Polynomials

By: E.J. Barbeau

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Paperback | 1 January 1989

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484 Pages

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22.86 x 15.24 x 3.18

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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.

Industry Reviews

E.J. Barbeau Polynomials "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. If we have any difficulties, we can refer first to the hints, and, failing these, to the detailed solutions. These form an important and substantial part of the book, and often refer the reader on to the research literature. The book, like good literature, can be read successfully at different levels, and would not be out of place in any mathematician's library."--MATHEMATICAL REVIEWS

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Preface
Acknowledgment of Problem Sources
Fundamentals	p. 1
The Anatomy of a Polynomial of a Single Variable	p. 1
Quadratic Polynomials	p. 9
Complex Numbers	p. 14
Equations of Low Degree	p. 18
Polynomials of Several Variables	p. 25
Basic Number Theory and Modular Arithmetic	p. 31
Rings and Fields	p. 38
Problems on Quadratics	p. 40
Other Problems	p. 43
Evaluation, Division, and Expansion	p. 50
Horner's Method	p. 50
Division of Polynomials	p. 57
The Derivative	p. 66
Graphing Polynomials	p. 74
Problems	p. 78
Factors and Zeros	p. 83
Irreducible Polynomials	p. 83
Strategies for Factoring Polynomials over Z	p. 87
Finding Integer and Rational Roots: Newton's Method of Divisors	p. 93
Locating Integer Roots: Modular Arithmetic	p. 98
Roots of Unity	p. 104
Rational Functions	p. 110
Problems on Factorization	p. 114
Other Problems	p. 117
Equations	p. 125
Simultaneous Equations in Two or Three Unknowns	p. 125
Surd Equations	p. 128
Solving Special Polynomial Equations	p. 130
The Fundamental Theorem of Algebra: Intersecting Curves	p. 142
The Fundamental Theorem: Functions of a Complex Variable	p. 146
Consequences of the Fundamental Theorem	p. 150
Problems on Equations in One Variable	p. 154
Problems on Systems of Equations	p. 155
Other Problems	p. 159
Approximation and Location of Zeros	p. 163
Approximation of Roots	p. 163
Tests for Real Zeros	p. 174
Location of Complex Roots	p. 183
Problems	p. 190
Symmetric Functions of the Zeros	p. 198
Interpreting the Coefficients of a Polynomial	p. 198
The Discriminant	p. 201
Sums of the Powers of the Roots	p. 202
Problems	p. 205
Approximations and Inequalities	p. 210
Interpolation and Extrapolation	p. 210
Approximation on an Interval	p. 218
Inequalities	p. 225
Problems on Inequalities	p. 230
Other Problems	p. 231
Miscellaneous Problems	p. 236
Answers to Exercises and Solutions to Problems	p. 250
Notes on Explorations	p. 403
Glossary	p. 427
Further Reading	p. 430
Index	p. 449
Table of Contents provided by Blackwell. All Rights Reserved.

Polynomials

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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