Provides a smooth and pleasant transition from first-year calculus to
upper-level mathematics courses in real analysis, abstract algebra and
number theory
Most universities require students majoring in mathematics to take a
"transition to higher math" course that introduces mathematical proofs
and more rigorous thinking. Such courses help students be prepared for
higher-level mathematics course from their onset. Advanced Mathematics:
A Transitional Reference provides a "crash course" in beginning pure
mathematics, offering instruction on a blendof inductive and deductive
reasoning. By avoiding outdated methods and countless pages of theorems
and proofs, this innovative textbook prompts students to think about the
ideas presented in an enjoyable, constructive setting.
Clear and concise chapters cover all the essential topics students need
to transition from the "rote-orientated" courses of calculus to the more
rigorous "proof-orientated" advanced mathematics courses. Topics include
sentential and predicate calculus, mathematical induction, sets and
counting, complex numbers, point-set topology, and symmetries, abstract
groups, rings, and fields. Each section contains numerous problems for
students of various interests and abilities. Ideally suited for a
one-semester course, this book:
- Introduces students to mathematical proofs and rigorous thinking
- Provides thoroughly class-tested material from the authors own course
in transitioning to higher math
- Strengthens the mathematical thought process of the reader
- Includes informative sidebars, historical notes, and plentiful
graphics
- Offers a companion website to access a supplemental solutions manual
for instructors
Advanced Mathematics: A Transitional Reference is a valuable guide for
undergraduate students who have taken courses in calculus, differential
equations, or linear algebra, but may not be prepared for the more
advanced courses of real analysis, abstract algebra, and number theory
that await them. This text is also useful for scientists, engineers, and
others seeking to refresh their skills in advanced math.
