Polynomials (Problem Books in Mathematics) [Paperback]

E.J. Barbeau (Author)

Book Description

Publication Date: October 9, 2003 | ISBN-10: 0387406271 | ISBN-13: 978-0387406275

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.

Editorial Reviews

Review

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

Product Details

• Paperback: 477 pages
• Publisher: Springer (October 9, 2003)
• Language: English
• ISBN-10: 0387406271
• ISBN-13: 978-0387406275
• Product Dimensions: 9.2 x 6.2 x 1 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #820,302 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

33 of 33 people found the following review helpful:

5.0 out of 5 stars 5 stars as an introduction, December 30, 2001

By A Customer

This review is from: Polynomials (Problem Books in Mathematics) (Hardcover)

I found this book many months back when it was still out of print(terribly hard to find back then, but I got it!). This book is fantastic as an introduction to the deep theory involved with polynomials. Covers things such as generating functions, quadratics, complex numbers, Cardan's method for cubics and Ferrari's and Descartes' method for quartics, elementary symmetric polys. in 2, 3, and 'n' variables, some number theory, Rings, Fields, applications of the calculus, a thorough chapter on factoring and zeros of a function, and much more including exercises and some very nice problems.
Overall this is an outstanding book(like many of the other books in the Springer-Verlag Problem books series--though a bit pricey). Highly recommended for anyone interested in extending their knowledge beyond what is required in high school or at the university level. Students participating in competitions may also find this quite useful.

31 of 31 people found the following review helpful:

5.0 out of 5 stars 6 stars! one of my favourites!, April 12, 2004

By 

another reader - See all my reviews

This review is from: Polynomials (Problem Books in Mathematics) (Hardcover)

This book would be helpful for anyone in high school or 4th-year abstract algebra, or anywhere in between! There's hardly any text to read, I would say ~85% of the learning is done by solving the problems. Barbeau guides the reader by giving directions on how to solve them sometimes, so learning from this book is MUCH MORE interactive (I think that's the right word...) than with others where you just read. It covers complex numbers, how to solve quadratics, cubics & quartics by radicals, symmetric functions of the roots, some number theory (like congruences), numerical methods & approximating roots, factors & zeros and symmetric functions of the roots. Another good one (more advanced than this though) is by Theory of Equations by Uspensky, out of print though unfortunately.

3 of 7 people found the following review helpful:

5.0 out of 5 stars Polynomials Rule!, May 8, 2007

By 

Alan Westcott "solitary pilgrim" (Berkeley, CA USA) - See all my reviews
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Amazon Verified Purchase

This review is from: Polynomials (Problem Books in Mathematics) (Paperback)

This book is packed with all kinds of information on polynomials and is a great resource for both instructors and students. I don't think there is any other book that has so much information assembled between two covers - it is a gold mine and a joy to read.