b$ that occur on Plimpton 322.
The goal of a problem text like YBC 6967 is then to derive 
the $x$ and $1/x$ from knowledge of $c$ and $b$.   
It would have been good to say something
about Rudman's alternative explanation for the genesis of
Plimpton 322 -- see page 97 in his book.

More importantly, in a paper like this, when you draw on a statement 
in a source for one of the things you are claiming, even if you are
only giving a paraphrase (a rewording in your own words), you need
to provide a reference to the place in the source you are referring to.  
I did not see any of this in your paper.  You should get into the habit 
of doing this as a matter of course for research papers in all of your classes.
Not doing this, in fact, can be considered a form of {\it plagiarism} and
as such it might be dealt with using the Academic Honesty policy.  I know you are 
not trying to conceal your sources and I did not find any direct 
copying.  So I am only lowering you score in the ``cites quotations
properly'' category for this.  {\it But be careful about this point
in the future.}  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  You have clearly understood and appreciated Robson's ideas about the importance of 
taking the historical context and what is known about ancient languages 
into account in order to avoid anachronistic interpretations of ancient 
mathematics based on modern mathematical ideas.
But it is important, I think, to realize that the people
Robson is criticizing here are primarily people who were
trained as {\it mathematicians} and then have done some 
exploration of ancient mathematics.  Some of them have been
``amateur'' historians, as you
say, but that is not true of Neugebauer, who devoted
his whole professional career to this kind of study.   In general, 
mathematicians are somewhat notorious for this sort of ahistorical approach to 
the history of mathematics, 
so this sort of criticism is probably something we should hear more often!  
On the other hand, if it were not for the mathematicians who have looked at this 
material, we might not know {\it anything} about the mathematical ideas
involved.  Many of the {\it ``straight'' historians} who would be in the 
position to make more historically accurate appraisals do not
know any mathematics!  Robson is one of a group of pioneers in this
area.  
\item{2.}  This is an accurate and well-written summary of Robson's argument for
rejecting the trigonometry table idea.  However, I think it is 
important to realize that there are possible objections to what
she is saying too.  For instance, when she says that the the Babylonians
did not have a notion of measuring angles and did not visualize circles
as being traced out by a radius making a varying angle with the 
positive $x$-axis, she is certainly correct.  But to me that seems 
to be {\it almost} the same sort of anachronistic reasoning from modern-day
mathematical ideas for which she criticizes the others.  It 
is certainly within the Babylonian scheme of things
to think of describing the {\it shape} of triangles or rectangles by 
using {\it ratios of the lengths of their sides}.  This effectively leads
to the same sorts of quantities we call trigonometric functions of the 
angle.  It also gives another possible explanation for the left-hand column
of the remaining part of Plimpton 322 that would make sense in the 
Babylonian context.  Whether you call the tablet a trigonometric table
or not based on this is a matter of terminology, I would say.  But I think
that it easily 
could have been a table of quantities related to differently shaped rectangles 
or triangles to the Babylonian scribe who wrote it.  And by the way, that would also give a way
to reconcile this interpretation with Robson's ideas about the
table format.  Suppose the relevant number to the Babylonians
was the ratio $c^2/b^2$ -- a sort of ``shape parameter'' --
(not the $p$ or $q$ from Neugebauer's generating formulas for 
Pythagorean triples).  Then the remaining part of the table would
fit the ``formatting rules'' Robson infers.  
\item{3.}  See general comments above about the reciprocal pairs.
\item{4.}  That is actually understandable since the article you 
read was published in 2002, and Rudman's book appeared in 2009.
\item{5.}  A technical point -- this is fine as a citation for the
MAA web site where you can download the article.  However, since
the article appeared first in a print journal, I think it would
be more appropriate to give the reference for the original print form:
\medskip
\centerline{Author, ``Title of Article.'' Name of Journal, volume number (year), pages.}
\bigskip
\noindent  
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately and completely presents facts and viewpoints of sources -- 15
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 10
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas --10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented  -- 10 
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 15
\item{8.}  (10) Cites quotations and/or references correctly -- 3
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 95; Style and English Usage -- 93.
\vfill\eject
\noindent
{\it Matt Kasuba -- ``No Luck for Sherlock''}
\bigskip
What you say about Robson's reinterpretation of 
Plimpton 322 and her ideas about the correct approach
to the study of ancient mathematics is generally excellent and
well written.  You have understood her main points well
and summarized them clearly.  

However, the paper does not go quite far enough
in some cases.  (This would also have ``filled out''
the paper somewhat; it is significantly under the 
target length.)  Since we discussed some of
this in quite a bit of detail in class, it would 
have been good to say more.  First, you need to be 
careful with the ``reciprocal pair'' terminology since
the way the actual numbers on Plimpton 322 are derived
is {\it not} just the listing of $x, 1/x$ pairs as on the 
MLC 1670 tablet that Robson reproduces in her Figure 9.  The numbers
on Plimpton 322 are really {\it derived from} reciprocal pairs
by the same sort of formulas we saw in the analysis of 
YBC 6967:  from the pair $x,1/x$, the numbers
$$\eqalign{c &= (x + 1/x)/2\cr
           a & = 1\cr
           b & = (x - 1/x)/2\cr}$$
are formed and then $c^2 = a^2 + b^2$. It is essentially 
the numbers $c$ and $b$ that occur on Plimpton 322.
The goal of a problem text like YBC 6967 is then to derive 
the $x$ and $1/x$ from knowledge of $c$ and $b$.   
It would have been good to say something
about Rudman's alternative explanation for the genesis of
Plimpton 322 -- see page 97 in his book.

