\documentclass[11pt]{article}
\def\Z{\mathbb{Z}}
\def\Q{\mathbb{Q}}
\def\R{\mathbb{R}}
\def\C{\mathbb{C}}
\usepackage{latexsym,amsmath,amssymb}
\usepackage[all]{xy}
\setlength{\textwidth}{6.5in}
\setlength{\oddsidemargin}{0in}
\setlength{\topmargin}{-0.2in}
\setlength{\textheight}{9in}
\begin{document}
\centerline{Montserrat 107Q -- Thinking About Mathematics}
\centerline{Syllabus -- Spring 2017}
\vskip 10pt
\leftline{Professor: John Little}
\leftline{Office: Swords Hall 331}
\leftline{Office Phone: (508) 793-2274}
\leftline{Office Hours: Monday 10 - 11am, Tuesday 9 - 10am, Wednesday 1 - 2pm, Thursday, 2 - 3pm,}
\leftline{$\qquad$ Friday 10 - 11am, and by appointment}
\leftline{Course Homepage:  {\tt http://mathcs.holycross.edu/\~{}little/Montserrat201617/Spring.html}}
\vskip 10pt
\noindent
{\it Core Human Questions Cluster Theme}
\vskip 10pt
If borders define us but we want to transcend them, how then shall we live?
\vskip 10pt
\noindent
{\it Course Description}
\vskip 10pt 
This course is a part of the {\it Core Human Questions (CHQ) Cluster} of the Montserrat 
program.  This means that at various times we will be addressing one 
or several of the following objectives:
\vskip 10pt
\begin{itemize}
\item addressing the general aims of Montserrat -- continued development of your
thinking, writing, and communication skills, and the fostering of connections between
living, learning and doing in your college education,
\item engaging with the common readings and theme of this year's CHQ Cluster, 
\item participating in various common activities (tentatively) scheduled for all of the 
seminars in the CHQ Cluster, including:
\begin{enumerate}
\item[(a)] Showing of film {\it Pan's Labyrinth}, 7:30pm Monday, January 30, Seelos Theater.
\item[(b)] Montserrat cross-cluster public speaking night, Thursday, February 23, 
Hogan Campus Center (more details to follow!).
\item[(c)] Field trip to MASS MoCA and Hancock Shaker Village, Saturday, March 25.
\item[(d)] Performance of ``The Royal Family,'' 8:00pm Thursday, April 6, Fenwick Theater.
\item[(e)] End-of-year cluster banquet, 6:00pm Tuesday May 2, Hogan Ballroom.
\end{enumerate}   
\item and finally, studying the specific subject matter of this seminar.  
\end{itemize}
\vskip 10pt
In a 2005 poll discussed in {\it Loving $+$ Hating Mathematics}, 
almost 40\% of the adults surveyed said they actively 
hated mathematics in school, more than any other subject.  Yet at the same 
time, almost 25\% said they liked mathematics best, often because they
liked its unambiguous, ``right or wrong'' nature.  A few people even devote
their lives to studying the subject, but (in my experience, at least) 
many of them would disagree strongly about what makes it appealing -- they would
point out the possiblity of exercising real creativity to discover beautiful
new patterns in the mathematical realm as the most attractive feature!  What 
is it about mathematics that creates such divergent reactions?  

It is certainly true that most of the reactions to mathematics 
described above come from the way the subject is taught in elementary
and secondary schools.  For instance, consider the way you were 
probably taught in algebra class to solve quadratic equations:
$$ax^2 + bx + c = 0,$$
when simpler techniques such factorization do not apply directly.
If your training was typical, you were probably told that you 
``just need to memorize the quadratic formula:''
\begin{equation}
\label{quadform}
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
\end{equation}
And then you were drilled, and drilled, and drilled some more on solving
lots of equations of this form using that.  You may have developed a phobia
about remembering the complicated formula and come to hate what should 
be a basic and important algebraic technique.  

