Ebook: Mathematical Vistas: From a Room with Many Windows

Focusing YourAttention We have called this book Mathematical Vistas because we have already published a companion book MathematicalRefiections in the same series;1 indeed, the two books are dedicated to the same principal purpose - to stimulate the interest ofbrightpeople in mathematics.Itis not our intention in writing this book to make the earlier book aprerequisite, but it is, of course, natural that this book should contain several references to its predecessor. This is especially - but not uniquely- true of Chapters 3, 4, and 6, which may be regarded as advanced versions of the corresponding chapters in Mathematical Reflections. Like its predecessor, the present work consists of nine chapters, each devoted to a lively mathematical topic, and each capable, in principle, of being read independently of the other chapters.' Thus this is not a text which- as is the intention of most standard treatments of mathematical topics - builds systematically on certain common themes as one proceeds 1Mathematical Reflections - In a Room with Many Mirrors, Springer Undergraduate Texts in Math­ ematics, 1996; Second Printing 1998. We will refer to this simply as MR. 2There was an exception in MR; Chapter 9 was concerned with our thoughts on the doing and teaching of mathematics at the undergraduate level.

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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 far in the chapter. This book is a sequel to the authors's popular book "Mathematical Reflections" and can be read independently.

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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 far in the chapter. This book is a sequel to the authors's popular book "Mathematical Reflections" and can be read independently.
Content:
Front Matter....Pages i-xiv
Paradoxes in Mathematics....Pages 1-21
Not the Last of Fermat....Pages 23-47
Fibonacci and Lucas Numbers: Their Connections and Divisibility Properties....Pages 49-69
Paper-Folding, Polyhedra-Building, and Number Theory....Pages 71-125
Are Four Colors Really Enough?....Pages 127-158
From Binomial to Trinomial Coefficients and Beyond....Pages 159-198
Catalan Numbers....Pages 199-233
Symmetry....Pages 235-269
Parties....Pages 271-297
Back Matter....Pages 299-337

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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 far in the chapter. This book is a sequel to the authors's popular book "Mathematical Reflections" and can be read independently.
Content:
Front Matter....Pages i-xiv
Paradoxes in Mathematics....Pages 1-21
Not the Last of Fermat....Pages 23-47
Fibonacci and Lucas Numbers: Their Connections and Divisibility Properties....Pages 49-69
Paper-Folding, Polyhedra-Building, and Number Theory....Pages 71-125
Are Four Colors Really Enough?....Pages 127-158
From Binomial to Trinomial Coefficients and Beyond....Pages 159-198
Catalan Numbers....Pages 199-233
Symmetry....Pages 235-269
Parties....Pages 271-297
Back Matter....Pages 299-337
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