More importantly, in a paper like this, when you draw on a statement 
in a source for one of the things you are claiming, even if you are
only giving a paraphrase (a rewording in your own words), you need
to provide a reference to the place in the source you are referring to.  
I did not see any of this in your paper.  You should get into the habit 
of doing this as a matter of course for research papers in all of your classes.
Not doing this, in fact, can be considered a form of {\it plagiarism} and
as such it might be dealt with using the Academic Honesty policy.  I know you are 
not trying to conceal your sources and I did not find any direct 
copying.  So I am only lowering you score in the ``cites quotations
properly'' category for this.  {\it But be careful about this point
in the future.}  

A final technical point:  The entries in the bibliography are not complete.   
A standard format for citing journal articles is:  
\medskip
\item{}
Author, ``Title of Article.'' Name of Journal, volume number (year), pages.  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  You have caught Robson's ideas about the importance of 
taking the historical context and what is known about ancient languages 
into account in order to avoid anachronistic interpretations of ancient 
mathematics based on modern mathematical ideas.
But it is important, I think, to realize that the people
Robson is criticizing here are primarily people who were
trained as {\it mathematicians} and then have done some 
exploration of ancient mathematics.   Neugebauer and Buck
certainly fit into that category.  (And in general, mathematicians are somewhat 
notorious for this sort of ahistorical approach to ancient mathematics, 
so this sort of criticism is something we need to hear!)  On the other hand,
if it were not for the mathematicians who have looked at this 
material, we might not know {\it anything} about the mathematical ideas
involved.  Many of the {\it historians} who would be in the 
position to make more historically accurate appraisals do not
know any mathematics!  Robson is one of a group of pioneers in this
area.  
\item{2.}  This is an accurate summary of Robson's argument for
rejecting the trigonometry table idea.  However, I think it is 
important to realize that there are possible objections to what
she is saying too.  For instance, when she says that the the Babylonians
did not have a notion of measuring angles and did not visualize circles
as being traced out by a radius making a varying angle with the 
positive $x$-axis, she is certainly correct.  But to me that is 
almost the same sort of anachronistic reasoning from modern-day
mathematical ideas that she accuses Neugebauer of doing.  It 
is certainly within the Babylonian scheme of things
to think of describing the {\it shape} of triangles or rectangles by 
using {\it ratios of the lengths of their sides}.  This effectively leads
to the same sorts of quantities we call trigonometric functions of the 
angle.  But it also gives another possible explanation for the left-hand column
of the remaining part of Plimpton 322 that would make sense in the 
Babylonian context.  Whether you call that a trigonometric table
or not is a matter of terminology, I would say.  But it easily 
could have been a table of differently shaped rectangles or triangles 
to the Babylonians!  
\item{3.}  (Continuing from the previous comment):  
And by the way, that would also give a way
to reconcile this interpretation with Robson's ideas about the
table format.  Suppose the relevant number to the Babylonians
was the ratio $c^2/b^2$ -- a sort of ``shape parameter'' --
(not the $p$ or $q$ from the generating formulas for 
Pythagorean triples).  Then the remaining part of the table would
fit the ``formatting rules'' Robson infers.  

\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately and completely presents facts and viewpoints of sources -- 15
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 10
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas --10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented  -- 10 
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 8
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 14
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 9
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 15
\item{8.}  (10) Cites quotations and/or references correctly -- 3
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 95; Style and English Usage -- 89.
\vfill\eject
\noindent
{\it Dan Finn -- ``Last Word on Plimpton 322''}
\bigskip
This is a very good paper on Eleanor Robson's ideas about
Plimpton 322's place in Babylonian mathematics.   You have
caught her ideas about the importance of taking the historical
context and what is known about ancient languages into account in
order to avoid anachronistic interpretations of ancient mathematics
based on modern mathematical ideas.  (Mathematicians are somewhat 
notorious for doing that, by the way, so it is something we need 
to hear!)  

The major comments I have are the following.
First, it would been better to acknowledge that, even though you 
may be convinced by Robson's reasoning, this is still an 
area of active debate, and her ideas have by no means been
completely accepted.  For instance, see point 3 below for
a possible objection to her rejection of the trigonometry 
table interpretation.  Second, you need to be a bit more
careful with the ``reciprocal pair'' terminology since
the way the actual numbers on Plimpton 322 are derived
is {\it not} just the listing of $x, 1/x$ pairs as on the 
MLC 1670 tablet that Robson reproduces in her Figure 9.  The numbers
on Plimpton 322 are really {\it derived from} reciprocal pairs
by the same sort of formulas we saw in the analysis of 
YBC 6967:  from the pair $x,1/x$, the numbers
$$\eqalign{c &= (x + 1/x)/2\cr
           a & = 1\cr
           b & = (x - 1/x)/2\cr}$$
are formed and then $c^2 = a^2 + b^2$. It is essentially 
the numbers $c$ and $b$ that occur on Plimpton 322.
The goal of a problem text like YBC 6967 is then to derive 
the $x$ and $1/x$ from knowledge of $c$ and $b$.   
Third and finally, it would have been good to say something
about Rudman's alternative explanation for the genesis of
Plimpton 322 -- see page 97 in his book.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1)}  I think Robson lists Joyce's web site as a source
for this idea because it is so readily accessible.  However, there
are other historians who have proposed the trigonometry table
interpretation as well.
\item{2)}  When you say the ``first column'' here, I think you are
referring to the conjectural missing part of the tablet on the left
side.  (I saw the actual Plimpton 322 last weekend at the exhibit in New York that 
I mentioned briefly in class, and it is very clear from the shape of the back
that there must have originally been an additional section on the left, perhaps
as wide as one third of the remaining tablet -- certainly enough
space for two additional columns of numbers).  When and why that
portion got separated and what it contained may never be known (unless
we get really lucky and someone finds the missing piece and 
recognizes that it fits with the other portion!).
\item{3)}  This is an accurate summary of Robson's argument for
rejecting the trigonometry table idea.  However, I think it is 
important to realize that there are possible objections to what
she is saying too.  For instance, when she says that the the Babylonians
did not have a notion of measuring angles and did not visualize circles
as being traced out by a radius making a varying angle with the 
positive $x$-axis, she is certainly correct.  But to me that is 
almost the same sort of anachronistic reasoning from modern-day
mathematical ideas that she accuses Neugebauer of doing.  It 
is certainly within the Babylonian scheme of things
to think of describing the {\it shape} of triangles or rectangles by 
using {\it ratios of the lengths of their sides}.  This effectively leads
to the same sorts of quantities we call trigonometric functions of the 
angle.  But it also gives another possible explanation for the left-hand column
of the remaining part of Plimpton 322 that would make sense in the 
Babylonian context.  Whether you call that a trigonometric table
or not is a matter of terminology, I would say.  But it easily 
could have been a table of differently shaped rectangles or triangles 
to the Babylonians!  And by the way, that would also give a way
to reconcile this interpretation with Robson's ideas about the
table format.  Suppose the relevant number to the Babylonians
was the ratio $c^2/b^2$ -- a sort of ``shape parameter'' --
(not the $p$ or $q$ from the generating formulas for 
Pythagorean triples).  Then the remaining part of the table would
fit the ``formatting rules'' Robson infers.  
\item{4)}  {\it First modern owner} would be more accurate(!)
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 17
\item{3.}  (10) Provides sufficient textual evidence about the main topic -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 7
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 8 
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 18 
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 13
\item{8.}  (10) Cites quotations and/or references correctly -- 10
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 92; Style and English Usage -- 96.
\vfill\eject
\noindent
{\it Astrid Ludwig -- ``Plimpton 322: Evaluating Theories}
\bigskip
This is a good paper on Eleanor Robson's ideas about
Plimpton 322's place in Babylonian mathematics.   You have
caught her ideas about the importance of taking the historical
context and what is known about ancient languages into account in
order to avoid anachronistic interpretations of ancient mathematics
based on modern mathematical ideas.  (Mathematicians are somewhat 
notorious for doing that, by the way, so it is something we need 
to hear!)  I like the way you tried to think independently about
Robson's conclusions and evaluate her reasoning.  That is 
just what a good research paper should do.  

