mean that they are incapable of using it with precision if required to do so. Teaching
students to be precise in their use of the language tools that they already possess
is one of the main objectives of the course. We do not believe that beginning the
course with a study of formal logic would be of much help in this regard and, in
fact, might just get in the way.
We could also have included a chapter on Fourier series. However, we felt that
the material that has been included makes for a text that is already a challenge
to cover in a two-semester course. We feel it to be unrealistic to think that an
additional chapter at the end would often get covered. In any case, the study of
Fourier series is most naturally introduced at the undergraduate level in a course
in differential equations.
We have included an appendix on cardinality at the end of the text. We discuss
finite, countable, and uncountable sets. We show that the rationals are countable
and the reals are not. We show that given any set, there is always a set of larger
cardinal. We also include a discussion of the Axiom of Choice and its consequences,
although it is not used anywhere in the body of the text.