Math 484 - Art of Problem Solving - Syllabus
Course: The Art of Problem Solving
Term: Fall 2010
Time: TR 6:00-7:15pm and beyond
Location: Room STT314
Instructor: Dr. Ken Monks
Office: STT163A
Phone: (570) 941-6101
Email: monks@scranton.edu
Office Hours: T-Th
5:15-6:00pm, 7:15-7:45pm and beyond (or following the end of Math
484, whichever comes last) and by appointment or email
[Note:
Office hours may be held in either STT314, HYL 102, or STT163A.
Check all three locations.]
Required Textbooks: P. Zeitz, The Art and Craft of
Problem Solving, Wiley, 2nd edition, ISBN: 0-471-78901-1
Course Prerequisites: intense love of mathematics
Course Objective: To provide the student with an
introduction to the joys of mathematical problem solving by actually
solving problems. Students should strive to improve their ability to
solve mathematical problems through hands-on practice and obtain an
understanding of the strategies, tactics, and tools of the problem
solver as illustrated by the textbook and the instructor.
Course Format: This course will not be a traditional
lecture-style mathematics course, but rather is a training session in
problem solving mathematics. Consider the difference between
taking a course on the theory of running (where you learn about the
nutrition, form, training programs, types of sneakers, various
events, strategies, and history of the sport) vs. taking a training
program in running (where you actually run and run and run lots of
miles to get in shape even if you hardly know what your are doing) or
taking a course in music and piano theory (where you learn how to
interpret sheet music and learn the parts of the piano and listen to
famous piano compositions on CD) vs. taking piano lessons where you
actually practice and practice and practice playing the piano
yourself. Similarly our course is not a course about the theory of
problem solving (where you learn about what others say about problem
solving or the history of famous solutions to problems) but rather it
is hands-on training in problems solving that will be primarily
focused on having you solve problems yourself, no matter how good or
bad at it you may be. Just as any runner, no matter how fit or
talented benefits from lots of running in training, so shall you
benefit from lots of problem solving. Rather than interacting with
you in the role of instructor, I will interact with you in the role
of coach.
Thus, rather than learn material related to problem solving, and
then working exercises related to that material, we will do things
the other way around. You will be given problems to solve, and
if a particular problem requires that you learn a particular topic in
mathematics, then we will learn that topic at that point. So
the course will be problem-driven, rather than topic-driven.
The problems will motivate the topics rather than the other way
around.
Course requirements: There are no traditional homework
assignments or exams in the course. The following are mandatory
however.
- Problem Training notebook: All of the problems you
solve, in addition to all of the scratch work you do when trying to
solve a problem should be kept in a single bound notebook (or
several if you run out of paper). This does not include write
ups of problems that you hand in which should be done on separate
paper.
-
Training Log: Each student must keep a training log in
which they record (a) the starting and ending times for each
training session in which they are solving problems from the
course exclusively, whether in class or outside of class.
The log should be neat and organized, with daily totals, weekly
totals, and a running cumulative total for the entire semester.
Each entry should list the problem or problems that you were
working on during that time. You should use the following sample spreadsheet for your
training log. If you don't have Excel, you can install the free Open Office
program and use this version of
the Training Log spreadsheet instead. A weekly summary should
be emailed to me each Tuesday before class summarizing everything
from the previous Tuesday to Monday inclusive.
The subject line of the message you send me MUST be
exactly this format (so my email filter can handle the
attachments correctly):
[LOG] - lastname
where "lastname" is replaced with your last name in
all lowercase letters. Also, "LOG" should be in all
uppercase. Include the brackets '[' and ']' and leave exact
one space between the second bracket and the '-' and exactly one
space between the '-' and your last name. In addition the name of
your attachment must be:
lastname.ods
or lastname.xls if you are using Excel instead of
Open Office and can't save your file as .ods format (if you can,
I prefer .ods format). In either case "lastname" is replaced with
your last name in all lowercase letters.
