
Introduction to Advanced Mathematics, 2/e
William J Barnier
Norman Feldman, both of Sonoma State University
Coming December, 1999 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 300 pp.
Cloth
ISBN 0130167509

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Transition to Advanced MathematicsMathematics

For a onequarter/semester, sophomorelevel transitional
(“bridge”) course that supplies background for students going
from calculus to the more abstract, upperdivision mathematics courses.
Also appropriate as a supplement for juniorlevel courses such as
abstract algebra or real analysis.
Focused on “What Every Mathematician Needs to Know,”
this text provides material necessary for students to succeed in upperdivision
mathematics courses, and more importantly, the analytical tools necessary
for thinking like a mathematician. It begins with a natural progression
from elementary logic, methods of proof, and set theory, to relations
and functions; then provides application examples, theorems, and student
projects.
NEW—Streamlined Ch. 1—Gets more
quickly to proofs involving topics more commonly encountered in mathematics
courses.
NEW—Functions are now covered before relations
(Chs. 4 and 5).
NEW—New chapter on rings and integral domains
(Ch. 8).
NEW—Extensively revised chapter on number
theory and algebra. (Chs. 6, 7, and 9).
 The flow from cardinality to rings is now very smooth.
NEW—“Find the Flaw” problems—At
the beginning of exercise sets in Chs. 15.
 Help students learn to read proofs critically.
NEW—A collection of True/False questions—Begins
each set of review exercises in Chs. 25.
NEW—Many new exercises of all kinds—More
than in any other textbook of its kind.
Five core chapters (Chs. 15)—In a natural progression:
elementary logic, methods of proof, set theory, functions, and relations.
Each chapter contains a full exposition of topics with many examples
and practice problems to reinforce the concepts as they are introduced.
 Anticipates many of the questions students might have
and develops the subject slowly and carefully. Students are then able
to work more independently—and with much greater understanding
of the material.
Four chapters of examples, theorems, and projects (Chs.
69)—Many theorems have no proof or only a hint or outline
for the proof. Likewise, the examples may have no solutions or just
a hint for the solution.
 The intent is that the material be used as a basis for
students to construct their own proofs or solutions and perhaps present
them to the class.
Clearly written examples and practice problems—
Provides solutions to practice problems, oddnumbered exercises, and
review problems.
Supplementary exercises—Extend or relate to some
of the concepts discussed in the text but are not necessary for the
continuity of the subject matter.
1. Introduction to Logic.
2. Methods of Proof.
3. Set Theory.
4. Cartesian Products and Functions.
5. Relations.
6. Cardinality.
7. Number Theory.
8. Rings and Integral Domains.
9. Limits and the Real Numbers.
