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\centerline{Montserrat 109N -- Mathematics Across Cultures}
\centerline{Syllabus -- Spring 2010}
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\leftline{Professor: John Little}
\leftline{Office: Swords Hall 331}
\leftline{Office Phone: (508) 793-2274}
\leftline{Office Hours: M,W,F 10am - 11am and 1 - 2 pm, T,R 1 - 2pm}
\leftline{Course Homepage:  {\tt http://mathcs.holycross.edu/\~{}little/Montserrat1011/Spring.html}}
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\noindent
{\it Food For Thought}
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\begin{verse}
No society, however small or remote, has ever lacked the\\
basic curiosity and ``number sense'' that is part of\\
the global mathematical experience.\\
$\qquad\qquad\qquad$\emph{G.G. Joseph, The Crest of the Peacock, p. 512}\\  
\end{verse}
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\noindent
{\it Course Description}
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Where did the arithmetic, algebra, and geometry that we all learn
come from?  Who invented (or discovered?) this material and when and why did it 
happen?  In the fall semester, we addressed these and other questions through a 
study of several topics from basic algebra and geometry -- most notably
\begin{packed_item}
\item the solution of quadratic equations by techniques including the \emph{quadratic formula} 
from algebra, and 
\item the \emph{Pythagorean theorem} from geometry.  
\end{packed_item}
We presented a fairly standard ``modified Eurocentric'' account of this, showing
how the mathematical ideas of the ancient Egyptians and Babylonians were expanded
and developed by the Greeks through the classical and Hellenistic periods, codified
in the {\it Elements} of Euclid, then transmitted to modern Europe by way of the
medieval Islamic caliphates (especially the center of learning at Baghdad) and
finally extensively reexamined and greatly extended (in particular through the discovery of non-Euclidean
geometries) in modern Europe.  

This semester, we will continue our study of mathematics across cultures and through time.
We will begin by casting our net quite a bit wider and looking
at how ``mathematical thinking'' can be found in many aspects of 
diverse cultures from all over the world:
\begin{itemize}
\item in the ways people have conceptualized and developed systems for
recording and measuring the passage of {\it time},
\item in the ways people have developed maps and models for the 
organization of {\it space} for orientation and navigation,
\item in the ways people have created {\it games and puzzles},
\item in some of the ways people have used ideas of symmetry and other  
mathematical structures to create {\it decorative elements in architecture, 
textiles and other everyday artifacts, art and music}.
\end{itemize}
Why is this important?  The examples we will look at should 
be pretty strong evidence for accepting the basic premise from
G.G. Joseph's book articulated above.  And if we accept that, 
then we open ourselves to the possibility that perhaps our
``modified Eurocentric'' account of the history of mathematics
needs to be modified {\it even more} in order to obtain a more historically
accurate picture of {\it the global mathematical experience}!
We will close out the semester and the year by
seeing how Indian, Chinese, and Islamic mathematicians were 
often centuries ahead of their European counterparts and
consider how even the ``modified Eurocentric'' picture is
something of a distortion because it obscures when and where
important ideas were first developed.   
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\noindent
{\it Course Objectives}
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\noindent
The major objectives of the course will be:
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\begin{packed_enum}
\item[1)] To examine examples of mathematical 
thinking across cultures and through time to understand
how and why those ideas were developed.
\item[2)] To deepen your understanding of mathematics as an 
area of human study.  
\item[3)] To further your development as writers and speakers.
\item[4)] To participate in and contribute to the common activities of the 
Natural World Cluster of the Montserrat program -- 
\begin{packed_enum}
\item[(a)] Medical Ethics Presentation -- Thursday, February 17 (7:30 - 8:30pm).
\item[(b)] Boston ``Emerald Necklace'' Conservancy and Museum trip -- Saturday, April 16 (full day).  
\item[(c)] Natural World Cluster End-of-Year Dinner -- Monday, May 2 (5 - 7pm). 
\end{packed_enum} 
\end{packed_enum}
\noindent
{\it Texts}
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\noindent
The main mathematical texts for the course are:
\begin{packed_enum}
\item[1)]  G. G. Joseph, \emph{The Crest of the Peacock}, Princeton University Press.
\item[2)]  M. Ascher, \emph{Mathematics Elsewhere}, Princeton University Press.
\end{packed_enum}
We will also read and discuss some sections of the Natural World Cluster common reading:
\begin{enumerate}
\item[2)]  J. Diamond, \emph{Collapse}, Penguin Books.  
\end{enumerate}
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\noindent
{\it Course Schedule}
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A detailed day-by-day course schedule and listing of required and suggested outside events
will be maintained on the course homepage.  That listing is a tentative, evolving schedule,
so you will probably want to refer to it frequently.  Any important changes will also
be announced in class well in advance.   
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\noindent
{\it Assignments and Grading}
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\begin{packed_enum}
\item[1)]  Midterm Exam (20 \% of course grade) -- tentative date: Friday, March 18.
\item[2)]  Final Project and Presentation (30 \% of course grade) -- The major assignment
this semester will be a research project done in pairs, and leading to a 
longer paper (about 15 to 20 pages) and an oral presentation of roughly 20 minutes.  The presentations
will be given the final two weeks of the semester.  
\item[3)]  Problem Sets (about 6 through the semester -- 10 \% of course grade)
\item[4)]  In-class group work (about 6 assignments -- 10 \% of course grade)
\item[5)]  Two shorter (roughly 5 page) papers related to the readings 
and other topics.  (More information and guidelines to be distributed later) (25 \% of course grade)   
\item[6)]  Class participation (5 \% of course grade)
\end{packed_enum}
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I will be keeping your course average in numerical form throughout the semester, and only converting to a letter for the final course grade. The course grade will be assigned according to the following conversion table (also see Note below):
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\begin{packed_item}
\item A -- 94 and above
\item A- -- 90 - 93
\item B+ -- 87 - 89
\item B -- 84 - 86
\item B- -- 80 - 83
\item C+ -- 77 - 79
\item C -- 74 - 76
\item C- -- 70 - 73
\item D+ -- 67 -- 69
\item D -- 60 - 66
\item F -- 59 and below.
\end{packed_item}
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\noindent
Note: Depending on how the class as a whole is doing, some downward adjustments of the above letter grade boundaries may be made. No upward adjustments will be made, however. (This means, for instance, that an 85 course average would never convert to a letter grade of B- or below, although it might be a B+ in some circumstances.) If you ever have a question about the grading policy or your standing in the course, don't hesitate to ask me.
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\noindent
{\it Advice On How To Succeed In This Class}
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\noindent
{\bf A good ``work ethic" is key.}  As you should be able to tell
from the course description above, you do not need to be a 
``math genius'' to do well in this course.  But you will need 
to put in a consistent effort and keep up with the reading and 
assignments.

