Course Responsibilities:
This course serves as a transition between the calculus courses where
you are primarily using mathematics to upperlevel math courses
where you are actually doing mathematics. We will spend a lot of
time thinking about how to interpret definitions and mathematical
statements, and especially how to prove them. Writing will play a
significant role in this course, but this writing is of a formal type,
with certain rules and accepted practices. It is not creative
writing, though you need to be creative in your thinking. In many ways,
this is more like poetry than prose, as it is very concerned with the form
of the writing as well as its subtle meanings.
This has the following consequences for Math 99:
 You must know the definitions precisely. Typically, a quick
restatement in your own words, while fine at an intuitive level, will lack
the precision necessary for a correct use of the concept. You are
responsible for all definitions from class, and you may be asked to
reproduce these on exams and quizzes. For example, an exam question might
begin: "Give the precise definition of ..."
 You need to understand the theorems and proofs from
class; it is not sufficient simply to know how to apply them. The
examples we give in class are designed to help you be able to produce
similar proofs on your own, so a clear understanding of each proof is
crucial. You may be asked to reproduce specific proofs from class, as
well as perform similar proofs of facts that you have not seen before.
 You must be very careful of the details. Simply getting "the
right idea" is not enough in a mathematical proof. The real proof lies in
the details, and your treatment of them will determine whether you get
the proof right or not. Be particularly careful about the different
"levels" involved; for example, the difference between a subset of a set
and an element of a set. These are sources of trouble for many beginning
students.
Some students are not sure of how much detail to go into, and where to
draw the line in terms of justifying the steps of their proofs. I can
offer you two pieces of advice here: first, if you had to think about it
for more than a moment or two, you should explain and justify your steps;
and second, if your steps involve facts or definitions that we have
discussed in class, you should justify your conclusions, but if they only
involve things we haven't treated in the course, you can assume the reader
is aware of the fact you are using. For example, we will treat the
relationship "A is a subset of B" in considerable detail, so
arguments involving subsets need to be handled precisely and be fully
explained. However, we will not treat the relationship "x <
y" in detail, so if you know that "2x < 4", you can
claim "x < 2" without further justification. I hope this will
become clearer as we move through the course.

Math 99 (Fall 2000) web pages
Created: 26 Aug 2000
Last modified: 28 Aug 2000 14:13:26
Comments to: dpvc@union.edu



 