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Polynomials (Problem Books in Mathematics)
Binding: Paperback
Author: E.J. Barbeau
Manufacturer: Springer
Availability: Usually ships in 24 hours
Average Rating: 5.0
Total Customer Reviews: 4
List Price: $49.95
Our Price: $44.63
Sales Rank: 321063
Product Description
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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Users Product Reviews: |
Product Review Summary: Math pleasure Barbeau has really outdone himself.He shows you the ins and outs of polynomials and the real beauty of mathematics in a understandable and easy way!
Product Review Summary: Polynomials Rule! 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.
Product Review Summary: 6 stars! one of my favourites! 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.
Product Review Summary: 5 stars as an introduction 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.
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