The major criticism I have, though, is that for completeness 
it would have been good to go into somewhat more detail about
the technical points.  First, it would have been better
to explain the $p,q$ in Neugebauer's interpretation and
how they generate Pythagorean triples via the formulas
$a = p^2 - q^2$, $b = 2pq$ and $c = p^2 + q^2$.  Second, see 
point 1 below.
Third and finally, it would have been good to consult
another source that has a lot to say on these questions -- the 
Rudman book we used as a text for the course.  For instance,
it would have been very good to say something
about Rudman's alternative explanation for the genesis of
Plimpton 322 -- see page 97 in his book.  

On the technical side, you need to be more careful
in using direct quotations!  When you use one, 
you should {\it always} identify the source.  As described
in the assignment, an acceptable way would be to 
say (Robson, 108) to identify a quotation from 
Robson's article taken from page 108.  Do this even
if you have only one source.  By the way, the 
name of the journal Robson's article appeared in
is the {\it American Mathematical Monthly}.  
The {\it Mathematical Association of America} is
the professional organization that publishes it
and holds the copyright to materials published
there.  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  You need to be a bit more careful with the ``reciprocal pair'' 
terminology since the way the actual numbers on Plimpton 322 are derived
is {\it not} just the listing of $x, 1/x$ pairs as on the 
MLC 1670 tablet that Robson reproduces in her Figure 9.  The numbers
on Plimpton 322 are really {\it derived from} reciprocal pairs
by the same sort of formulas we saw in the analysis of 
YBC 6967:  from the pair $x,1/x$, the numbers
$$\eqalign{c &= (x + 1/x)/2\cr
           a & = 1\cr
           b & = (x - 1/x)/2\cr}$$
are formed and then $c^2 = a^2 + b^2$. It is essentially 
the numbers $c$ and $b$ that occur on Plimpton 322.
The goal of a problem text like YBC 6967 is then to derive 
the $x$ and $1/x$ from knowledge of $c$ and $b$.
\item{2.}  This seems like a relatively minor point to me.
\item{3.}   This is an accurate summary of Robson's argument for
rejecting the trigonometry table idea.  However, I think it is 
important to realize that there are possible objections to what
she is saying too.  For instance, when she says that the the Babylonians
did not have a notion of measuring angles and did not visualize circles
as being traced out by a radius making a varying angle with the 
positive $x$-axis, she is certainly correct.  But to me that is 
almost the same sort of anachronistic reasoning from modern-day
mathematical ideas that she accuses Neugebauer of doing.  It 
is certainly within the Babylonian scheme of things
to think of describing the {\it shape} of triangles or rectangles by 
using {\it ratios of the lengths of their sides}.  This effectively leads
to the same sorts of quantities we call trigonometric functions of the 
angle.  But it also gives another possible explanation for the left-hand column
of (the remaining part of) Plimpton 322 that would make sense in the 
Babylonian context.  Whether you call that a trigonometric table
or not is a matter of terminology, I would say.  But it easily 
could have been a table of differently shaped rectangles or triangles 
to the Babylonians!  And by the way, that would also give a way
to reconcile this interpretation with Robson's ideas about the
table format.  Suppose the relevant number to the Babylonians
was the ratio $c^2/b^2$ -- a sort of ``shape parameter'' --
(not the $p$ or $q$ from the generating formulas for 
Pythagorean triples).  Then the remaining part of the table would
fit the ``formatting rules'' Robson infers.  
\item{4.}  See comment immediately above!
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 7
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 17
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 10
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 10.
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 18
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 14
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences  -- 8 
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 13
\item{8.}  (10) Cites quotations and/or references correctly -- 5
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 94; Style and English Usage -- 88.
\vfill\eject
\noindent
{\it Sarah Cahn -- ``Investigating Different Interpretations of Plimpton 322''}
\bigskip
This is a very good paper on Eleanor Robson's ideas about
Plimpton 322's place in Babylonian mathematics.   You have
caught her ideas about the importance of taking the historical
context and what is known about ancient languages into account in
order to avoid anachronistic interpretations of ancient mathematics
based on modern mathematical ideas.  (Mathematicians are somewhat 
notorious for doing that, by the way, so it is something we need 
to hear!)  I like the way you tried to think independently about
Robson's conclusions and evaluate her reasoning (following 
my suggestions on your first draft).  That is 
just what a good research paper should do.   However, I think
it would also have been good to bring some of Rudman's ideas
into the mix here. See comment 3 below.  And Robson's interpretation
of Plimpton 322 is
not really that it is a set of {\it solutions to problems}
as you say in the conclusion.  It's really more like the raw material
or data for {\it creating statements of problems} of a particular
type.
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  In addition to the uses the Babylonian scribe might
have made of this tablet, there are also the question 
of just how the information on it was generated, of course!
\item{2.}  Robson's reasoning is somewhat more careful than 
this, of course.  She is referring specifically to tablets 
generated at that particular time in the temple at Larsa.
\item{3.}  This section is not quite correct.  There is only 
one problem on YBC 6967.  It is of a particular type and the 
numbers on Plimpton 322 could have been used to generate
{\it similar} problems with different numerical values.  (This
is something like the way WebAssign can generate different 
individually-tailored calculus problems of the same type for all the 
students using it!)  It might have been good here to consider
Rudman's proposed reconstruction of how Plimpton 322 came
to be as well -- see page 97 in his book {\it The Babylonian
Theorem}.
\item{4.}  The sexagesimal
system the Babylonians was used consistently throughout this period.
The key point here is not that the sexagesimal computations
were used in generating the tables of reciprocal pairs.  It's