I think part of the problem here is that (\ref{quadform}) seems
to come out of thin air. The formula (1) also uses the full power
(and potential ambiguity and scariness) of symbolic algebraic notation.  
There are an awful lot of questions that should come to mind when you start 
to dig deeper into what is going on here:  Why are letters used in a formula
like this?  What is it about  
$x$ that makes it a ``variable,'' and how is it different from the other symbolic
constants $a,b,c$?  Does $x$ have a value from the start?  What exactly
is the sequence of operations you need to do to evaluate the formula 
on the right?  Others might come to mind as well. 
 Bright students often ask these questions, but the
response is often ``don't worry about that--just memorize the formula,
plug and chug.''  And woe unto anyone who makes a mistake carrying
that out -- that's when the teacher's red pen comes out!  {\it Is 
it any wonder a lot of people end up hating mathematics?}  

I personally believe that another aspect of the problem is that 
most students have no appreciation of
\begin{itemize}
\item how hard it was, and 
\item how long it took people 
\end{itemize}
to come up with this compact and powerful symbolic form.  They are 
just told to memorize the formula without any indication of how or why it
is true or where it came from.  

I don't necessarily want to claim that knowing the history of
things like this is a panacea for learning that will solve all the 
problems of mathematics education.  However, I do think that 
realizing that it took a lot of ``fumbling around'' before things like this were
really understood and codified in the form we use now has to help some
students.  Real, smart people struggled in exactly the ways they still
do, and mastering mathematics is more a matter of confidence and persistence
than any sort of ``innate talent.''

So in MONT 107Q, one of our major themes will be an examination of
where the mathematics you have learned, in particular the quadratic formula (\ref{quadform}),
came from and how the historical development of algebra, 
(and geometry and arithmetic) might influence the ways the subject is taught.  

We will do this by considering passages from 
some of the most important original texts, in as close as possible
to their original form (but translated into English):
\begin{itemize}
\item some Old Babylonian problem texts -- actual records
of students learning mathematics in scribal schools from around 1800 BCE,
\item several sections of one of the most famous
Greek mathematical texts -- the {\it Elements} of Euclid (around 300 BCE),
\item the {\it Arithmetica} of Diophantus (around 250 CE), one of the
first surviving attempts at a symbolic algebra
\item the very influential {\it Hisab al-jabr w'al muqabala}
(around 830 CE) of Muhammad ibn Musa al-Khwarizmi
\item the {\it Ars Analytica} of Fran\c cois Vi\`ete, and
\item {\it La G\'eometrie} of Ren\'e Descartes.
\end{itemize}
\vskip 10pt
\noindent
{\it Some Groundrules}
\vskip 10pt
Most class meetings will be devoted to discussions, oral presentations,
or work in smaller groups, so your active participation will be important
for the success of what we do. 
\begin{itemize}
\item Unless specifically directed otherwise, please \emph{turn off}
all cell phones, tablet or laptop computers and other similar
electronic devices for the duration of each class meeting -- your full 
attention and participation will be necessary.
\item No distracting or ``provocative'' clothing, headgear, or other 
personal items in class, please.
\item In on-campus events, possible off-campus trips next semester, etc. you are representing
this seminar, the Montserrat program, and, by extension, Holy Cross in a wider 
community.  Take responsibility and regulate your behavior accordingly. 
\item In discussions, there may be times that you disagree with Prof. Little
or with a classmate.  Please feel free to express that disagreement 
and be prepared to say why you disagree and back up your ideas with evidence.  
But please keep the conversation civil and respectful.
\end{itemize}
\vskip 10pt
\noindent
{\it Course Texts}
\vskip 10pt
\noindent
The main mathematical texts for the course are:
\begin{enumerate}
\item[1)]  G. G. Joseph, \emph{The Crest of the Peacock}, Princeton University Press (carried over from last semester)
\item[2)]  Reuben Hersh and Vera John-Steiner, {\it Loving $+$ Hating Mathematics}, Princeton University Press, ISBN 978-0-691-142470
\end{enumerate}
We will also read and discuss the Core Human Questions Cluster common readings:
\begin{enumerate}
\item[3)] Cormac McCarthy, {\it All the Pretty Horses}, Vintage Paperback, ISBN 978-0-679-74439-9,
\item[4)]  The {\it Metamorphoses} of Ovid, verse translation by Allen Mandelbaum, Harvest Books, ISBN 978-0-15-600126-7,
\item[5)] Ursula Le Guin, {\it The Left Hand of Darkness}, Penguin Paperback, ISBN 978-0-441-47812-5.  
\end{enumerate}
It is expected that Holy Cross students will have textbooks and other required class materials in order to achieve academic success.  If you are unable to purchase course materials, please speak to a representative at the Office of Financial Aid for assistance.
\vskip 10pt
\noindent
{\it Course Schedule}
\vskip 10pt
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.   
\vfill\eject
\noindent
{\it Assignments and Grading}
\vskip 10pt
\begin{enumerate}
\item[1)]  Midterm Exam (15 \% of course grade) -- tentative date: Friday, March 31.
\item[2)]  Final Project (30 \% of course grade: bibliography, paper, and oral presentation) -- presentations will be scheduled for the final four class
meetings in May; papers due Monday, May 8.
\item[3)]  Problem Sets (about 5 through the semester -- 10 \% of course grade)
\item[4)]  In-class group work leading to oral presentations 
(about 4 assignments -- 10 \% of course grade).
More information about these assignments will be distributed later.
\item[5)]  Two essays related to the readings and other topics.  
More information and guidelines for each of these assignments to be 
distributed later (20 \% of course grade)   
\item[6)]  Reflection paper (10 \% of course grade) -- this can be written
in response to any of our CHQ common events (the film {\it Pan's Labyrinth}, 
the field trip to MASS MoCA and the Hancock Shaker Village, or the play 
{\it The Royal Family}.
\item[7)]  Participation in preparations for and program of 
Montserrat public speaking night (5 \% of course grade) 
\end{enumerate}
\vskip 10pt
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):
\vskip 10pt
\begin{itemize}
\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{itemize}
\vskip 10pt
\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.
\vskip 10pt
\noindent
{\it Advice On How To Succeed In This Class}
\vskip 10pt
\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.

