Page 6 - Applied Probability

Preface

Despite the fears of university mathematics departments, mathematics
educat,ion is growing rather than declining. But the truth of the matter
is that the increases are occurring outside departments of mathematics.
Engineers, computer scientists, physicists, chemists, economists, statisti-
cians, biologists, and even philosophers teach and learn a great deal of
mathematics. The teaching is not always terribly rigorous, but it tends to
be better motivated and better adapted to the needs of students. In my
own experience teaching students of biostatistics and mathematical biol-
ogy, I attempt to convey both the beauty and utility of probability. This
is a tall order, partially because probability theory has its own vocabulary
and habits of thought. The axiomatic presentation of advanced probability
typically proceeds via measure theory. This approach has the advantage
of rigor, but it inwitably misses most of the interesting applications, and
many applied scientists rebel against the onslaught of technicalities. In the
current book, I endeavor to achieve a balance between theory and appli-
cations in a rather short compass. While the combination of brevity apd
balance sacrifices many of the proofs of a rigorous course, it is still consis-
tent with supplying students with many of the relevant theoretical tools.
In my opinion, it better to present the mathematical facts without proof
rather than omit them altogether.
In the preface to his lovely recent textbook (1531, David Williams writes,
“Probability and Statistics used to be married; then they separated, then
they got divorced; now they hardly see each other.” Although this split
is doubtless irreversible, at least we ought to be concerned with properly