Philip J Davis – författare

A number of years ago, Harriet Sheridan, then Dean of Brown University, organized a series oflectures in which individual faculty members described how it came about that they entered their various fields. I was invited to participate in this series and found in the invitation an opportunity to recall events going back to my early teens. The lecture was well received and its reception encouraged me to work up an expanded version. My manuscript lay dormant all these years. In the meanwhile, sufficiently many other mathematical experiences and encounters accumulated to make this little book. My 1981 lecture is the basis of the first piece: "Napoleon's Theorem. " Although there is a connection between the first piece and the second, the four pieces here are essentially independent. The sec­ ond piece, "Carpenter and the Napoleon Ascription," has as its object a full description of a certain type of scholar-storyteller (of whom I have known and admired several). It is a pastiche, contain­ ing a salad bar selection blended together by my own imagination. This piece purports, as a secondary goal, to present a solution to a certain unsolved historical problem raised in the first piece. The third piece, "The Man Who Began His Lectures with 'Namely'," is a short reminiscence of Stefan Bergman, one of my teachers of graduate mathematics. Bergman, a remarkable person­ ality, was born in Poland and came to the United States in 1939.

A circulant matrix is one in which a basic row of numbers is repeated again and again, but with a shift in position. Such matrices have connection to problems in physics, signal and image processing, probability, statistics, numerical analysis, algebraic coding theory, and many other areas. At the same time, the theory of circulants is easy, relative to the general theory of matrices. Practically every matrix-theoretic question for circulants may be resolved in closed form. Consequently, circulant matrices constitute a nontrivial but simple set of objects that the reader may use to practice, and ultimately deepen, a knowledge of matrix theory. They can also be viewed as special instances of structured or patterned matrices. This book serves as a general reference on circulants, as well as provides alternate or supplemental material for intermediate courses on matrix theory. There is some general discussion of matrices: block matrices, Kronecker products, decomposition theorems, generalised inverses. These topics were chosen because of their application to circulants and because they are not always found in books on linear algebra. More than 200 problems of varying difficulty are included.

From the Preface: This book is addressed to all who are curious about the nature of mathematics and its role in society. It is neither a text book nor a specialists'' book. It consists of a number of loosely linked essays that may be read independently and for which I have tried to provide a leitmotif by throwing light on the relationship between mathematics and common sense. In these essays I hope to foster a critical attitude towards both the existence of common sense in mathematics and the ambiguous role that it can play.

In this charming memoir, a renowned mathematician and winner of the American Book Award traces his career in mathematics from early lessons in horse racing and the realities of life to his adventures on the lecture circuit. A thought-provoking mix of autobiography, history, and insights into the role of mathematics in everyday life, this highly ent

"Ah, I''m Pingree. We meet again. Splendid. Won''t you sit down?"I looked around David''s room. Short of the library stacks, I had never seen so many books piled into a single room. Where could I sit down? Every square inch of horizontal surface was covered. Books, papers, notes, manuscripts-all congregated in random and chaotic disorder.This small en

"Ah, I’m Pingree. We meet again. Splendid. Won’t you sit down?"I looked around David’s room. Short of the library stacks, I had never seen so many books piled into a single room. Where could I sit down? Every square inch of horizontal surface was covered. Books, papers, notes, manuscripts—all congregated in random and chaotic disorder.This small encounter and the snapshot of the protagonist on the cover of this book introduce the reader to David E. Pingree, the eminent classicist, Orientalist, historian of ancient science, and member of the Department of the History of Mathematics at Brown University. This is a book of his stories, retold by Phil Davis, award-winning author and raconteur par excellence, who reconstructs them from letters and many conversations with his friend Pingree. The stories trace connections between ancient characters, historical and mythical, and recreate a world in which the pursuit of knowledge for its own sake leads to unexpected pleasures and associations. They capture a world best described by Saul Lieberman’s quip about Gershom Scholem’s great work on the Kabala: "Trash is trash; but the study of trash is scholarship," and David Pingree’s imagined response, "Yes, but there’s always something of value to be learned."The book is dedicated to preserving and promoting the specialized knowledge and thoughts of David Pingree, a truly remarkable person and to inspire readers to follow academic tradition and at the same time explore unusual connections.