\vskip 10pt
\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. 
please plan on showing up here at 9:00 am every Monday, Wednesday, 
and Friday this semester.  As mentioned before, many of the class meetings will be 
structured around discussions or student presentations.  Your regular attendance
and participation is expected and needed for the success of the course!

\vskip 10pt
\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.

\vskip 10pt
\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.  

\vskip 10pt
\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.

\vskip 10pt
\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.

\vskip 10pt
\noindent
{\it Statement on Academic Integrity}
\vskip 10pt
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 is available at
\vskip 10pt
\centerline{\tt http://www.holycross.edu/catalog/academic-honesty-policy.pdf}
\vskip 10pt
\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 or the campus Writer’s Workshop.
NOTE:  If you are in doubt about whether what you plan to do or write violates academic honesty
guidelines, PLEASE ASK!
%, or visit one of the links below.
%
%\noindent
%Department of History: 
%\vskip 10pt
%\centerline{\tt http://www.holycross.edu/departments/history/website/academichonesty.htm}
%\vskip 10pt
%\noindent 
%Department of English (link to Houghton Mifflin booklet, "Understanding Plagiarism: A Student Guide to %Writing Your Own Work"):
%\vskip 10pt
%\centerline{\tt
%http://college.cengage.com/english/plagiarism\_prevention.html}
%\vskip 10pt
%\noindent
%Houghton Mifflin, ``The Plagiarism Zone'' 
%\vskip 10pt
%\centerline{\tt http://college.hmco.com/english/plagiarism\_prevention.html}
%\vskip 10pt
%\noindent

\vskip 10pt
\noindent
{\it Specific Guidelines for this Course}
\vskip 10pt
In this course, all examinations will be closed-book. No sharing of information with other 
students or consultation of electronic or physical sources 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 essays, 
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}
\vskip 10pt
\noindent
{\bf Why is academic integrity important?}
\vskip 10pt
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.
\vskip 10pt
\noindent
{\bf How does this apply to our courses?}
\vskip 10pt
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.
\vskip 10pt
\noindent
{\bf What are the responsibilities of faculty?}
\vskip 10pt
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.
\vskip 10pt
\noindent
{\bf What are the responsibilities of students?}
\vskip 10pt
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

