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.
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Transition to Advanced Mathematics-Mathematics
For a one-quarter/semester, sophomore-level transitional
(bridge) course that supplies background for students going
from calculus to the more abstract, upper-division mathematics courses.
Also appropriate as a supplement for junior-level 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 upper-division
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
NEWStreamlined Ch. 1Gets more
quickly to proofs involving topics more commonly encountered in mathematics
NEWFunctions are now covered before relations
(Chs. 4 and 5).
NEWNew chapter on rings and integral domains
NEWExtensively revised chapter on number
theory and algebra. (Chs. 6, 7, and 9).
NEWFind the Flaw problemsAt
the beginning of exercise sets in Chs. 1-5.
- The flow from cardinality to rings is now very smooth.
NEWA collection of True/False questionsBegins
each set of review exercises in Chs. 2-5.
- Help students learn to read proofs critically.
NEWMany new exercises of all kindsMore
than in any other textbook of its kind.
Five core chapters (Chs. 1-5)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.
Four chapters of examples, theorems, and projects (Chs.
6-9)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.
- Anticipates many of the questions students might have
and develops the subject slowly and carefully. Students are then able
to work more independentlyand with much greater understanding
of the material.
Clearly written examples and practice problems
Provides solutions to practice problems, odd-numbered exercises, and
- 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.
Supplementary exercisesExtend 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.
7. Number Theory.
8. Rings and Integral Domains.
9. Limits and the Real Numbers.