Preface vii"rigorous" means, in mathematics, being free from blunders. "Giving
all the rigor that a student can appreciate" means avoiding all the blun-
ders that the student can detect. The author will not say that this book
is rigorous because minor errors are inevitable and major blunders are
possible, but he will say that he has tried to be rigorous. Thus students
can be and should be invited to be critical. Detection of a blunder should
be a major accomplishment.
The author will be delighted if students discover everything that is
bad in the book and everything that is good in mathematics. Teachers
need not and perhaps should not give as much attention to the theoretical
aspects of the subject as the text does. Because the text contains many
of those comments and explanations that teachers are normally called
upon to supply as answers to questions, teachers are enabled to devote
more of their attention to problems. Problems and applications are
important and, particularly when tests and examinations consist almost
exclusively of problems, major emphasis must be placed upon the prob-
lems. We will be unfair to our students if we behave like the president
of a construction company who trains an employee to be an architect
and then discharges him because he fails to lay bricks properly.
Ralph Palmer Agnew