In this charming memoir, a renowned mathematician and winner of the American Book Award traces his career in mathematics from early lessons in horse racing and the realities of life to his adventures on the lecture circuit. A thought-provoking mix of autobiography, history, and insights into the role of mathematics in everyday life, this highly ent

From the Preface: This book is addressed to all who are curious about the nature of mathematics and its role in society. It is neither a text book nor a specialists'' book. It consists of a number of loosely linked essays that may be read independently and for which I have tried to provide a leitmotif by throwing light on the relationship between mathematics and common sense. In these essays I hope to foster a critical attitude towards both the existence of common sense in mathematics and the ambiguous role that it can play.

A number of years ago, Harriet Sheridan, then Dean of Brown University, organized a series oflectures in which individual faculty members described how it came about that they entered their various fields. I was invited to participate in this series and found in the invitation an opportunity to recall events going back to my early teens. The lecture was well received and its reception encouraged me to work up an expanded version. My manuscript lay dormant all these years. In the meanwhile, sufficiently many other mathematical experiences and encounters accumulated to make this little book. My 1981 lecture is the basis of the first piece: "Napoleon''s Theorem. " Although there is a connection between the first piece and the second, the four pieces here are essentially independent. The sec­ ond piece, "Carpenter and the Napoleon Ascription," has as its object a full description of a certain type of scholar-storyteller (of whom I have known and admired several). It is a pastiche, contain­ ing a salad bar selection blended together by my own imagination. This piece purports, as a secondary goal, to present a solution to a certain unsolved historical problem raised in the first piece. The third piece, "The Man Who Began His Lectures with ''Namely''," is a short reminiscence of Stefan Bergman, one of my teachers of graduate mathematics. Bergman, a remarkable person­ ality, was born in Poland and came to the United States in 1939.

A number of years ago, Harriet Sheridan, then Dean of Brown University, organized a series oflectures in which individual faculty members described how it came about that they entered their various fields. I was invited to participate in this series and found in the invitation an opportunity to recall events going back to my early teens. The lecture was well received and its reception encouraged me to work up an expanded version. My manuscript lay dormant all these years. In the meanwhile, sufficiently many other mathematical experiences and encounters accumulated to make this little book. My 1981 lecture is the basis of the first piece: "Napoleon's Theorem. " Although there is a connection between the first piece and the second, the four pieces here are essentially independent. The sec­ ond piece, "Carpenter and the Napoleon Ascription," has as its object a full description of a certain type of scholar-storyteller (of whom I have known and admired several). It is a pastiche, contain­ ing a salad bar selection blended together by my own imagination. This piece purports, as a secondary goal, to present a solution to a certain unsolved historical problem raised in the first piece. The third piece, "The Man Who Began His Lectures with 'Namely'," is a short reminiscence of Stefan Bergman, one of my teachers of graduate mathematics. Bergman, a remarkable person­ ality, was born in Poland and came to the United States in 1939.

"Ah, I’m Pingree. We meet again. Splendid. Won’t you sit down?"I looked around David’s room. Short of the library stacks, I had never seen so many books piled into a single room. Where could I sit down? Every square inch of horizontal surface was covered. Books, papers, notes, manuscripts—all congregated in random and chaotic disorder.This small encounter and the snapshot of the protagonist on the cover of this book introduce the reader to David E. Pingree, the eminent classicist, Orientalist, historian of ancient science, and member of the Department of the History of Mathematics at Brown University. This is a book of his stories, retold by Phil Davis, award-winning author and raconteur par excellence, who reconstructs them from letters and many conversations with his friend Pingree. The stories trace connections between ancient characters, historical and mythical, and recreate a world in which the pursuit of knowledge for its own sake leads to unexpected pleasures and associations. They capture a world best described by Saul Lieberman’s quip about Gershom Scholem’s great work on the Kabala: "Trash is trash; but the study of trash is scholarship," and David Pingree’s imagined response, "Yes, but there’s always something of value to be learned."The book is dedicated to preserving and promoting the specialized knowledge and thoughts of David Pingree, a truly remarkable person and to inspire readers to follow academic tradition and at the same time explore unusual connections.