- Must-know notebook: As various mathematical topics
("tools" as Zeitz calls them) come up in the course as required by
particular problems I will tell you "must know" facts. Those
facts must be entered in a Must-know notebook, and memorized before
the next class meeting. At any point in the course we will
have unannounced quizzes to determine if you know what you must
know.
- In-class problem sets: We will have some timed problem
sets that are to be worked in class. Some will be done individually
and some as a group.
- Out of class problem sets: We will also have more
extensive problems and problem sets that are to be done outside of
class and written up to hand in. Some will be done individually and
some as a group.
- In-class presentations: All students will be required to
present problems at the board, discuss solutions with other
students, and work in groups at solving problems.
Attendance Policy: Since the course is intended to provide
hands-on problem solving training as opposed to a traditional lecture
format, class attendance is a necessary component of the
course. Should you miss a class for any reason, you are still
responsible for all announcements made and all material discussed
during that class.
Email and the Web: All students in this course are required
to have a university email account and are expected to check their
email frequently for announcements and other information I may send
to you. I will use email and the internet quite extensively in the
course. If you prefer to check your home email instead of your
university email you can forward your university email to you home
account by following these
instructions. I will not change your email address in my email
address book from its default university account so you must either
read your university email or forward it to your home account. Each
student is also expected to be able to access any information that I
post on the world wide web which is related to your course. You may
access this information from the mathematics department computer lab
in STT161. Contact the Help Desk if you need assistance.
Cheating: Cheating is repugnant to the very nature of
problem solving. Please drop the course immediately if you feel the
urge to cheat for you have clearly failed miserably as a problem
solver and nobody in the class will like you.
Grading: There will be no exams, no homework, and no
grades in the course. There will just be LOTS of problems, some
of which will be worked in class, some as group projects that will be
written up and handed in, others presented in class, some worked for
your own enjoyment and benefit and training. Grades and exams
and deadlines and time limits on class meetings are antithetical to
the spirit and nature of the art of problem solving. If you are
concerned about what grade you are getting in the course, then you
are definitely not doing well. On the other hand if all you
care about is solving the current batch of problems with no concern
for your grade in the course, then you are doing fine. Problem
solving must be motivated by love and curiosity and passion and
desire and pride and the need to overcome a challenge and experience
new vistas by climbing to great heights, not by mundane paranoid
concerns over grades and gpa.
Still, the university does require that each student receive a
grade in the course when the course is completed. The grade you
receive will be completely determined by me based on my subjective
professional judgment of your performance taking into account your
written and oral presentations, your interaction with the other
students, your class attendance, peer evaluations, the amount of
training indicated in your logbook, the amount of problem solving
indicated in your notebook, the quality and quantity of the problems
you attempt and hand in, the uniqueness of your approach to
particular problems, and other such criteria. This mechanism for
determining course grades is consistent with the spirit of problem
solving and training in general where the coach of the activity
selects the team members who will constitute his "A" team, "B" team,
etc. Note that you will not be judged on your level of skill as a
problem solver but rather on how much you improve, how much you
learn, and how much effort you put into the course.
Also, since attendence and class participation is a major
component of the course we will have the following grading policy.
There are approximately 27 classes in this course. In order for a
class to count towards your attendance you should be present
throughout the entire class, and participate in the day's activities
(e.g. participate in group activities, no sleeping, etc). You may
miss up to two classes due to sickness or conflicts without penalty,
but will be penalized one letter grade (A to A-. A- to B+, etc) for
each class you miss after that.
Finally, you will be required to participate in several actual
mathematics competitions throughout the semester. These will be
weighed heavily when determining your final course grade. The most
important of these contests is the Putnam Exam, which is usually held
on the first Saturday in December (Dec. 4 this year). You are
required to participate in this contest, so mark your calendar!!
I hear and I forget.
I see and I remember.
I do and I understand
- Chinese Proverb
Adaptability: I retain the right to modify or change any of
the policies stated in this syllabus during the term if I feel it is
in the best interests of the students and the course.
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