Convex functions - Roberts A.W., Varberg D.E.

Название: Convex functions
Автор: Roberts A.W., Varberg D.E.
Категория: Математика
Тип: Книга
Дата: 30.12.2008 16:41:34
Скачано: 91
Описание: The idea of writing this book grew out of an Undergraduate Research Program cooperatively directed by the authors. It has been well recognized, especially by Russian mathematicians, that the topic of convex sets affords an excellent means of introducing high school students to the beauty and fascination of advanced mathematics. (See for example Yaglom and Boltyanskil, "Convex Figures," 1961.) We came to feel that the study of convex functions was similarly suited to undergraduate college students of mathematics. There are several reasons for this: (a) it has high geometric and intuitive content, (b) it uses and reinforces in a significant way ideas the student has learned in his linear algebra and calculus courses, (c) it permits easy generalization to an abstract setting, (d) it naturally illuminates a number of mathematical gems, developing a taste for beauty and elegance, and (e) it is easy to pose challenging and even unsolved problems. With this in mind, we set out to collect in one place all the basic ideas and present them at a level appropriate to a college senior, to put together an extensive list of problems ranging from easy to very difficult, and to indicate areas that can be investigated as individual or group projects. Selected elementary properties of convex functions are often developed as needed in texts by authors whose main interest is another topic. Other properties appear as applications of theorems in real analysis or in the geometry of convex sets. As a result, known facts about convex
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