%  Syllabus
%  21-110: Problem Solving in Recreational Mathematics, spring 2010
%  Brian Kell <bkell@cmu.edu>

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\centerline{\titlefont 21-110: Problem Solving in Recreational Mathematics}
\centerline{\smfont Section~A, spring~2010, 9~units}
\centerline{\bf Syllabus}

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\hrule\medskip

{\bf Time and place:} Mondays, Wednesdays, and Fridays, 1:30--2:20~p.m., in
Porter Hall~A22

{\bf Textbooks:} {\it Problem Solving Through Recreational Mathematics}, by
Bonnie Averbach and Orin Chein, ISBN 0-486-40917-1; {\it Thinking
Mathematically}, by John Mason, Leone Burton, and Kaye Stacey, ISBN
0-201-10238-2

{\bf Web page:} {\tt http://www.math.cmu.edu/\char126 bkell/21110-2010s/}

\smallskip

{\bf Instructor:} Brian Kell

{\setbox0=\hbox{\bf Office: }\advance\leftskip by\wd0

\noindent\llap{\copy0}%
Physical Plant Building (PPB)~342. To get there: Go to Wean Hall. Take the
elevator to the first floor. Exit Wean Hall (you will be facing north). Follow
the sidewalk across the street and around the corner of the next building you
come to (the FMS~Building). You will come to a small plaza. At the southwest
corner of this plaza is a small building with four big water chillers on the
roof (or some kind of steam-producing things, anyway). That's the Physical
Plant Building. My office is just inside the door.

}

{\bf Office phone:} 412-268-1447

{\bf E-mail:} {\tt bkell@cmu.edu}

{\bf Office hours:} Mondays and Wednesdays, 2:30--4:00~p.m.

If you want to meet at a different time, that's fine; please e-mail me to let
me know. The most up-to-date version of my weekly schedule is available online
at\par
\centerline{\tt http://www.zifyoip.com/me/sched/2010/spring.html}
\noindent and is posted outside my office door; I am often in my office when
I'm not doing something else.

\smallskip

{\bf Math department office:} Wean Hall~6113, 412-268-2545

} % end \parindent=0pt

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\noindent{\titlefont Welcome to Problem Solving in Recreational Mathematics!}

\nobreak\smallskip

\noindent The goals of this course are threefold:

\nobreak\smallskip

\item{$\bullet$} to develop problem-solving techniques that can be used to
tackle various mathematical and logical problems;

\item{$\bullet$} to improve your abilities to organize and analyze information,
to think creatively about a problem, and to clearly communicate and justify
your ideas; and

\item{$\bullet$} to investigate some of the areas of recreational mathematics
in the spirit of pure curiosity.

\smallskip

\noindent I welcome comments and feedback about this course at any time. Please
feel free to send me an e-mail with your thoughts, stick a note under my office
door, or deliver a note to the math department office and ask them to put it in
my mailbox. For totally anonymous comments, visit the course Web page; there is
a link to a form you can fill out that will send your comments to me
anonymously.

\medbreak

\noindent{\bf Academic integrity}

\nobreak\smallskip

\noindent The most important rule in this course is this: You are expected to
be honest. This is a simple matter of respect toward me and the other students
in the class. You must abide by the Carnegie Mellon Statement on Academic
Integrity, available online at {\tt http://www.studentaffairs.cmu.edu\slash
theword\slash acad\_standards\slash integrity.html}. In this course, this
primarily means that you should never turn in work that is not your own.

This does not mean that you are not allowed to work with other students. You
are certainly welcome to collaborate on homework problems; it is often more
fruitful and enjoyable to work with other people when trying to figure
something out. They can give you a different perspective or fresh insight on
the problem. Conversely, explaining one of your ideas to another problem forces
you to clarify your thoughts and can help to highlight flaws you may have
previously overlooked. However, if you work with others to come up with a
solution, afterward you should go away and write it up on your own. You should
not base your written homework on another student's written homework, and never
put your name on anything you do not understand.

Please familiarize yourself with the Policy on Cheating and Plagiarism at
{\tt http://www.cmu.edu\slash policies\slash documents\slash Cheating.html} and
the Undergraduate Academic Disciplinary Actions Over\-view at
{\tt http://www.cmu.edu\slash policies\slash documents\slash AcadRegs.html}. I
will be happy to answer any questions you may have about academic integrity.

\medbreak

\noindent{\bf What is ``recreational mathematics,'' anyway?}

\nobreak\smallskip

\noindent Some people think of mathematics as the process of adding and
multiplying lots of numbers together. Others see it as a big collection of
rules and formulas that need to be memorized and regurgitated when necessary to
find ``The Answer.'' There are also people who view mathematics merely as a
tool that must be used in order to get useful things done in science,
engineering, medicine, and so on.