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\noindent
{\bf Come to class.}  Unless you are deathly ill, have a genuine family 
emergency, are away at a game or meet of a college athletic team, etc. 
plan on showing up here at 9:00 am every Monday, Wednesday, 
and Friday this semester.  Many of the class meetings will be 
structured around discussions or student presentations.  Your participation 
is expected and needed for the success of the course!

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\noindent
{\bf Take notes and use them.} This may seem obvious, but it is worth 
saying!  Used intelligently, your notes can be a valuable resource as 
you work on problem sets and prepare for exams.

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\noindent
{\bf Use the texts and class notes actively.} Reading about mathematics
is not like reading a novel.  You will probably need to read and think over things 
more than once.  You may want to work through examples or draw your own 
diagrams to understand some of the Euclidean proofs that we do.  

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\noindent
{\bf Set up a regular study schedule and work at a steady pace.} It's not easy 
to play catch-up in a mathematics course (even when the course is part of a 
first-year program with additional goals beyond the mathematics).  You should 
expect to budget at least 6 hours in a typical week for work outside of class. 
The best way to use your time is to do a few problems, some reading from the 
books, and reviewing of class notes every day.

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\noindent
{\bf Most importantly, if you are having difficulty learning something, 
get help as soon as possible.}  You can do this by asking questions during 
class (any time something isn't clear), or seeing me during office hours.

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\noindent
{\it Statement on Academic Integrity}
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All education is a cooperative enterprise between teachers and students.  This cooperation works well only when there is trust and mutual respect between everyone involved.  To be become an engaged and advanced learner, you must be able to think and work both independently and in concert with your peers.  
 
The College academic honesty policy states: 
``As an institution devoted to teaching, learning, and intellectual inquiry, Holy Cross expects all members of the College community to abide by the highest standards of academic integrity. Any violation of academic honesty undermines the student-teacher relationship, thereby wounding the whole community. The principal violations of academic honesty are plagiarism, cheating, and collusion.

Plagiarism is the act of taking the words, ideas, data, illustrative material, or statements of someone else, without full and proper acknowledgment, and presenting them as one's own.

Cheating is the use of improper means or subterfuge to gain credit or advantage. Forms of cheating include the use, attempted use, or improper possession of unauthorized aids in any examination or other academic exercise submitted for evaluation; the fabrication or falsification of data; misrepresentation of academic or extracurricular credentials; and deceitful performance on placement examinations. It is also cheating to submit the same work for credit in more than one course, except as authorized in advance by the course instructors.

Collusion is assisting or attempting to assist another student in an act of academic dishonesty.”

The full statement on Academic Honesty in the College Catalog will be posted on the Natural World/Montserrat Moodle site and is available at
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\centerline{\tt http://www.holycross.edu/catalog/academic-honesty-policy.pdf}
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\noindent
The temptation to engage in an act of academic dishonesty will almost certainly arise, but the chance to possibly enhance a single grade is not worth the loss of your personal integrity.  If you do not know how to correctly cite reference materials, consult with your professor, the campus Writer’s Workshop, or visit one of the links below (also posted on the Natural World/Montserrat Moodle site).

