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Polynomials
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Paperback
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Artikel-Nr:
9780387406275
Veröffentl:
2003
Einband:
Paperback
Erscheinungsdatum:
09.10.2003
Seiten:
484
Autor:
Edward J Barbeau
Gewicht:
727 g
Format:
235x155x27 mm
Serie:
Problem Books in Mathematics
Sprache:
Englisch
Beschreibung:
From the reviews:
"This book uses the medium of problems to enable us, the readers, to educate ourselves in matters polynomial. In each section we are led, after a brief introduction, into a sequence of problems on a certain topic. If we do these successfully, we find that we have mastered the basics of the topic ... I approached this book with some prejudice against its non-textbook approach; but it won me over entirely. It is not easy to write a book that will interest both the bright high-school student and the practicing mathematician. That it does so is a tribute to the author's scholarship, style, choice of material, and careful attention to detail." -Mathematical Reviews
"This book uses the medium of problems to enable us, the readers, to educate ourselves in matters polynomial. In each section we are led, after a brief introduction, into a sequence of problems on a certain topic. If we do these successfully, we find that we have mastered the basics of the topic ... I approached this book with some prejudice against its non-textbook approach; but it won me over entirely. It is not easy to write a book that will interest both the bright high-school student and the practicing mathematician. That it does so is a tribute to the author's scholarship, style, choice of material, and careful attention to detail." -Mathematical Reviews
The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 "explorations" invite the reader to investigate research problems and related topics.
From the reviews:
Summary of the Contents:
- Fundamentals
- Evaluation, Division, and Expansion
- Factors and Zeros
- Equations
- Approximation and Locations of Zeros
- Symmetric Functions of the Zeros
- Approximations and Inequalities
- Miscellaneous Problems
- Fundamentals
- Evaluation, Division, and Expansion
- Factors and Zeros
- Equations
- Approximation and Locations of Zeros
- Symmetric Functions of the Zeros
- Approximations and Inequalities
- Miscellaneous Problems