Polynomials (Problem Books in Mathematics)

Rating:
Summary: 5 stars as an introduction
Review: 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.

Rating:
Summary: 6 stars! one of my favourites!
Review: 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.