question you have about the subject should be asked, and we will be happy to
try to answer it. Don't let your questions sit around gathering dust, because
later portions of the course will make use of what came earlier. The longer
you wait, the harder it is to catch up. You learn the subject by solving
problems. But we'd like you to do more than get correct answers to the
problems. We want you to learn to write mathematics clearly. Remember that
you are writing in English about mathematics, and your purpose is to present
a readable (as opposed to merely legible) document. Therefore, your
mathematical writing should be more than a sequence of calculations, but
should consist of complete sentences, in which are embedded the mathematical
expressions. (A good way to test whether you have produced a readable
document is to try to read it aloud without adding words that are not on the
page. If it says what you want to say, you're ok.)
In grading exams in the past, we have thought that students need to
understand better what we expect of them. Below are some notes that could be
useful for students.
In an exam problem, we do not give you a selection of five possible answers
and ask you to find the correct answer. We give you a problem, and we ask you
to provide a *solution*. Some problems are explicitly "show-that"
problems: they ask for an argument, an explanation, a proof. Other problems
may simply ask for a computation. But even such problems should be understood
as "show-that" problems. We do not want to see an answer alone; we
want to see the steps of the computation that lead to the answer. If
correctly written, these steps constitute a proof that the answer is correct.
Correct answers given with no justification may receive no credit.
Correct answers with incorrect justification are only *accidentally* correct;
they may receive no credit.
Incorrect answers given with some correct justification may receive partial
However, in a long problem, it may happen that you receive no credit for any
work done after your first mistake (if you make a mistake). Therefore you
should be especially careful in the early steps of a problem.
Always check your work, if you have time. Some answers are easy to check. For
example, to check the proposed solution to an equation, just substitute into
the equation. To check an indefinite integral, just differentiate. In the
grading of problems whose answers are easily checked, possibly no partial
credit will be given.
Write your solutions in the conventional fashion: left to right, top to
bottom. Otherwise, the reader cannot tell how to read what you have written,
and you may lose credit. Remember, we graders do not have the benefit of
watching you write (or of having you stand by to explain what you have
written); all we have is the finished product of you writing, and this is
what you are graded on.
We graders are not mind-readers. It is not our job to *figure out* what you might
mean; it is your job to *say* what you mean, in the manner of expression
established in lectures and textbooks.
It is possible to write down *too much* justification for your answers. How
much is enough, and how much is too much? There is no clear answer; you just
have to develop a feeling by reading books and observing and questioning
If your solution contains irrelevant information, then the grader may
conclude that you do not understand the problem fully, and you may lose
Write your symbols clearly. A "3" should not look like a
"7"; a "t" should not look like a "+".
Use mathematical symbols correctly. For example, the double-shafted arrow
"=>" is a logical symbol meaning "implies", so that
"A => B" means "A implies B", that is, "If A,
then B," that is, "A is false, or B is true." Do *not* use
this arrow to mean "therefore" or "now read the