"Ah, I''m Pingree. We meet again. Splendid. Won''t you sit down?"I looked around David''s room. Short of the library stacks, I had never seen so many books piled into a single room. Where could I sit down? Every square inch of horizontal surface was covered. Books, papers, notes, manuscripts-all congregated in random and chaotic disorder.This small en

This book is a mathematical potpourri. Its material originated in classroom presentations, formal lectures, sections of earlier books, book reviews, or just things written by the author for his own pleasure. Written in a nontechnical fashion, this book expresses the unique vision and attitude of the author towards the role of mathematics in society. It contains observations or incidental remarks on mathematics, its nature, its impacts on education and science and technology, its personalities and their philosophies. The book is directed towards the math buffs of the world and, more generally, towards the literate and interested public.Philip Davis is known for his work in numerical analysis and approximation theory, as well as his investigations in the history and philosophy of mathematics. Currently a Professor Emeritus from the Division of Applied Mathematics at Brown University, Davis is known for his books both in the areas of computational mathematics and approximation theory and for books exploring certain questions in the philosophy of mathematics and the role of mathematics in society.

The further adventures of a feline philosopher and friend. Could it be? Hans Christian Andersen - who wrote so lovingly of inchworms and ugly ducklings - an unrepentant despiser of cats? That''s the rumor that the philosophical feline, Thomas Gray, and her (yes, her) cohort, Cambridge don Lucas Fysst, are determined to snuff out. In Copenhagen to attend a philosophers'' convention, they go on the hunt for a missing Andersen manuscript that will set the record straight. A sequel to the popular Thomas Gray, Philosopher Cat, Philip J. Davis'' latest is a whimsically written and illustrated tale - part history, part parody, and all fun.

The further adventures of a feline philosopher and friend.Could it be? Hans Christian Andersen - who wrote so lovingly of inchworms and ugly ducklings - an unrepentant despiser of cats? That's the rumor that the philosophical feline, Thomas Gray, and her (yes, her) cohort, Cambridge don Lucas Fysst, are determined to snuff out. In Copenhagen to attend a philosophers' convention, they go on the hunt for a missing Andersen manuscript that will set the record straight. A sequel to the popular Thomas Gray, Philosopher Cat, Philip J. Davis' latest is a whimsically written and illustrated tale - part history, part parody, and all fun.

Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.

From the Preface: "This book is addressed to all who are curious about the nature of mathematics and its role in society. It is neither a text book nor a specialists' book. It consists of a number of loosely linked essays that may be read independently and for which I have tried to provide a leitmotif by throwing light on the relationship between mathematics and common sense. In these essays I hope to foster a critical attitude towards both the existence of common sense in mathematics and the ambiguous role that it can play."

The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change again in the future? The authors include mathematicians, philosophers, computer scientists, cognitive psychologists, sociologists, educators and mathematical historians; each brings their own expertise and insights to the discussion. Contributors to this volume:Jeremy AvigadJody AzzouniDavid H. BaileyDavid BerlinskiJonathan M. BorweinErnest DavisPhilip J. DavisDonald GilliesJeremy GrayJesper LützenUrsula MartinKay O’HalloranAlison PeaseSteven PiantadosiLance RipsMicah T. RossNathalie SinclairJohn StillwellHellen Verran

The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change again in the future? The authors include mathematicians, philosophers, computer scientists, cognitive psychologists, sociologists, educators and mathematical historians; each brings their own expertise and insights to the discussion. Contributors to this volume:Jeremy AvigadJody AzzouniDavid H. BaileyDavid BerlinskiJonathan M. BorweinErnest DavisPhilip J. DavisDonald GilliesJeremy GrayJesper LützenUrsula MartinKay O’HalloranAlison PeaseSteven PiantadosiLance RipsMicah T. RossNathalie SinclairJohn StillwellHellen Verran