While all of these impressions of mathematics are valid to a greater or lesser
extent, there is another side of mathematics that most people do not see. This
is the side of mathematics that is beautiful and intriguing in its own right.
Many mathematicians study mathematics for its own sake---they think about
mathematical problems and puzzles purely out of curiosity, not because these
problems are particularly {\it useful\/} for anything. (On the other hand,
again and again throughout history mathematical problems that were originally
studied with no ``useful'' purpose in mind have found very important practical
uses later. Why this should be so is a topic of much philosophical debate.)

This is what recreational mathematics is---mathematical problems that people
play with for no other reason than that they are interesting. Topics in
recreational mathematics include magic squares, chessboard problems, logical
puzzles, paradoxes, Sudoku, Pythagorean triples, polyominoes, shapes and
symmetry, origami, fractals, Pascal's triangle, probability, prime numbers,
number bases, Fibonacci numbers, palindromes, Nim, knots, and even coloring
shapes on the surface of a donut! We will look at some of these topics in this
course.

In recreational mathematics the {\it answer\/} is not the important point. Much
more important is the {\it process\/} used to find the answer. For one thing,
the process can often be reused to solve other problems. Also, careful
examination of the process not only can provide a proof that the answer is
correct but also can lead to the discovery of deeper mathematical truths. For
this reason, most of the points on homework assignments will be given for clear
and thorough explanations and justifications of the reasoning underlying your
solution.

The problems and puzzles in this class should be interesting to you. Hopefully
you will find yourself thinking about these problems at odd times: in bed
before falling asleep, in the shower, or walking around campus. That's a good
sign!

\medbreak

\noindent{\bf Necessary background}

\nobreak\smallskip

\noindent There are no official prerequisites for 21-110. We will be using
ideas from high-school algebra and geometry; if at any time you feel shaky with
some of these ideas, please come talk to me and I will be glad to help refresh
your memory. I doubt we will use much trigonometry, and there will be no
calculus knowledge required.

\medbreak

\noindent{\bf Class structure}

\nobreak\smallskip

\noindent Usually at the end of class I will give a reading assignment or a
problem to work on before the next class. If I give a problem, I would like at
least one person to present a solution to it at the beginning of the next
class. Everyone should aim to present two or three such solutions over the
course of the semester.

As far as possible, I would like to avoid standing at the front of the
classroom and just delivering a lecture (though I can do this if the class
would prefer it). I think that the course will be more interesting and
enjoyable if we can have meaningful and lively discussions. However, this
requires you to take this course seriously, do the assigned reading, and think
about problems outside of class. If everyone does this, then when class starts
everyone will have a basic idea of what's going on, and we can spend more time
exploring the details and tackling some of the more interesting and challenging
ideas.

\medbreak

\noindent{\bf Grading}

\nobreak\smallskip

\noindent There will be roughly 10 graded homework assignments given over the
course of the semester, all of equal weight. Together these homework
assignments will constitute 70\% of your course grade. Another~20\% will be a
project. The remaining 10\% of your course grade will be for class
participation. Your final grade for this course will be determined according to
the following scale.

\nobreak\medskip

\centerline{\hss\vbox{\offinterlineskip
\hrule\vskip2pt\halign{\strut\hfil#\enspace&&\enspace\hfil#\hfil\cr
If you get at least this percentage:&
	92\%&84\%&76\%&68\%\cr
Then you are guaranteed at least this grade:&
	A&B&C&D\cr
}\vskip2pt\hrule}\hss}

\medbreak

\noindent{\bf Graded homework}

\nobreak\smallskip

\noindent You should start thinking about the homework problems early. Most of
the problems will require time, so that you can think about them from several
different angles. It is not wise to wait until the night before the homework is
due to start---this will lead to frustration. If you start early you can stay
rested and {\it have fun\/} with the problems!

As described in the ``Academic integrity'' section above, you are welcome to
work with other students on the homework, but write up your solution yourself.
If you are really stuck on a homework problem, put it aside and come back to it
later. If you still can't make progress, feel free to come talk to me about it.

Explaining your solutions will require a lot of writing. Often English
sentences and paragraphs will constitute much more of your solution than
mathematical symbols will (though symbols have their place too, of course). For
this reason I recommend typing your solutions (except perhaps figures), so that
you can easily and cleanly revise what you have written. The homework you
hand~in should be a polished final draft, but it will take several intermediate
drafts to get there. Do not expect to produce your final draft on your first
attempt!

