The author's interest in the history and development of this area is evident, and we have pleasant glimpses of progress over the last three centuries. He exercises nice judgment in selection of arguments, with respect to both representativeness of approaches and elegance, so that the reader gains a synopsis of and guide to the literature, in which more detail can be found.
What is unusual is to have a text that embraces and intermingles both analytic and algebraic aspects of the theory. Although the subject is about such basic objects, many tough results of considerable generality are incorporated and it is striking that refinements, both in theorems and proofs continued throughout the latter part of the Twentieth Century. This book presents a few of them, some being classical, but partly probably unknown even to experts, some being quite recently discovered. Victor V.
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Over 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. 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. 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.
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Description Table of Contents Product Details Click on the cover image above to read some pages of this book! Industry Reviews From the reviews: E. Barbeau Polynomials "This book uses the medium of problems to enable us, the readers, to educate ourselves in matters polynomial.
Preface Acknowledgment of Problem Sources Fundamentals p.