PREFACE ixamong colleges and universities where such courses exist, the subject matter
varies considerably. For this reason, an attempt has been made to include
in this text a wide variety of topics and to avoid interdependence among
topics whenever possible. Furthermore, a conscious decision was made to
avoid any primary focus on material that is the specific content of main-
stream junior-senior courses.
A number of articles in Book One (1.5,2.4,3.5,4.3,6.3,6.4) are designated
"optional." The nonoptional material in Book One (i.e., Articles 1.1 - 1.4,
2.1-2.3, 3.1-3.4, 4.1, 4.2, 5.1-5.4, 6.1, and 6.2) constitutes what the author
regards as the core content for achieving the objectives of a bridging course
and for permitting passage to Book Two. Though no topics in Book Two
have been explicitly designated as optional, they can be covered selectively
to fit the needs of a particular course. Many different syllabi can be based
on this text, depending on the number of available class sessions, the initial
level of the students, and the judgment of individual instructors or curric-
ulum committees. For example, a two-credit course focused on sets, logic,
and proof could cover the core material from Book One. A three-credit
course for sophomores, in which a relatively leisurely pace and strong focus
on fundamentals is desired, might proceed:
[Core plus 1.5, 2.4, 3.51 -+ [Ch. 71 + C8.1, 8.
[Core plus 2.4, 4.3, 6.1 (E - 6 proofs)] + C7.1, 7.2, 7.31 + C8.1, 8.21.
Possibilities for three-credit courses with a more advanced or accelerated
point of view include:
[Core plus 1.5, 2.4, 6.31 + [Ch. 71 -, [Ch. 81
and
[Core plus 6.31 -+ C7.1, 7.2, 7.31 -+ [Ch. 91 -+ [lo. 11.
A number of alternative syllabi are contained in the instructor's manual,
available free from the publisher to instructors using the text. This manual
also provides a list of objectives for each article, as well as commentary on
pedagogical issues related to various portions of the text.
ACKNOWLEDGMENTSA large number of people contributed in iniportant ways to the inception,
development, and completion of this text. First among these was my editor
at Random HouselBirkhauser, Wayne Yuhasz, without whose early en-
couragement my set of class notes would have remained in that state. I
am indebted to him also for highly professional support, as the project
progressed.