Math 170, Fall 2005 Ideas
in Mathematics
This
course will cover much diverse material, the time for presentation of
which will be limited.
For many of you this will be your first college math course (and
possibly the last). Your
responsibilities will be greater than those in high school or
preparatory school since some of the
material you are required to read and know may be covered only very
briefly in class.
Grading:
Your grade will be based on
Final examination (Friday,
December 16, 9-11 am) 30%
Term paper 30%
Midterm (tentatively Thursday,
November 3) 20%
Homework and quizzes 20%
Here is a short outline of the material to be covered:
The text for this course is For All Practical Purposes, 6 th edition,
COMAP, W H Freeman & Co.
Time will not permit us to cover all the chapters. Some very important
material will be inserted
which is not in the book.
The text is divided into six parts. Here is the order in which we will
discuss the three that will
constitute the core of the course.
Part I, “Management Science” consists of four chapters and will be
covered very rapidly. Chapter
4 on Linear Programming will, however, be supplemented by a short
discussion of the
transportation problem, a special case which was partly responsible for
the development of the
theory.
Part II, “Statistics: The Science of Data” will be discussed more
thoroughly. We will add to the
material in the text a discussion of probability distributions other
than the normal or Gaussian
(the “bell-shaped curve”). These have important applications and you
will have to know how to
use the tables of their values. In addition there will be some
discussion of the uses (and abuses)
of statistics in law and in the courts. You will be directed to sources
on the web. (In particular we
will discuss Bayes’ theorem.)
Part VI. “Modeling in Mathematics” contains three chapters of which the
first two contain some
very practical information for consumers. The third, The Economics of
Resources, may become
an increasingly important issue in national policy.
If we manage to keep to our projected schedule there may be time to
include some material from
Part IV, “Social Choice and Decision Making”, in particular, Chapter 16
on Game Theory.
The term paper:
Since this
will constitute 30% of your grade there
will be some very strict requirements.
Most important,
remember that this is a mathematics course and it is essential that the
paper have
some mathematical content. It may, for example, be a discussion of some
theorem or theory
(whether discussed in the course or not), or some issue of social
policy or a legal issue in which
there is an important mathematical or statistical question, which you
must (in some measure at least)
analyze, not merely state. The book has thumbnail biographies
of some people who have been important in the history or applications
of mathematics. You may
be interested in studying one of these in greater detail, but a bare
biography will not receive a
passing grade. An acceptable paper on one of these must discuss some
important work (or
works) of the person in question and demonstrate that you understand
its meaning and
significance. It is not adequate, for example to allude to Nash’s
famous theorem on the
embedding of manifolds unless you can demonstrate in your paper that
you understand what it
means and says. Merely quoting an important theorem is not adequate
Length: The paper must be typed, approximately 7 to 10 pages long
exclusive of diagrams or
illustrations, double spaced, and in addition must have a title page
with a short abstract of the
contents (not more than a single paragraph). Please put your name,
“Math 170, Fall 2005” and
your section and recitation time in the upper right.
Sources: The paper must be adequately referenced; at least four are
required beyond the text.
(You may, of course, refer to the text, but it will not count as one of
the references.) A paper in
which the discussion of a subject does not go beyond what is in the
text will not receive a passing
grade. You may certainly use web sources but not more that one
reference can be to Wikipedia.
(The articles in Wikipedia are not refereed; anyone can post or edit
one, be he or she an expert or
not. By contrast articles in the Encyclopedia Brittanica and most
commercial encyclopedias are
generally signed by recognized experts.)
Date due: Your term paper must be handed in by Tuesday, December 6, at
3:30pm. Lateness
without excuse will cost one grade level, e.g. it would drop the grade
from A to A- or from C+ to C.
(The due date is firm because all papers must be read and graded by
both Mr. Thompson and
myself before the final exam in order for us to be able to submit
grades promptly after the exam.)
In addition, to insure that that the topic and direction which you have
chosen for your paper
are acceptable, you must submit to me no later than Thursday, November
17, at 3:30pm a
proposed outline of your paper. I will read these and, if necessary,
suggest changes in what you
propose to do to bring it in line with the requirements. These outlines
must be on a full sheet of
paper, typed or legibly written (and must, of course, contain your name
and section number
and/or recitation time). No paper will be accepted unless an outline
has previously been
submitted. The outline counts as a homework exercise; lateness will be
penalized.
CALENDAR
Our calendar this semester is
difficult because of the Jewish holidays, which I observe. (You
should not expect to see me on a
day that is important to me, and conversely, I will not expect to
see you and certainly will not
penalize your absence due to any observance of yours.) If on any of
my absence for those who feel that
they need some extra review. I will not be available on
Tuesday, October 4 (Rosh
ha-Shanah, Jewish New Years)
Thursday, October 13 (Yom Kippur,
Day of Atonement)
Tuesday, October 18 (Sukkot,
Festival of Tabernacles)
Tuesday, October 25 (Shemini
Azeret, Eighth Day of Solemn Assembly; memorial services)
Unfortunately, this takes a large
bite out of the semester, which I will try to make up with
generous office hours in which
those of you who need more individual attention can get it.)
OFFICE HOURS
I will generally be available Wednesdays from noon on (earlier by
appointment) except for a
seminar from 3 to 4, but not on Wednesday, October 12 (eve of Yom
Kippur). Also, I will be
available Tuesdays and Thursdays after a class which finishes at 3pm
and by appointment also
before our class.
IN CASE OF PROBLEMS
Please contact me as soon as possible if you are having difficulty with
the course work or with
something that interferes with your course work. Help is available. You
may contact me by
email: mgersten@math.upenn.edu
MISSED RECITATIONS
If you must miss a recitation and can make another in the same week
please contact Mr.
Thompson. It is important that you attend recitation each week to get
credit for quizzes.
HOMEWORK
Our text has exercises on the web and results are submitted to me.
Whenever these are available
they constitute part of the homework. In addition you will submit one
or two written exercises
each week.
ATTENDANCE
While attendance is not strictly required be warned that there may be
an occasional spot quiz!
(You are, of course, responsible for material presented in class, even
if not in the text, such as all
the supplemental material.)
Click for the posting of Bayes' Theorem