Geometry of Curves ANNOTATION
"...presents an easily-understood mathematical structure, minimizing use of theorems & including examples, problems & solutions designed to enhance reader's comprehension & interest along with practical projects for the reader."
FROM THE PUBLISHER
Interest in the study of geometry is currently enjoying aresurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, a need exists for an introduction with modest prerequisites-one that stimulates interest and focuses on problem solving.
Here is the book that meets that need. Integrating the three main areas of curve geometry-parametric, algebraic, and projective curves-Geometry of Curves offers a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. Almost entirely self-contained, this book begins with the basics then takes readers on a fascinating journey from conics, higher algebraic curves, and transcendental curves, through the standard properties of parametric curves, the classification of limaﾽons, and an account of envelopes of curve families, to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness.
The uniqueness of this volume lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations.
The result is a practical work that not only imparts a deeper understanding of the theory, but a heightened appreciation of geometry and interest in more advanced studies.
FROM THE CRITICS
Booknews
This textbook for a first semester course integrates the three main areas of curve geometryparametric, algebraic, and projective curvesoffering a unique approach to problem solving rather than a catalog of theorems. Rutter (U. of Liverpool) begins with the basics, then covers topics such as conics, high algebraic curves, transcendental curves, the properties of parametric curves, envelopes of curve families, and the application of projective curves to asymptotes and boundedness. Students should be familiar with elementary calculus including partial differentiation, the elementary theory of complex numbers, and elementary coordinate geometry. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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