Synopses & Reviews
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.
This book provides a backdrop for study in calculus, modern algebra, numerical analysis and complex variable theory, through examples. Includes some 300 problems drawn from journals, contests, and examinations to test understanding, ingenuity, and skill.
Table of Contents
Fundamentals.- Evaluation, Division, and Expansion.- Factors and Zeros.- Equations.- Approximation and Location of Zeros.- Symmetric Functions of the Zeros.- Approximations and Inequalities.- Miscellaneous Problems.- Answers to Exercises and Solutions to Problems.- Notes on Explorations.- Glossary.- Further Reading.- Index.