really that the tables of reciprocal pairs were a key component
of the way they approached numerical computations using their
sexagesimal system.
\item{5.}  This is an accurate summary of Robson's argument for
rejecting the trigonometry table idea and a possible objections to what
she is saying too.  For instance, when she says that the the Babylonians
did not have a notion of measuring angles and did not visualize circles
as being traced out by a radius making a varying angle with the 
positive $x$-axis, she is certainly correct.  But to me that is 
almost the same sort of anachronistic reasoning from modern-day
mathematical ideas that she accuses Neugebauer of doing.  It 
is certainly within the Babylonian scheme of things
to think of describing the {\it shape} of triangles or rectangles by 
using {\it ratios of the lengths of their sides}.  This effectively leads
to the same sorts of quantities we call trigonometric functions of the 
angle.  But it also gives another possible explanation for the left-hand column
of (the remaining part of) Plimpton 322 that would make sense in the 
Babylonian context.  Whether you call that a trigonometric table
or not is a matter of terminology, I would say.  But it easily 
could have been a table of differently shaped rectangles or triangles 
to the Babylonians!  And by the way, that would also give a way
to reconcile this interpretation with Robson's ideas about the
table format.  Suppose the relevant number to the Babylonians
was the ratio $c^2/b^2$ -- a sort of ``shape parameter'' --
(not the $p$ or $q$ from the generating formulas for 
Pythagorean triples).  Then the remaining part of the table would
fit the ``formatting rules'' Robson infers.  
\item{6.}  This citation is not complete.   A standard format
for citing journal articles is:  
\medskip
\item{}
Author, ``Title of Article.'' Name of Journal, volume number (year), pages.  
\medskip
\item{}
It would also have been good cite Rudman as a reference and take what
he has to say about this into account.  
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 17
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 16
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 10
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 9  
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 18
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 9
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 14
\item{8.}  (10) Cites quotations and/or references correctly -- 7
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 92; Style and English Usage -- 93.
\vfill\eject
\noindent
{\it Tom Santa Maria -- ``Hypatia''}
\bigskip
This is a very good and balanced paper on Hypatia.  I'm glad that you 
were able to incorporate some comments on the film {\it Agora}, and I 
agree with you (for the most part) about the liberties the authors of the screenplay took
with the invented characters and the depiction of Hypatia's possible
discovery of the elliptical orbits of planets (the ``wanderers'').  
There is no historical evidence for Hypatia anticipating
Kepler by about 1200 years.  But I would say it is an {\it interesting speculation}
since we do know:
\bigskip
\item{1.} about Hypatia's interest in astronomy, 
\item{2.} the fact that the previous ideas
of Aristarchus on a heliocentric solar system would have been known
at her time and in her intellectual circles, and 
\item{3.} about Hypatia's own expertise
in the theory of conic sections (based on her commentary on Apollonius).
\bigskip
\noindent
The role of the slave Davus in the film is entirely 
fictional, as you point out, but inserted to further the plot
and to personalize some of the conflicts that people around
Hypatia would have felt.    

The only critical comments I have are all technical writing issues.
First, although you are a strong and fluent writer, I think there are
times when you tend to say things in an overly flowery, slightly self-consciously
``learned'' way that actually comes across differently than you might
intend.  I'm thinking of things like the sentence ``Alexandria was
Christianizing fanatically and with celerity.''  There are times when
simpler and more direct ways of saying things are preferable, and this
is one, at least to me.   

Second, I think you should review what a good
English style manual has to say about commas and semicolons.  I'm looking
at an old copy of the Harbrace College Handbook that says, essentially:
\medskip
\item{1.}  Use a semicolon between main clauses (i.e. complete sentences
in themselves) not joined by and, but, or, nor, for, so or yet, and 
\item{2.}  Do not use a semicolon between two parts of unequal grammatical
rank.  For instance:  ``Then came the attack; this
frightened the unprepared''  (two equal main clauses).  On the 
other hand:  ``Then came the attack, frightening
the unprepared''  (second clause subsidiary, modifying the noun ``attack'').
\item{3.}  Semicolons may also be used for clarity when the clauses 
to be separated themselves contain commas. 
``However'' only needs a semicolon when it introduces a second
complete clause.    
\medskip 
\noindent
There are times when you have semicolons that should be commas, 
and vice versa.   
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  Technical point -- a ``see'' is the office or position of bishop (essentially the same
as saying ``bishopric'').  The person holding the office is a {\it bishop}.  That
is what you mean here.
\item{2.}
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 20
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 7
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly 
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 8
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 10
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 16
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 9
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 6
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 14
\item{8.}  (10) Cites quotations and/or references correctly -- 10
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 98; Style and English Usage -- 90.
\vfill\eject
\noindent
\noindent
{\it Catherine Caracciolo -- The Infamous Life of Hypatia of Alexandria}
\bigskip
This is a good summary of Hypatia's life and contributions, but it does
not show much independent thought or evaluation of what you 
found in the different sources.  On the other hand, it is definitely good
that you looked beyond the easy Internet sources about her -- I think you
got a more balanced and complete picture that way.  Still,
it might have been good to try to say more about what Hypatia's mathematics
consisted of and how it connected with topics we have discussed in this course. 

