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{\bf Subject:}	Information about   {\bf Math 104 } 
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{\bf From:}  Prof. Matthew Dyer
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{\bf Prepared by:}  A. Alexandrou Himonas
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{\bf For:}  The Undergraduate Committee
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{\bf Date:}  November 26, 1996
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{\bf 1. Syllabus:}  Attached.
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{\bf 2.  Comments about course content:}  
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{\bf a.}  Even if one restricts to the most basic counting techniques required for
realistic probability problems, students find such counting problems hard and
for many this carries over to difficulty with (and dislike for) the probability 
material covered.  It may perhaps be useful to shift the probability/statistics
balance somewhat more towards statistics, but possible topics (i.e. more on
estimation, least squares, hypothesis testing) would be harder than the very
rudimentary statistics currently covered.
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{\bf b.}  Aside from the core probability/statistics component, other topics
treated have varied from year to year.  I recommend that mathematics of finance
always be included, because of its usefulness (which the students strongly
appreciate).  Apart from the Markov chains (which require material on
matrices),  the other standard topic is game theory (requiring matrices and at
least geometric linear programming).  Both these topics involve probability,
have many practical applications and are of some interest to the students, but
neither is likely to be used elsewhere by many students.
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{\bf 3.  Name of Textbook and comments about its quality:} 
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Textbook:  Finite Mathematics and its applications (5th edition) by Larry J. Goldstein,
David I. Schneider, Martha J. Siegel and published by Prentice Hall, Inc.
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For the material covered in 104, this is the best of the Finite Math texts I have seen.
One of its principal advantages is the large number of problems worked out in the
text.  A few things I'd prefer differently done:  binomial trials introduced in the
chapter on probability instead of the one on statistics, more on descriptive
statistics, more examples and exercises illustrating how the material can be used for
rudimentary hypothesis testing.  Generally, I'd like to see a somewhat  broader
coverage of statistics, but I don't know any finite math text that does that
adequately.
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{\bf 4.  Are computers used in the teaching, homework,
and in which way?  Should computers be incorporated in this course?}
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Computers have been used in class in one of the sections to illustrate the normal
approximation to the binomial distribution, and may be used to illustrate limiting
distributions for Markov processes.  It seems they would be of limited use for most of the
material on counting and probability.  Certainly computers could be used for analysis of
large data sets, though with the current rudimentary statistical component of the course I
don't feel much would be gained this way:  computation of the statistics treated could be
accomplished simply by entering the data into a suitable statistical package, and I feel
students would gain better appreciation for the meaning of the statistics by working by
hand or calculator with small or medium-sized examples.  If the statistical component of
the course was increased, there would be much greater scope for use of the computer for
class demonstration, but I feel it would not be appropriate to expect most of the students
to acquire familiarity with statistical packages etc. for use in homework.
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Another possible direction for use of computers would be in an expanded treatment of
game theory; a computer-savvy instructor could arrange demonstrations of tournaments
amongst various competing strategies in games (i.e. iterated prisoner's dilemma
tournament) which could be quite stimulating for the students (especially if they helped
select the competing strategies).
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{\bf 5.  What is the pace of teaching in this course? Fast? Slow? About
right?}
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The appropriate pace for this course is slow.  i.e. it is really necessary to spend much time
doing a number of examples of each type of problem which differ from one another only in
trivial ways.  It would be possible to proceed slightly faster if one wanted to cover Game
Theory instead of Markov Processes, but it would be too rushed if one tried to cover both.
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{\bf 6.  How are the Teaching Assistants doing in this course?  Any suggestion for a better
use of the TA's?}
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The TA is used at the moment to run a twice-weekly help session for the students, who
find it very useful.  The first year of studies also offers workshops and a collaborative
learning program  for 104, but it seems helpful to have the midweek math sessions so
students have an opportunity to sort out difficulties without waiting for the weekend LRC
workshop.  The course also uses an assigned grader, which is essential for classes of the
size here ($\@$ 80 in each section).
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It would possibly be useful to have a  \lq\lq lab\rq\rq set up in which students would
work under a TA's supervision on statistical analysis of data sets, if the statistical
component of the course was greatly expanded.  However, at present there is really only
about a week of class devoted to descriptive statistics.
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 {\bf 7.  How is the testing and grading done in this course?  Any suggestions for
improvements?}
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$$\align
\text{3 - 1 hr. midsemester exams   \quad  } &3 \times 100 \text{ points}\\
\text{1 - 2 hr. final exam \quad   } &\underline{1 \times 150}\\
\hskip .25 in\text{ Total:\quad} &\qquad 450\endalign$$
Homework (generally 5-10 problems from the text) is assigned daily and collected next
lecture.  Grade cutoffs are assigned for each exam and totalled to give grade cutoffs for
the course; a students grade is determined by their exam total in relation to the cutoffs,
except that their homework performance is used to adjust their exam total by at most 5
points up or down.
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 {\bf 8.  What are the failing rates in this course?} 
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Failure rates for individual exams are generally 5-10$\%$, but for the course itself they
are much lower.  As of the third midsemester, no one in the course is below the failing
grade.  Three students have dropped the course late, one because of poor course
performance.
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{\bf 9.  Specific suggestions you may have for the next teacher of this course:}
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{\bf 1.}  Avoid counting or probability problems which require special tricks  not useful in a
broad variety of such problems.
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{\bf 2.}  It might be useful to discuss Binomial trials earlier so students can calculate
probabilities for coin tosses, etc. without having to go through the counting arguments
each time.
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{\bf 3.}  Either topic (Game theory or Markov processes) is a good choice; the Markov
process option is perhaps easier for the students.
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