The Best Writing on Mathematics 2011 - Softcover

Softcover

ISBN 10: 0691153159 ISBN 13: 9780691153155

Verlag: Princeton University Press, 2011

Inhaltsangabe

This anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else - and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schattschneider identifies some of the mathematical inspirations of M. C. Escher's art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more.

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Über die Autorin bzw. den Autor

Mircea Pitici holds a PhD mathematics education from Cornell University, where he teaches math and writing. He has edited The Best Writing on Mathematics since 2010.

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The BEST WRITING on MATHEMATICS 2011

PRINCETON UNIVERSITY PRESS

Copyright © 2012 Princeton University Press
All right reserved.
ISBN: 978-0-691-15315-5

Contents

Foreword: Recreational Mathematics Freeman Dyson.............................................................................xiIntroduction Mircea Pitici...................................................................................................xviiWhat Is Mathematics For? Underwood Dudley....................................................................................1A Tisket, a Tasket, an Apollonian Gasket Dana Mackenzie......................................................................13The Quest for God's Number Rik van Grol......................................................................................27Meta-morphism: From Graduate Student to Networked Mathematician Andrew Schultz...............................................35One, Two, Many: Individuality and Collectivity in Mathematics Melvyn B. Nathanson............................................43Reflections on the Decline of Mathematical Tables Martin Campbell-Kelly......................................................51Under-Represented Then Over-Represented: A Memoir of Jews in American Mathematics Reuben Hersh...............................55Did Over-Reliance on Mathematical Models for Risk Assessment Create the Financial Crisis? David J. Hand......................67Fill in the Blanks: Using Math to Turn Lo-Res Datasets into Hi-Res Samples Jordan Ellenberg..................................75The Great Principles of Computing Peter J. Denning...........................................................................82Computer Generation of Ribbed Sculptures James Hamlin and Carlo H. Séquin...............................................93Lorenz System Offers Manifold Possibilities for Art Barry A. Cipra...........................................................115The Mathematical Side of M. C. Escher Doris Schattschneider..................................................................121Celebrating Mathematics in Stone and Bronze Helaman Ferguson and Claire Ferguson.............................................150Mathematics Education: Theory, Practice, and Memories over 50 Years John Mason...............................................169Thinking and Comprehending in the Mathematics Classroom Douglas Fisher, Nancy Frey, and Heather Anderson.....................188Teaching Research: Encouraging Discoveries Francis Edward Su.................................................................203Reflections of an Accidental Theorist Alan H. Schoenfeld.....................................................................219The Conjoint Origin of Proof and Theoretical Physics Hans Niels Jahnke.......................................................236What Makes Mathematics Mathematics? Ian Hacking..............................................................................257What Anti-realism in Philosophy of Mathematics Must Offer Feng Ye............................................................286Seeing Numbers Ivan M. Havel.................................................................................................312Autism and Mathematical Talent Ioan James....................................................................................330How Much Math is Too Much Math? Chris J. Budd and Rob Eastaway...............................................................336Hidden Dimensions Marianne Freiberger........................................................................................347Playing with Matches Erica Klarreich.........................................................................................356Notable Texts.................................................................................................................367Contributors..................................................................................................................371Acknowledgments...............................................................................................................379Credits.......................................................................................................................381

Chapter One

What Is Mathematics For?

Underwood Dudley

A more accurate title is "What is mathematics education for?" but the shorter one is more attention-getting and allows me more generality. My answer will become apparent soon, as will my answer to the sub-question of why the public supports mathematics education as much as it does.

So that there is no confusion, let me say that by "mathematics" I mean algebra, trigonometry, calculus, linear algebra, and so on: all those subjects beyond arithmetic. There is no question about what arithmetic is for or why it is supported. Society cannot proceed without it. Addition, subtraction, multiplication, division, percentages: though not all citizens can deal fluently with all of them, we make the assumption that they can when necessary. Those who cannot are sometimes at a disadvantage.

Algebra, though, is another matter. Almost all citizens can and do get through life very well without it, after their schooling is over. Nevertheless it becomes more and more pervasive, seeping down into more and more eighth-grade classrooms and being required by more and more states for graduation from high school. There is unspoken agreement that everyone should be exposed to algebra. We live in an era of universal mathematical education.

This is something new in the world. Mathematics has not always loomed so large in the education of the rising generation. There is no telling how many children in ancient Egypt and Babylon received training in numbers, but there were not many. Of course, in ancient civilizations education was not for everyone, much less mathematical education. Literacy was not universal, and I suspect that many who could read and write could not subtract or multiply numbers. The ancient Greeks, to their glory, originated real mathematics, but they did not do it to fill classrooms with students learning how to prove theorems. Compared to them, the ancient Romans were a mathematical blank. The Arab scholars who started to develop algebra after the fall of Rome were doing it for their own pleasure and not as something intended for the masses. When Brahmagupta was solving Pell's equation a millennium before Pell was born, he did not have students in mind.

Of course, you may think, those were the ancients; in modern times we have learned better, and arithmetic at least has always been part of everyone's schooling. Not so. It may come as a surprise to you, as it did to me, that arithmetic was not part of elementary education in the United States in the colonial period. In A History of Mathematics Education in the United States and Canada (National Council of Teachers of Mathematics, 1970), we read

Until within a few years no studies have been permitted in the day school but spelling, reading, and writing. Arithmetic was taught by a few instructors one or two evenings a week. But in spite of the most determined opposition, arithmetic is now being permitted in the day school.

Opposition to arithmetic! Determined opposition! How could such a thing be? How could society function without a population competent in arithmetic? Well, it did, and it even thrived. Arithmetic was indeed needed in many occupations, but those who needed it learned it on the job. It was a system that worked with arithmetic then and that can work...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 0691153159
• ISBN 13: 9780691153155
• Einband: Taschenbuch
• Anzahl der Seiten: 416
• Herausgeber: Pitici Mircea
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar