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 "2*x* < 4", you can
claim "*x* < 2" without further justification. I hope this will
become clearer as we move through the course.

Comments to: dpvc@union.edu

Created: Mar 24 1999 --- Last modified: Mar 26, 1999 10:58:45 AM