MCS 236 --  Relation-Based Structures
Spring 2000
Moira McDermott

Course Objectives:

Prerequisites: There are no formal prerequisites for this course,  but I will assume that you have some exposure to thinking abstractly.

Text:  Discrete Mathematics with Graph Theory by Goodaire and Parmenter.

Evaluation:   Your final grade will be assigned using the following percentages as a guide:
 
Homework 20%
Proof Portfolio 10%
Paper 10%
Exams 60%

Academic Integrity:  The academic honesty policy can be found on page 31 of the 1999-2000 college catalogue.  I call your attention to the following excerpt:  "In all academic exercises, examinations, papers, and reports, students shall submit their own work. Footnotes or some other acceptable form of citation must accompany any use of another's words or ideas."

Exams:  We will have two exams during the semester and a final exam.

The exams are tentatively scheduled for March 9 and April 13.
The final exam will be given May 23,  10:30-12:30,  in OHS 319.

Class Format:

A good lecture is usually systematic, complete, precise -- and dull; it is a bad teaching instrument.
                                                                                                          -- Paul Halmos
The best way to learn anything is to discover it by yourself... .  What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises.
                                                                                                          -- George Polya
We learn by thinking and doing, not by watching and listening.  Learning is an active process:  it is something we must do, not have done to us.  Class time will be a mixture of lectures, discussions, problem solving and presentation of proofs.  At various times you will be asked to present problems, reflect on the reading and generate questions for your classmates.  It is essential that you come to class prepared to do the day's work.  In particular, you should read the text and attempt homework before coming to class.   Class meetings are not intended to be a complete encapsulation of the course material.  You will be responsible for learning some of the material on your own.

Homework:

I hear, and I forget;
I see, and I remember;
I do, and I understand.
                               - Proverb
I encourage you to work with other students on the homework provided that you do so in such a way that every one in your group learns the material.  The most effective way to do this is to first discuss each problem as a group and then have each person work on the problem individually.  When you're done (or stuck) compare your work and discuss it.  Remember that doing the homework is how you learn the material  and that you are not allowed to work cooperatively on tests.

If you do work with other students on the homework, I would like you to follow these guidelines:

  1. Each person should write up the answers independently.
  2. Each person should be able to work each one of the problems independently.
  3. Each person gives credit to the others who helped.


Writing:

Thought and expression of thought are so closely interrelated that to
require the latter will engender the former.
                                                        -- George Gopen and David Smith
MCS236  is a ``W'' course.   Writing assignments will take several forms.  First, homework assignments will often require written proofs.   These proofs will be checked for logical and grammatical accuracy, as well as for style and exposition.   It is important to be able to express your mathematical thoughts in writing, using clear, well organized paragraphs comprised of English sentences.  This means more than separating your equations with a few well placed ``Thus it follows that...'' or ``Plugging (a) into (b) shows that ...''  During the course we will work on writing  mathematical prose effectively and clearly.  In addition,  you will be compiling a proof portfolio containing one example of each type of proof discuss.  You will also be be expected to write one expository paper.   Details of the paper, including deadlines for drafts and revisions, will be described later in the course.

Syllabus:   I expect to cover the following topics.

Some notes on taking an upper level MCS course:

In this course, many of you will be making the transition from assignments that are primarily computational to those that require original, creative thinking.  Be persistent and realize that homework problems will take time and inspiration.  You might not be able to solve every  homework problem  each week.

Be prepared to work hard and to start assignments early.  It often helps to start with an example or two or a simpler version of the problem assigned, so that you really get a feel for  what it is that you're trying to prove.  If the proof or solution does not come to you after a while, it is best to put the problem aside and take a break.   I get my best mathematical ideas while I am out doing something else.

For those of you with some experience in upper level courses, start to work on making your arguments clear and concise and  on making judicious use of  notation and pictures.


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