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The goal of Mathematical Vistas is to stimulate the interest of bright people in mathematics. The book consists of nine related mathematical essays which will intrigue and inform the curious reader. In order to offer a broad spectrum of exciting developments in mathematics, topics are treated at different levels of depth and thoroughness. Some chapters can be understood completely with little background, others can be thought of as appetizers for further study. A number of BREAKS are included in each chapter. These are problems designed to test the reader's understanding of the material thus…mehr

Produktbeschreibung
The goal of Mathematical Vistas is to stimulate the interest of bright people in mathematics. The book consists of nine related mathematical essays which will intrigue and inform the curious reader. In order to offer a broad spectrum of exciting developments in mathematics, topics are treated at different levels of depth and thoroughness. Some chapters can be understood completely with little background, others can be thought of as appetizers for further study. A number of BREAKS are included in each chapter. These are problems designed to test the reader's understanding of the material thus far in the chapter. This book is a sequel to the authors's popular book "Mathematical Reflections" and can be read independently.
  • Produktdetails
  • Undergraduate Texts in Mathematics
  • Verlag: Springer, Berlin
  • 2002
  • Seitenzahl: 356
  • Erscheinungstermin: 8. Januar 2002
  • Englisch
  • Abmessung: 260mm x 183mm x 24mm
  • Gewicht: 806g
  • ISBN-13: 9780387950648
  • ISBN-10: 0387950648
  • Artikelnr.: 10050386
Inhaltsangabe
From the contents:
- Paradoxes in Mathematics
- Not the Last of Fermat
- Fibonacci and Lucas Numbers: Their Connections and Divisibility Properties
- Paper-Folding, Polyhedra-Building and Number Theory
- Are Four Colors Enough?
- From Binomial to Trinomial Coefficients and Beyond
- Catalan Numbers
- Symmetry
- Parties
Rezensionen
From the reviews:

MAA ONLINE"...much of the material is about the authors' own research. This is a positive thing; its good for students at all levels to get information straight from the horse's mouth, not only for accuracy but also for enthusiasm and authenticity. The authors put their writing where their talents are, and students get to see just how alive mathematics is...there is much to comment the book. It contains plenty of interesting mathematics, often going in unusual directions. I like the diagrams; the authors have chosen mathematics that involves especially pretty ones. And readers with some mathematical experience are sure to find things here and there that will delight them. In elementary school, before first-year algebra had made me conscious of being a mathematician, I called my favorite pastime 'number tricks.' The section 'A Number Trick and its Explanations' brought back fond memories."P.Hilton, D.Holton, and J. Pedersen

Mathematical Vistas

From a Room with Many Windows"The authors put their writing where their talents are, and students get to see just how alive mathematics is . . . there is much to comment the book. It contains plenty of interesting mathematics, often going in unusual directions. I like the diagrams; the authors have chosen mathematics that involves especially pretty ones. And readers with some mathematical experience are sure to find things here and there that will delight them."- THE MATHEMATICAL ASSOCIATION OF AMERICA"Readers will find in ... Vistas more than another couple of collections of popular tidbits. ... a lively selection of mathematical topics delivered in a casual writing style, in which technical arguments are richly interspersed with comments on the guiding principles of mathematical investigation ... . Finally, a word of praise is due for the many illustrations appearing throughout ... these are carefully rendered and appropriate, never gratuitous. ... Enjoy!" (John Grant McLoughlin, Crux Mathematicorum Mathematical Mayhem, 2003)"All chapters have in common that they speak about their subject in a light manner. But in each chapter there are so-called breaks consisting of problems designed to enable the readers to test their understanding of the material. Answers to some of the problems appear at the end of the book. The reading of this book can be recommended for high school and college students who are interested in mathematics, and it may stimulate them to read more about it." (Helmut Koch, Zentralblatt MATH, Vol. 1011, 2003)"The purpose of this book ... is to provide a relaxed and informal treatment of several mathematical topics that will convey to the reader ... a sense of the pleasurable excitement that accompanies genuine mathematical discovery. ... topics range from Andrew Wile's famous proof of Fermat's Last Theorem ... to the discussion of paradoxes in which all relevant arguments are given in full. Each chapter is provided with 'Breaks', in which readers can test their understanding of the material just presented by answering questions." (Zentralblatt für Didaktik der Mathematik, August, 2003)"Peter Hilton, Derek Holton and Jean Pedersen have produced a gem ... . The authors have written a set of independent mathematical essays ... for which there is rarely room in the undergraduate curriculum. ... To be sure, there is a lot ... that forces reader participation and that is, frankly, fun. ... a joy to read, and I'm certain ... a delight to teach from! ... The writing is seamless, thought-provoking and entertaining. You and your students deserve to read ... !" (Marvin Schaefer, MAA Online, July, 2002)"The reader should not only approach this delightful book with pen and paper but also will find it worthwhile to consider attempting the geometric constructions." (F. J. Papp, Mathematical Reviews, Issue 2003 e)"It's good for students ... to get information straight from the horse's mouth, not only for accuracy but also for enthusiasm and auth…mehr