I don't think the word ``infamous'' means quite what you think it does:
``having an extremely bad reputation, deserving of or causing an evil reputation, 
detestable.'' If you {\it do mean to say this} about Hypatia, for instance
if you are using the word ``infamous'' ironically, 
then it can only be from the point of view of someone like Cyril or
one of the Christians responsible for her death.  It is questionable, then,
whether those opinons of her are justified(!) 

On the technical side, as you get into the paper, the paragraphs start
to get very long.  The division into paragraphs does not respect 
the logical structure of what you are saying either.  This is something
to work on. 
\bigskip  
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  Synesius is probably best known (apart from his relation with
Hypatia) as bishop of Ptolemais in Egypt.  His role in possible inventions 
such as the astrolabe and hydroscope as (as far
as I know) mostly the product of his contact with Hypatia.
\item{2.}  As noted above, most people think that Synesius's role
in these inventions came mostly or entirely through his relation
with Hypatia, and that Hypatia might in fact be responsible
for the main ideas.  On the other hand, some people doubt that Hypatia
originated either of these ideas.  Astrolabes, for instance, might
have been constructed quite a long time before Hypatia's time.
\item{3.}  I'm not entirely sure what this phrase ``person intellectual
stimulation'' means.  Are you thinking that she advocated that
women should have the freedom to pursue their intellectual development?
\bigskip
\noindent 
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 18
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 5
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question  -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 8
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 8
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 9
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10 
\item{6.}  (10) Uses correct punctuation -- 8
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 13
\item{8.}  (10) Cites quotations and/or references correctly -- 10
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 88; Style and English Usage -- 94.
\vfill\eject
\noindent
{\it Kyle Kadlick -- Hypatia of Alexandria}
\bigskip
This is a reasonably good paper about the life and contributions of Hypatia,
but it does not show much independent thought or evaluation of what you 
found in the different sources.  
I do like that you tried to include some of the actual mathematics that has
been attributed to her personally with the discussion of problems on 
conics.  However there is more you could have said there (see comment 2 below).

There is also a technical point about citations that you need to 
think about.  The Deakin article you looked at is not really
cited correctly.    A standard format
for citing journal articles is:  
\medskip
\item{}
Author, ``Title of Article.'' Name of Journal, volume number (year), pages.  
\medskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  ``Family of mathematicians'' might be an overstatement, since
we do not know anything about others in her family beyond Theon.
\item{2.}  This is good, but you might have said more.  For instance, 
if you think in geometric terms (in Cartesian coordinates), the solutions of 
these equations are essentially finding the intersections of a line and 
a hyperbola.  With modern algebra, of course, the solution is 
not difficult.  You can solve the equation of the line for $y$, substitute
into the other equation, and then factor or use the quadratic formula
to solve for $x$.  
\item{3.}  This really has to be treated as a legend.
Saying she was physically beautiful is one way that some people have
tried to make her seem more like a tragic heroine.  
\item{4.}  There is also a major question whether Cyril was directly
responsible for Hypatia's death or not.  Some people would say
that he just provoked others to do it, or even just helped
to create the conflict that led to it, without giving a direct order
for her death.  
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 9
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 16
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 5
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 8
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly 
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 8
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 7
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 8
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 16
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 8
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 13
\item{8.}  (10) Cites quotations and/or references correctly -- 8
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 81; Style and English Usage -- 88.
\vfill\eject
\noindent
{\it Kylee Sullivan -- ``Reserve your Right to Think"}
\bigskip
This is a good paper about the life and contributions of Hypatia,
but it does not show much independent thought or evaluation of what you 
found in the different sources.  It is true that her mathematical attainments
were very unusual for her time and place, and that aspect of her story is
an appealing one for many people today who want to encourage women 
to pursue careers in mathematics and the sciences. It would have been good, though 
if you ahd tried to include some of the actual mathematics that has
been attributed to her personally with a discussion of problems on 
conics from her commentary on Apollonius.  I think that the sources you 
consulted were probably not sufficient for getting a complete picture
of what is known, though.  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  But this is somewhat questionable.  For instance, astrolabes
might have been known quite a bit earlier.  And the discussion of the 
hydrometer comes from one of the letters Synesius wrote to her, asking
her to construct one of the devices.  So it is not clear whether
she was responsible for the idea behind the device, or whether she was just in a 
better position to have one made or provide advice on how they should be made.
\item{2.}  ``Neo-Platonist School'' sounds like a formal title, which would not
have been used at the time.  Be more careful about things like this.
\item{3.}  Cyril was bishop of Alexandria.  I think that even at this time, 
the term Pope was probably only used for the bishop of Rome.  
\item{4.} There is also a major question whether Cyril was directly
responsible for Hypatia's death or not.  Some people would say
that he just provoked others to do it, or even just helped
to create the conflict that led to it, without giving a direct order
for her death.  So this is another point that is open to debate.  
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 7
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 18
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 8
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 5
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented  -- 10
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 10
\item{2.}  (10) Is free of misspellings -- 7
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 13
\item{8.}  (10) Cites quotations and/or references correctly -- 10
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 88; Style and English Usage -- 93.
\vfill\eject
\noindent
{\it Kevin Sutman -- The Life and Times of Hypatia of Alexandria}
\bigskip
This is a decent, but rather perfunctory paper about the life and contributions of Hypatia.
It does not show much independent thought or evaluation of what you 
found in the different sources you consulted.  The whole paper reads, 
in fact, like an almost undigested collection of paraphrases from those
sources.    

