xxiv To the Student
this book as you would read a newspaper or a novel. You must "read"
this book with pencil and paper. Write out the key steps yourself as you
progress through the text, working out the details as you go. (This may be
called "active reading.") It will keep your attention focused and facilitate
your learning.- Treat the exercises sets as a continuation of the learning begun in class or
in the text. They are carefully graded so that you learn as you progress
through an exercise set. There are plenty of exercises; generally you can
get along fine by doing only every other one and omitting some of the
later ones. If you can't get anywhere on an exercise after much effort,
find out from someone else how to do it and then work it through several
times until you can do it by yourself, without help. - In mathematics, as in other branches of human knowledge, truth is com-
municated in sentences. Even in mathematics, a sentence must have a
subject and a predicate and obey all the laws of grammar. For example,
the subject of the sentence x^2 + 3x - 7 = 11 is "x" and the predicate is
"=." Please remember, when you write your own proofs or solutions of
exercises, to express your ideas clearly and in complete sentences. Sloppy
writing is often a sign of sloppy thinking. An idea poorly expressed is
often poorly understood.