| dc.description.abstract | The subject of probability and random processes is an important one for a variety of
disciplines. Yet, in the author's experience, a first exposure to this subject can cause
difficulty in assimilating the material and even more so in applying it to practical
problems of interest. The goal of this textbook is to lessen this difficulty. To do
so we have chosen to present the material with an emphasis on conceptualization.
As defined by Webster, a concept is "an abstract or generic idea generalized from
particular instances." This embodies the notion that the "idea" is something we
have formulated based on our past experience. This is in contrast to a theorem,
which according to Webster is "an idea accepted or proposed as a demonstrable
truth". A theorem then is the result of many oth er persons' past experiences, which
mayor may not coincide with our own. In presenting the material we prefer to
first present "part icular instances" or examples and then generalize using a definition/
theorem. Many textbooks use the opposite sequence, which undeniably is
cleaner and more compact, but omits the motivating examples that initially led
to the definition/theorem. Furthermore, in using the definition/theorem-first approach,
for the sake of mathematical correctness multiple concepts must be presented
at once. This is in opposition to human learning for which "under most conditions,
the greater the number of attributes to be bounded into a single concept, the more
difficult the learning becomes" 1 . The philosophical approach of specific examples
followed by generalizations is embodied in this textbook. It is hoped that it will
provide an alternative to the more traditional approach for exploring the subject of
probability and random processes. | en_US |