Your submitted homework assignment is expected to meet the guidelines described
in the ``Quality expectations for submitted work'' below.

\medbreak

\noindent{\bf Project}

\nobreak\smallskip

\noindent There will be a project in this course. You may work in a group of up
to four people on the project. It will tie together several topics we will talk
about in the course and will require creative thinking to complete. More
information will be given about the project later.

\medbreak

\noindent{\bf Attendance and participation}

\nobreak\smallskip

\noindent Many math courses focus on technical mastery of a relatively fixed
set of facts, techniques, and concepts. However, this course is somewhat
different. It focuses primarily on the exploration and interpretation of
mathematical ideas and problem-solving techniques, rather than the memorization
and manipulation of formulas. An important part of this course will be group
discussion and activities in class, so attendance and participation are
strongly encouraged.

The class participation portion of your course grade will be based on such
things as presenting problems at the beginning of class (see ``Class
structure'' below), answering (and asking!) questions in class, contributing to
class discussions, and so forth.

Just as it is important that you attend class, it is also important that you
arrive on time. Coming in late is disruptive and disrespectful to me and your
fellow classmates. If you do arrive late, please enter the room and take your
seat quietly. Likewise, if you must leave class early, please do so as quietly
and considerately as you can.

While in class, please turn off your cell phone or set it to silent mode.

If you miss class, you can check the calendar on the course Web page to find
out what we did.

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\noindent{\bf Quality expectations for submitted work}

\nobreak\smallskip

\noindent Submitted work (including the project) is expected to meet the
following standards for quality. Work which does not meet these standards will
not be accepted.

\smallskip

\item{$\bullet$} {\bf Be academically honest.} Never put your name on work that
is not yours or work you do not understand, and always give credit where credit
is due. Remember: Taking someone else's work or ideas and presenting them as
your own is plagiarism, even if you change the wording. Provide a list of
sources other than the textbooks (if any) that you used to do the assignment,
and state clearly that you are copying or mimicking an example from the book
(if appropriate). If you worked with other students in the class to solve a
problem, be sure to write your results {\it in your own words}, and include a
list of your collaborators. Do~not ever copy text directly from another source,
even with attribution, unless it is a short quote properly marked as such.

\item{$\bullet$} Put your name (first and last) on the top of every page you
turn in. Do not include your student~ID number or your Social Security number.
On the first page, include a short description of the assignment (a few words
as a title would be fine---just so I know what it is I'm looking at).

\item{$\bullet$} Leave wide margins (1.5~inches all around is nice), so that I
have enough blank space on each page to write comments. Do not cram your work
together. If you cannot fit all of your solution on one page, please continue
onto another sheet of paper.

\item{$\bullet$} Use good quality paper, write or print on only one side, and
staple the pages together. If your work is typed, use a standard font and print
in black. If your work is handwritten, use a pencil or blue or black ink. Do
not hand in paper that has a fringe from being torn out of a notebook.

\item{$\bullet$} Include page numbers, in case the pages are accidentally
stapled in the wrong order.

\medbreak

\noindent{\bf How to read the textbooks}

\nobreak\smallskip

\noindent The textbooks are not meant to be read quickly, but slowly,
carefully, and thoughtfully. Both have many problems scattered throughout the
text, and at certain points they ask you to try the problems. When you come to
one of these points, {\it stop}. Try to figure it out. Spend some time thinking
about it. It may take you 15 or~20 minutes, or maybe longer. Don't continue
reading until you have solved the problem, or you are sure you are stuck and
can't get any further. The books are written to guide you through the process
of problem-solving, but this guidance will be hollow unless you are actually
attempting to solve problems!

\medbreak

\noindent{\bf Resources}

\nobreak\smallskip

\noindent In this room are many excellent resources for you: the other
students. Working with other students will help you and help the others.

I am also very happy to help you. As a math instructor, my goal---my job---is
to see you excel in math! Because time is limited, it may be difficult or
impossible to answer all of your questions during class itself. By all means,
please feel free to come talk to me if you have unanswered questions, if
something really isn't making sense to you, or if you just would like to talk
in greater detail about a topic we have covered. The best way to contact me is
by e-mail, but you are welcome to stop by my office at any time. Of~course, I
cannot guarantee I will be available outside my office hours unless you have
made an appointment.

\medbreak

\noindent{\bf Accommodations}

\nobreak\smallskip

\noindent Some students qualify for special accommodations due to various
needs. If you are such a student, please present documentation supporting such
a request as soon as possible, and I will do my best to assist you.

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\bye