I also think it would have been much better
to consult {\it more authoritative sources} than some of the ones you used.
For example, your first source is essentially a student paper written
by an undergraduate at Agnes Scott College.  It is superficial at best.
Only the third one is really suitable, and that only for a start.  There 
were several more scholarly sources for this topic on reserve in the science 
library that you could have consulted for more complete and more balanced 
presentations.  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  This is an overstated clich\'e.  Avoid trite phrases like this
in formal writing.
\item{2.}  I think this is a matter of interpretation.  Whether there
was a formal post of leader is not clear.  She may very well have
been an informal leader by reason of the respect she commanded.
\item{3.}  ``Efficiency as a teacher'' sounds strange here, and I
do not think it is what you mean to say.   (What does ``efficiency as a 
teacher'' mean?  Good time management in class?  Returning graded assignments quickly?) 
I think it would be more accurate to say it was a testament to the strength 
of her character, or to the respect that she was able to inspire in her students.
\item{4.}  If I understand you, ``legendary'' is another clich\'e. 
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 3
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 15 
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 8
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 5
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly 
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented  -- 10
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 9
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 12
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 9
\item{6.}  (10) Uses correct punctuation -- 8
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 11
\item{8.}  (10) Cites quotations and/or references correctly -- 10
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 81; Style and English Usage -- 89.
\vfill\eject
\noindent
{\it Lucia Bostrom -- Hypatia of Alexandria}
\bigskip
This is a good, but rather perfunctory paper about the life and contributions of Hypatia.
It does not show much independent thought or evaluation of what you 
found in the different sources you consulted.  The whole paper reads, 
in fact, like an almost undigested collection of paraphrases from those
sources.    

I also think it would have been much better
to consult {\it more authoritative sources} than some of the ones you used.
For example, several of your sources are essentially student paper written
by undergraduates.  They are is superficial at best.
Only a few are really suitable, and that only for a start.  There 
were several more scholarly sources for this topic on reserve in the science 
library that you could have consulted for more complete and more balanced 
presentations.

More importantly, in a paper like this, when you draw on a statement 
in a source for one of the things you are claiming, even if you are
only giving a paraphrase (a rewording in your own words), you need
to provide a reference to the place in the source you are referring to.  I did not
see any of this in your paper.  You should get into the habit 
of doing this as a matter of course for research papers in all of your classes.
Not doing this, in fact, can be considered a form of {\it plagiarism} and
as such it might be dealt with using the Academic Honesty policy.  I know you are 
not trying to conceal your sources and I did not find any direct 
copying.  So I am only lowering you score in the ``cites quotations
properly'' category for this.  {\it But be careful about this point
in the future.}  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.} This should be Ptolemais (the name of a city, not the 
name of the astronomer, or the general).
\item{2.}  This is an overstated clich\'e.  Avoid trite phrases like this
in formal writing.  
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 7
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 18
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 5
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 5
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented  --10
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 8
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 13
\item{8.}  (10) Cites quotations and/or references correctly -- 3
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 85; Style and English Usage -- 89.
\vfill\eject
\noindent
{\it Andrew Marzo -- Consequences of Non-Euclidean Geometry}
\bigskip
What you have to say about the topic is often good.  See the comments below
for some exceptions though, where I disagree with what what I think 
you are trying to say.  It may be that I am misunderstanding what you meant to 
say in some of those cases.  However, then the comment I would have
is that you need to be {\it really careful} about how you discuss some of 
these ideas because they are pretty deep and complicated.

The structure of the paper itself is so repetitive, though, that it 
seems as though you may have been concerned that you needed to ``pad'' 
it to get to some required length.  There was not any need to do that here.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  This is slightly incorrect historically.  Plato lived about two 
generations before the time of Euclid.  So ``Euclidean'' has to be 
qualified here as referring to the mathematical structure itself, not
the specific presentation of geometry in the work of Euclid.  It did not exist yet.
\item{2.}  This is the main disagreement I have with your claims.  It is
not correct to say that the discovery of non-Euclidean geometry ``disproved
Euclidean geometry.''  What it disproved was {\it the idea that there could
only be one kind of geometry} that made sense as mathematics.  Even though
non-Euclidean geometry is now around, both it and Euclidean geometry are
equally consistent.  Neither disproves the other!
\item{3.}  There seems to be a missing citation here.
\item{4.}  I don't agree with the first part of this either.  The existence
of several different forms of geometry as mathematical theories only 
says that which geometry describes physical space is a separate question!
It is probably correct to say that this destroyed one of the bases
for believing in rationalism, though.  
\item{5.}  This is a real ``which came first -- the chicken or the egg?''
situation.  Is Euclidean geometry based on our perception of space,
or is it the other way around?  Is our understanding of the properties
of the counting numbers based on our perception of time, or is 
it the other way around?  In order to believe as Plato or Kant did, you 
have to believe that geometry and arithmetic have some kind of an existence
independent of human beings.  I think that is somewhat hard to imagine!
\item{6.}  The discovery of non-Euclidean geometries came after
Kant's death, so this sounds strange from the historical point of 
view.  He never had to grapple with the implications of this discovery,
and he may very well have changed his mind if he knew about it.
\item{7.}  This is not really correct either.  It is not the non-Euclidean
geometry itself that is only valid in the extreme circumstances.
Non-Euclidean properties of {\it actual, physical
space} are only really observable when you get outside the normal
range of human experience (over most of human history, anyway).  
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 13
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 10
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 4
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence 
presented -- 8 
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 18
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 12
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 8
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 15
\item{8.}  (10) Cites quotations and/or references correctly -- 10
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 85; Style and English Usage -- 93.
\vfill\eject
\noindent
{\it John Macomber -- Mathematics and Its Philosophical Consequences}
\bigskip
What you have to say about the topic is often very good.  See the comments below
for some small exceptions though, where I disagree with what what I think 
you are trying to say.  It may be that I am misunderstanding what you meant to 
say in some of those cases.  However, then the comment I would have
is that you need to be {\it really careful} about how you discuss some of 
these ideas because they are pretty deep and complicated.

