Over and Over Again

Over and Over Again

eBook - 1997
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Book News
Studies iterations in number theory, analysis, and geometry, and applies them to various problems, many of them taken from international and national Mathematical Olympiad competitions. Topics include classical and not-so-classical inequalities, Sharkovskii's theorem, interpolation, Bernstein polynomials, BTzier curves and surfaces, and splines. Includes chapter exercises, hints, and solutions. Most material requires only high school mathematics; later chapters require elementary calculus. Useful as a supplement to courses in calculus, differential equations, numerical analysis, approximation theory, and computer-aided geometric design. Annotation c. by Book News, Inc., Portland, Or.

Cambridge Univ Pr
Iterations, that is transformations that are applied to objects over and over again, are the subject of this book. Three types of iteration are considered. The first, smoothing, is the process by which geometrical shapes can be transformed into standard types. Functional iteration is a way of describing the phenomenon of chaos. Finally, iterations involving curves and surfaces play an important role in computer aided design and graphics. These themes are explored and developed with no more background required than high school mathematics and a little calculus. Several basic strategies are highlighted which unlock solutions to problems involving iteration, and these are then applied to solve problems drawn from International Mathematical Olympiads.
Mathematical theme that relates chaos, graphics and geometry, all with just high school maths background.

Publisher: [Washington, DC] : Mathematical Association of America, Ă1997
ISBN: 9780883859537
Characteristics: 1 online resource : illustrations
Additional Contributors: Sederberg, Thomas W.


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