Over and Over Again by Gengzhe Chang (PDF)

Description

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.

User’s Reviews

Product description Book Description Mathematical theme that relates chaos, graphics and geometry, all with just high school maths background. Book Description Iterations are the subject of this book. Three types are considered. Smoothing is the process by which geometrical shapes can be transformed into standard types. Functional iteration is a way of describing chaos. Finally, iterations involving curves and surfaces play an important role in computer graphics.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book, like so many of their papers, can help clarify topics that you feel you should understand, but don’t. It covers topics that many college math graduates don’t understand well, with much of it at a high-school math level. For the self-taught computer programmer, it will cover many math topics that will help you in your career. As both authors have extensive backgrounds in computer graphics, you will notice that this book is slanted toward those ideas and algorithms. As a reference book, it explains the algorithms in clear language. It is well worth the money.Dr. Sederberg, one of the authors, has been said to make mathematics speak like poetry. He has written many papers in Computer Science and has had several publications in SIGGRAPH, the world’s most impressive computer graphics conference. Having just SIGGRAPH paper one is considered an accomplishment — he has 10 to date. Gengzhe Chang, I believe, was one of his Ph.D. students. Of their joint publications, I feel this is the most useful.

⭐There is a bright light in the iteration theory chapter, but overall it is pretty badly written and dull. The mathematics is all very good, but tastes like old soda crackers!

⭐This book, like so many of their papers, can help clarify topics that you feel you should understand, but don’t. It covers topics that many college math graduates don’t understand well, with much of it at a high-school math level. For the self-taught computer programmer, it will cover many math topics that will help you in your career. As both authors have extensive backgrounds in computer graphics, you will notice that this book is slanted toward those ideas and algorithms. As a reference book, it explains the algorithms in clear language. It is well worth the money.Dr. Sederberg, one of the authors, has been said to make mathematics speak like poetry. He has written many papers in Computer Science and has had several publications in SIGGRAPH, the world’s most impressive computer graphics conference. Having just SIGGRAPH paper one is considered an accomplishment — he has 10 to date. Gengzhe Chang, I believe, was one of his Ph.D. students. Of their joint publications, I feel this is the most useful.

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