The major criticism I have about the paper is that the concluding
paragraph seems to go off in a slightly new direction that addresses
your personal reactions to some of the ideas.  That doesn't seem
appropriate here, since the rest of the paper has not addressed 
that sort of question.  
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  I think ``circumstances'' is the wrong word here.  (Either 
that, or I don't understand what you mean by it.)  Don't you mean 
the original square of side 1 can be cut into two triangles?  Then
four copies of that triangle can be reassembled to make a square of 
side $\sqrt{2}$.  This is the heart of the mathematical reasoning
behind the dialog between Socrates and the slave boy in the {\it Meno}.  
\item{2.}  This is a real ``which came first -- the chicken or the egg?''
situation.  Is our understanding of the properties
of the counting numbers based on our perception of time, or is 
it the other way around?   Is Euclidean geometry based on our perception of space,
or is it the other way around?   In order to believe as Plato or Kant did, you 
have to believe that arithmetic and geometry have some kind of an existence
independent of human beings.  I think that is somewhat hard to imagine!
\item{3.}  I would agree with this if you deleted the word ``mathematical''
here.  Mathematicians have usually tended to ignore (even scoff at) some of
Kant's ideas, especially after the properties of non-Euclidean geometry 
got to be better known and it got to be hard to defend Kant's
idea that Euclidean geometry was the only conceivable one.  
\item{4.}  It is true that logicism and formalism did have some successes.
But since you brought this up, they ultimately {\it failed}.  As you 
may have read in the Davis and Hersh book, Kurt G\"odel eventually proved
a result called the Incompleteness Theorem which says, in effect, that
in any axiomatic mathematical system powerful enough to describe all of the arithmetic
of the integers, there are true statements that cannot be proved to be true within
the system and false statements that cannot be proved to be false within
the system.  Moreover, he also showed slightly later that 
one of these ``undecidable'' statements is that
that the system itself is consistent (that is, that it contains no 
contradictions).  
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 18
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in 
the sources and original thought -- 10
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly 
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 5
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 18
\item{2.}  (10) Is free of misspellings -- 9
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 9
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 13
\item{8.}  (10) Cites quotations and/or references correctly -- 10
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 93; Style and English Usage -- 92.
\vfill\eject
\noindent
{\it Max Pettinelli -- Euclid's Number Theory}
\bigskip
Your paper on some of the highlights of Euclid's treatment of number
theory is very good and well-written for the most part.  I have
a technical comment about citing your sources (see comment 1 below).
What you said about the Riemann zeta-function is not quite correct
either (see comment 4 below).  But I am glad you chose this topic
(you were the only one who did!) and I hope you found it interesting. 
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  This is mostly a technical point, but it is important.
 In a paper like this, when you draw on a statement 
in a source for one of the things you are claiming, even if you are
only giving a paraphrase (a rewording in your own words), you need
to provide a reference to the place in the source you are referring to.  
You do not do this consistently in this paper.  For instance, the location where
I marked comment 1 has a direct quotation for which you only 
identify the name of the author of the web page in the text of your paper.  
 David Joyce's web site should also be listed in 
the Works Cited, of course.  
The footnote you give on page 4 is closer to what should be done.  
The point is that you should get into the habit 
of including complete references as a matter of course {\it for every
quotation or paraphrase you use} for research papers 
in all of your classes.  Not doing this, in fact, can be considered a 
form of {\it plagiarism}.  As such it might be dealt with using the 
Academic Honesty policy.  I know you are 
not trying to conceal your sources.  
So I am only lowering you score in the ``cites quotations
properly'' category for this.  {\it But be careful about this point
in the future.}  
\item{2.}  I think it would be better to say it like this:  While Euclid
gives the argument for the three primes $A,B,C$, the argument
can be generalized to show that for {\it any finite list of primes}
with a $n$ entries, a number can be constructed
that must be divisible by some prime number not on the list.  
Hence the number of primes cannot be finite.  
\item{3.}  This sounds rather harsh.  It would be better to 
say something more neutral here -- perhaps ``Proving this statement
has turned out to be extremely difficult since all of the 
infinitely many even numbers must be accounted for.''
\item{4.}  The only place where you have run into some mathematical
difficulties is here in the description of the Riemann zeta-function.
What you say is not correct, but I have not penalized you too much
for this because this was certainly far beyond anything we
did in the course.  
The idea is that $\zeta(s)$ is defined as the sum of an infinite 
series:
$$\zeta(s) = \sum_{n=1}^\infty {1\over n^s}$$
for real $s > 1$.  (You may have seen series like this if you 
studied this topic in a calculus course.)
\medskip
\item{} Riemann (by the way, this is the same Riemann
we mentioned briefly toward the end of the course in connection
with non-Euclidean geometry) showed that it is possible to make
sense of this as a function of a variable $s$ taking {\it complex
number} values $s = u + it$.  The statement of the Riemann Hypothesis
is then that the only ``non-trivial'' zeroes of the function
$\zeta(s)$ occur at numbers of the form $s = {1\over 2} + it$.  This turns out to 
be related to properties of prime numbers because there
is another formula for $\zeta(s)$ coming from work of an
earlier mathematician named Leonhard Euler:
$$\zeta(s) = \prod_{p\ {\rm prime}} \left(1 - {1\over p^s}\right)^{-1}.$$
(The $\prod$ means to take the {\it product} of these factors.)
This is certainly the most famous currently unsolved problem in mathematics
and you might be interested to know that there is a $\$1$ million prize offered for a solution by the 
Clay Institute of Mathematics (whose web site you consulted).
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 18
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 10
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 10
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 18
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 9
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 15
\item{8.}  (10) Cites quotations and/or references correctly -- 5
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 98; Style and English Usage -- 92.
\vfill\eject
\noindent
{\it  Xuan Ha Nghiem -- Platonic Solids}
\bigskip
Your paper on the Platonic solids and some of the ways people have attempted
to use these shapes to understand properties of the physical world (some
valid and some invalid) is very good.  I especially like that you chose
a topic that no one else did and that you tied the topic of the paper
to our discussion of Raphael's {\it The School of Athens} in class.  
Your writing is also very strong here!

