Barbeau, Edward J. Polynomials

# Polynomials

## Barbeau, Edward J.

Valutazione media 4,27
( su 11 valutazioni fornite da GoodReads )

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.

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Book Description:

From the 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

“This is a two-faced book, and that’s a good thing. One face is a set of enrichment materials for bright high school students. The other face is a fairly comprehensive textbook on algebraic properties of polynomials. … The present book is an excellent introduction to the subject for anyone, from high schooler to professional.” (Allen Stenger, The Mathematical Association of America, August, 2011)

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Edizione Internazionale

## 1.Polynomials (Problem Books in Mathematics)

ISBN 10: 0387406271 ISBN 13: 9780387406275
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Descrizione libro Paperback. Condizione libro: New. New Softcover International Edition, Printed in Black and White, Different ISBN, Same Content As US edition, Book Cover may be Different, in English Language. Codice libro della libreria 3946

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## 2.Polynomials PB (English) 01 Edition

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ISBN 10: 0387406271 ISBN 13: 9780387406275
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Descrizione libro Springer. PaperBack. Condizione libro: Brand New. International Edition. International Edition, Cover & ISBN may be different from US edition, PAPERBACK. Book Condition: New. Brand New,Softcover,No Access code & No context dvd, But Contents are same as US Edition. Printed in English Language, Prompt shipping by USPS/,UPS/,DHL/,FedEx. Exceptional customer Service, Satisfaction Guaranteed. We may ship the books from Asian regions for inventory purpose. "Special Note" We do provide service on APO BOX & PO BOX addresses only in usa. Codice libro della libreria Aaddi23395

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## 3.Polynomials (Problem Books in Mathematics)

Editore: Springer 2003-11-03 (2003)
ISBN 10: 0387406271 ISBN 13: 9780387406275
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Descrizione libro Springer 2003-11-03, 2003. Condizione libro: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-LBR-00870667

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## 4.Polynomials (Paperback)

Editore: Springer-Verlag New York Inc., United States (2003)
ISBN 10: 0387406271 ISBN 13: 9780387406275
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Descrizione libro Springer-Verlag New York Inc., United States, 2003. Paperback. Condizione libro: New. 1st ed. 1989. 3rd printing 2003. 234 x 156 mm. Language: English . Brand New Book. 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. Codice libro della libreria LIB9780387406275

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## 5.Polynomials (Paperback)

Editore: Springer-Verlag New York Inc., United States (2003)
ISBN 10: 0387406271 ISBN 13: 9780387406275
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Descrizione libro Springer-Verlag New York Inc., United States, 2003. Paperback. Condizione libro: New. 1st ed. 1989. 3rd printing 2003. 234 x 156 mm. Language: English . Brand New Book. 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. Codice libro della libreria LIB9780387406275

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## 6.Polynomials

Editore: Springer-Verlag New York Inc. (2003)
ISBN 10: 0387406271 ISBN 13: 9780387406275
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Descrizione libro Springer-Verlag New York Inc., 2003. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780387406275

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## 7.Polynomials

Editore: Springer (2003)
ISBN 10: 0387406271 ISBN 13: 9780387406275
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Descrizione libro Springer, 2003. Paperback. Condizione libro: NEW. 9780387406275 Paperback, This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0411037

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## 8.Polynomials

ISBN 10: 0387406271 ISBN 13: 9780387406275
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Descrizione libro Condizione libro: New. Publisher/Verlag: Springer, Berlin | 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. | 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 &apos;1 Fundamentals.- 1.1 The Anatomy of a Polynomial of a Single Variable.- 1.1.5 Multiplication by detached coefficients.- 1.1.19 Even and odd polynomials.- E.1 Square of a polynomial.- E.2 Sets with equal polynomial-value sums.- E.3 Polynomials as generating functions.- 1.2 Quadratic Polynomials.- 1.2.1 Quadratic formula.- 1.2.4 Theory of the quadratic.- 1.2.14 Cauchy-Schwarz inequality.- 1.2.17 Arithmetic-geometric mean inequality.- 1.2.18 Approximation of quadratic irrational by a rational.- E.4 Graphical solution of the quadratic.- E.5 Polynomials, some of whose values are squares.- 1.3 Complex Numbers.- 1.3.8 De Moivre&apos;s theorem.- 1.3.10 Square root of a complex number.- 1.3.15 Tchebychef polynomials.- E.6 Commuting polynomials.- 1.4 Equations of Low Degree.- 1.4.4 Cardan&apos;s method for cubic.- 1.4.11 Descartes&apos; method for quartic.- 1.4.12 Ferrari&apos;s method for quartic.- 1.4.13 Reciprocal equations.- E.7 The reciprocal equation substitution.- 1.5 Polynomials of Several Variables.- 1.5.2 Criterion for homogeneity.- 1.5.5 Elementary symmetric polynomials of 2 variables.- 1.5.8 Elementary symmetric polynomials of 3 variables.- 1.5.9 Arithmetic-geometric mean inequality for 3 numbers.- 1.5.10 Polynomials with n variables.- E.8 Polynomials in each variable separately.- E.9 The range of a polynomial.- E.10 Diophantine equations.- 1.6 Basic Number Theory and Modular Arithmetic.- 1.6.1 Euclidean algorithm.- 1.6.5 Modular arithmetic.- 1.6.6 Linear congruence.- E.11 Length of Euclidean algorithm.- E.12 The congruence a? ? b (mod m).- E.13 Polynomials with prime values.- E.14 Polynomials whose positive values are.- Fibonacci numbers.- 1.7 Rings and Fields.- 1.7.6 Zm.- E.15 Irreducible polynomials of low degree modulo p.- 1.8 Problems on Quadratics.- 1.9 Other Problems.- Hints.- 2 Evaluation, Division, and Expansion.- 2.1 Horner&apos;s Method.- 2.1.8-9 Use of Horner&apos;s method for Taylor expansion.- E.16 Number of multiplications for cn.- E.17 A Horner&apos;s approach to the binomial expansion.- E.18 Factorial powers and summations.- 2.2 Division of Polynomials.- 2.2.2 Factor Theorem.- 2.2.4 Number of zeros cannot exceed degree of polynomial.- 2.2.7 Long division of polynomials; quotient and remainder.- 2.2.9 Division Theorem.- 2.2.12 Factor Theorem for two variables.- 2.2.15 Gauss&apos; Theorem on symmetric functions.- E.19 Chromatic polynomials.- E.20 The greatest common divisor of two polynomials.- E.21 The remainder for special polynomial divisors.- 2.3 The Derivative.- 2.3.4 Definition of derivative.- 2.3.5 Properties of the derivative.- 2.3.9 Taylor&apos;s Theorem.- 2.3.15 Multiplicity of zeros.- E.22 Higher order derivatives of the composition of two functions.- E.23 Partial derivatives.- E.24 Homogeneous polynomials.- E.25 Cauchy-Riemann conditions.- E.26 The Legendre equation.- 2.4 Graphing Polynomials.- 2.4.6 Symmetry of cubic graph.- E.27 Intersection of graph of polynomial with. Codice libro della libreria K9780387406275

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## 9.Polynomials

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Descrizione libro Condizione libro: New. This item is printed on demand. Codice libro della libreria 1997855-n

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## 10.Polynomials

Editore: Springer-Verlag New York Inc. (2003)
ISBN 10: 0387406271 ISBN 13: 9780387406275
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Descrizione libro Springer-Verlag New York Inc., 2003. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I2-9780387406275

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