\noindent
Department of History: 
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\centerline{\tt http://www.holycross.edu/departments/history/website/academichonesty.htm}
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\noindent 
Department of English (link to Houghton Mifflin booklet, "Understanding Plagiarism: A Student Guide to Writing Your Own Work"):
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\centerline{\tt
http://college.cengage.com/english/plagiarism\_prevention.html}
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\noindent
Houghton Mifflin, ``The Plagiarism Zone'' 
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\centerline{\tt http://college.hmco.com/english/plagiarism\_prevention.html}
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\noindent
NOTE:  If in doubt about what you plan to do or write violates academic honesty, PLEASE ASK!

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\noindent
{\it Specific Guidelines for this Course}
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In this course, all examinations will be closed-book. No sharing of information with other students in any form will be permitted during exams. On group discussion write-ups, 
close collaboration with the other members of your group is expected. 
On the individual problem sets, discussion of the questions with other 
students in the class and with me during office hours is allowed, 
{\it even encouraged}. However, your final problem solutions should 
be prepared individually and the wording and organization of your final 
problem solutions should be entirely your own work.  Moreover, if you do 
take advantage of any of the above options for discussion of problems with 
others, you will be required to state that fact in a footnote accompanying 
the problem solution. Failure to follow this rule will be treated as a violation 
of the College's Academic Integrity policy.  For the papers, 
if you do consult a source other than the course texts, include a full 
reference in a bibliography section at the end of your paper, and identify 
any direct quotations.  Information about the acceptable formats for doing 
this will be distributed with the paper assignments.  
\end{document}


{\it Departmental Statement on Academic Integrity -- Note:  This section will be 
changing -- common cluster statement for Montserrat program}
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\noindent
{\bf Why is academic integrity important?}
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All education is a cooperative enterprise between teachers and students. This cooperation works well only when there is trust and mutual respect between everyone involved. One of our main aims as a department is to help students become knowledgeable and sophisticated learners, able to think and work both independently and in concert with their peers. Representing another person's work as your own in any form (plagiarism or ``cheating''), and providing or receiving unauthorized assistance on assignments (collusion) are lapses of academic integrity because they subvert the learning process and show a fundamental lack of respect for the educational enterprise.
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\noindent
{\bf How does this apply to our courses?}
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You will encounter a variety of types of assignments and examination formats in mathematics and computer science courses. For instance, many problem sets in mathematics classes and laboratory assignments in computer science courses are individual assignments. While some faculty members may allow or even encourage discussion among students during work on problem sets, it is the expectation that the solutions submitted by each student will be that student's own work, written up in that student's own words. When consultation with other students or sources other than the textbook occurs, students should identify their co-workers, and/or cite their sources as they would for other writing assignments. Some courses also make use of collaborative assignments; part of the evaluation in that case may be a rating of each individual's contribution to the group effort. Some advanced classes may use take-home examinations, in which case the ground rules will usually allow no collaboration or consultation. In many computer science classes, programming projects are strictly individual assignments; the ground rules do not allow any collaboration or consultation here either.
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\noindent
{\bf What are the responsibilities of faculty?}
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It is the responsibility of faculty in the department to lay out the guidelines to be followed for specific assignments in their classes as clearly and fully as possible, and to offer clarification and advice concerning those guidelines as needed as students work on those assignments. The Department of Mathematics and Computer Science upholds the College's policy on academic honesty. We advise all students taking mathematics or computer science courses to read the statement in the current College catalog carefully and to familiarize themselves with the procedures which may be applied when infractions are determined to have occurred.
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\noindent
{\bf What are the responsibilities of students?}
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A student's main responsibility is to follow the guidelines laid down by the instructor of the course. If there is some point about the expectations for an assignment that is not clear, the student is responsible for seeking clarification. If such clarification is not immediately available, students should err on the side of caution and follow the strictest possible interpretation of the guidelines they have been given. It is also a student's responsibility to protect his/her own work to prevent unauthorized use of exam papers, problem solutions, computer accounts and files, scratch paper, and any other materials used in carrying out an assignment. We expect students to have the integrity to say ``no'' to requests for assistance from other students when offering that assistance would violate the guidelines for an assignment.
\vskip 10pt
\noindent
{\bf Specific Guidelines for this Course}
\vskip 10pt
In this course, all examinations will be closed-book. No sharing of information with other students in any form will be permitted during exams. On group discussion and computer lab write-ups, close collaboration with the other members of your group is expected. On the individual problem sets, discussion of the questions with other students in the class
and with me during office hours is allowed, {\it even encouraged}. However, your final problem solutions should be prepared individually and the wording and organization of your final problem solutions should be entirely your own work. Moreover, if you do take advantage of any of the above options for discussion of problems with others, you will be required to state that fact in a footnote accompanying the problem solution. Failure to follow this rule will be treated as a violation of the College's Academic Integrity policy.  For the papers, if you do consult a 
source other than the course texts, include a full reference in a 
bibliography section at the end of your paper, and identify any direct quotations.  Information
about the acceptable formats for doing this will be distributed with the paper assignments.  
\bye