The only thing I would have liked to see more of was more of the discussion
of the Euler relation and the resulting proof that only 5 platonic solids
can exist.  See comment 3 below for a sketch of the details that you 
asked about in your email message.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  It would be better to say ``...with their hands in gestures 
symbolizing different aspects of their philosophies.''  (It is not really
possible to ``gesture at an aspect of a philosophy'' in the literal sense!)
\item{2.}  I think you mean that if you had four polygons meeting
at a vertex with angles of $90^\circ$, then the surface would have
to be a part of a {\it plane} -- that is, it could not curve in 
three-dimensional space to enclose a volume since the four faces
meeting at that vertex would all be in the same plane.
\item{3.}  This is the point you asked about in your email.  This is
one way to see it.  First, it can be seen that the numbers 
$$\eqalign{V &= {\rm number\ of\ vertices}\cr
           E &= {\rm number\ of\ edges}\cr
           F &= {\rm number\ of\ faces}\cr}$$
of a convex polyhedron must always satisfy 
$$V - E + F = 2.$$  
This is 
called the Euler relation, after the mathematician Leonhard Euler.  
For a Platonic solid, where the sides, angles, and edges are all congruent,
each vertex must have the same number $m\ge 3$ of edges meeting there.  Similarly, 
each face must have the same number $n\ge 3$ of edges.  Each edge
has two different endpoints, so
$$2E = mV,$$
since the total number of edges meeting at all $V$ vertices is $mV$, but
that counts each edge twice.  Similarly, each edge is a part of two 
different faces, so 
$$2E = nF.$$  
Solve these equations for $V$ and $F$ and substitute into the Euler relation:
$${2E\over m} - E + {2E\over n} = 2.$$
Then divide by $2E$ and rearrange to get
$${1\over m} + {1\over n} = {1\over E} + {1\over 2}.$$
Then the idea is that there are only a few different ways to get solutions of 
this equation with whole numbers $m,n,E$.  Note first that the right side 
is always strictly bigger than $1/2$.  This says that $m,n$ cannot both be
large.  The only solutions, in fact, are:
$$\matrix{m & n & E & {\rm polyhedron}\cr
          3 & 3 & 6 & {\it tetrahedron}\cr
          3 & 4 & 12 & {\it cube}\cr
          4 & 4 & 12 & {\it tetrahedron}\cr
          3 & 5 & 30 & {\it dodecahedron}\cr
          5 & 3 & 30 & {\it icosahedron}\cr}$$
\item{4.}  You should also give a source for this quotation.  Where did you 
find it?
\bigskip
\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 10
\item{2.}  (20) Accurately presents facts and viewpoints of sources -- 18
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 8
\item{4.}  (10) Gives evidence of independent evaluation of the claims in 
the sources and original thought -- 10
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly 
identifiable main ideas --10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 10
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 10
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 15
\item{8.}  (10) Cites quotations and/or references correctly -- 9
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 96; Style and English Usage -- 97.
\vfill\eject
\noindent
{\it Kaitlin O'Hagan -- }
\bigskip
This is a good summary of Hypatia's life and contributions.  It does not 
really show a lot of independent thought or evaluation of what you 
found in the different sources.  On the other hand, it is definitely good
that you looked beyond the easier Internet sources about her -- I think you
got a more balanced and complete picture that way.  As a technical point, I think it was
probably {\it not necessary} to list some of the sources you put in your
Works Cited list.  Since you do have {\it more authoritative sources}, 
for example, the student paper written
by an undergraduate at Agnes Scott College could have been 
omitted.  It is superficial at best and the information about
the commentary on Apollonius is much better and more complete in several of the
other sources you list.  

It might have been good to try to say more about what is known about
what Hypatia's mathematics consisted of (in particular the commentary on
Apollonius's {\it Conics}) and how it connected with topics 
we have discussed in this course. 

Your paper is very well-written.
\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  Some people doubt that Hypatia
originated the astrolabe.  Similar devices might
have been constructed quite a long time before Hypatia's time.
What we do know is that Synesius credited Hypatia with the idea,
as you say.
\item{2.}  I would say that this really has to be treated as a legend.
Saying she was physically beautiful is one way that some people have
tried to make her seem more like a tragic heroine.
\item{3.}  This is really an interpretation and a statement of
opinion, of course.  I do not believe there is any direct 
evidence we have about Cyril's emotional state at the time.  
So this probably deserves a reference to the source where
you found the interpretation, and a qualification that there
is really no way that we can know this for sure. 
\item{4.}  The fact that Cyril was canonized (much) later
is an interesting sidelight to the story.  It probably 
deserves more comment than the quick footnote that you 
give it.  People inclined to blame Cyril for Hypatia's
death have used this to criticize the role of Christianity
in this story, for instance.   Because Cyril did not become a saint until
long after his death, it would probably be better either
to always refer to him by this title or not to do it at all.
Throwing in the title at this point seems a bit odd.  


\noindent
{\it  Content and Structure -- The paper}
\bigskip
\item{1.}  (10) Draws on suitable and sufficient sources -- 8
\item{2.}  (20) Accurately and completely presents facts and viewpoints of sources -- 18
\item{3.}  (10) Provides sufficient textual evidence to support the argument -- 10
\item{4.}  (10) Gives evidence of independent evaluation of the claims in
the sources and original thought -- 7
\item{5.}  Has a clearly articulated and logical structure: 
\bigskip
\itemitem{a.}  (10) First paragraph lays out the topic or question -- 10
\itemitem{b.}  (10) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 10
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\itemitem{d.}  (10) Is concise, clear, and not too repetitive -- 10
\itemitem{e.}  (10) Has a clearly identifiable conclusion that draws together the evidence
presented -- 10
\bigskip
\noindent
{\it Style and English Usage -- The paper}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (10) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (10) Uses correct punctuation -- 9
\item{7.}  (15) Is free of jargon, cliches, and misused words -- 13
\item{8.}  (10) Cites quotations and/or references correctly -- 10
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 93; Style and English Usage -- 97.


\bye
