Cover image for Polynomials
Title:
Polynomials
Author:
Barbeau, Edward, 1938-
Personal Author:
Publication Information:
New York : Springer-Verlag, [1989]

©1989
Physical Description:
xxii, 441 pages : illustrations ; 25 cm.
Language:
English
Subject Term:
ISBN:
9780387969190
Format :
Book

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QA281 .B37 1989 Adult Non-Fiction Non-Fiction Area
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Summary

Summary

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.


Reviews 1

Choice Review

This volume is a treasure chest of fascinating information about polynomials. Readers are led to develop for themselves many fundamental notions and techniques through more than 400 "exercises," nearly 300 "problems," and 69 "explorations," a number of which were compiled from journals and contests. These questions touch upon such diverse areas as classical factoring techniques, basic complex analysis, approximation of roots, combinatorics, and a smattering of geometry and number theory. There are full solutions to the problems and answers to the exercises, as well as numerous hints sprinkled throughout the text. The index is thorough and useful, and an extensive bibliography aids the reader in conducting further excursions. The mathematical background required is minimal--not even calculus is needed for most of the reading and problems. Highly recommended for motivated high school and college students as a supplement to the standard curriculum in algebra and calculus, and to anyone who might like to explore some beautiful, varied, and challenging mathematics. -S. J. Colley, Oberlin College