The Best Writing on Mathematics 2014 (ebook)

Argumento de The Best Writing on Mathematics 2014 (ebook)

This annual anthology brings together the years 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 2014 makes available to a wide audience many articles not easily found anywhere elseand you dont 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 todays hottest mathematical debates. Here John Conway presents examples of arithmetical statements that are almost certainly true but likely unprovable; Carlo Séquin explores, compares, and illustrates distinct types of one-sided surfaces known as Klein bottles; Keith Devlin asks what makes a video game good for learning mathematics and shows why many games fall short of that goal; Jordan Ellenberg reports on a recent breakthrough in the study of prime numbers; Stephen Pollard argues that mathematical practice, thinking, and experience transcend the utilitarian value of mathematics; and much, much more.

In addition to presenting the years most memorable writings on mathematics, this must-have anthology includes an introduction by editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken usand where it is headed.

"Abundant diversity and some truly exceptional writing make this collection stand out."--Gretchen Kolderup, Library Journal

"[The] essays cover a broad swath of mathematics that include entertaining puzzles, complicated proofs, pedagogical philosophy, and technical discussions of mathematical problems. The pedagogical entries are both serious and light. . . . Many of the technical articles are difficult and demand a mathematical background, other entries are well suited for readers more casual readers; the volume is intended to capture both audiences and does it well."--Publishers Weekly

"For those looking to broaden their knowledge of mathematics, including recent mathematical developments, this is a good option and an enjoyable read."--Frannie Worek, Math Teacher

"[Piticis] work fills a gap between expository mathematics and popular explanation. It is a welcome contribution to improving public perception of our discipline."--Phill Schultz, Australian Mathematical Society Gazette

"I would characterize the articles in the book as extreme in terms of several value functions: clarity, lucidity, instructiveness, wittiness, modern day pertinency, broad accessibility. . . . On the whole, the book is informative and thoroughly entertaining."--Alexander Bogomolny, Cut the Knot

"Written in a pleasant and alive style, with suggestive quotations and witty comments of the author (also many photos illustrating the text are made by the author), the book will be of great help for students in computer science specializing in computer vision and computer graphics. Other students who use mathematics in their disciplines (physics, chemistry, biology, economics) will find the book as a good source of rapid and reliable information."--Dana Cobza, Studia Mathematica0Introduction, Mircea Pitici ix
Mathematics and the Good Life, Stephen Pollard 1
The Rise of Big Data: How Its Changing the Way We Think about the World, Kenneth Cukier and Viktor Mayer-Schönberger 20
Conways Wizards, Tanya Khovanova 33
On Unsettleable Arithmetical Problems, John H. Conway 39
Color illustration section follows page 48
Crinkly Curves, Brian Hayes 49
Why Do We Perceive Logarithmically? Lav R. Varshney and John Z. Sun 64
The Music of Math Games, Keith Devlin 74
The Fundamental Theorem of Algebra for Artists, Bahman Kalantari and Bruce Torrence 87
The ArtsDigitized, Quantified, and Analyzed, Nicole Lazar 96
On the Number of Klein Bottle Types, Carlo H. Séquin 105
Adventures in Mathematical Knitting, Sarah-Marie Belcastro 128
The Mathematics of Fountain Design: A Multiple-Centers Activity, Marshall Gordon 144
Food for (Mathematical) Thought, Penelope Dunham 156
Wondering about Wonder in Mathematics, Dov Zazkis and Rina Zazkis 165
The Lesson of Grace in Teaching, Francis Edward Su 188
Generic Proving: Reflections on Scope and Method, Uri Leron and Orit Zaslavsky 198
Extreme Proofs I: The Irrationality of 2, John H. Conway and Joseph Shipman 216
Stuck in the Middle: Cauchys Intermediate Value Theorem and the History of Analytic Rigor, Michael J. Barany 228
Plato, Poincaré, and the Enchanted Dodecahedron: Is the Universe Shaped Like the Poincaré Homology Sphere? Lawrence Brenton 239
Computing with Real Numbers, from Archimedes to Turing and Beyond, Mark Braverman 251
Chaos at Fifty, Adilson E. Motter and David K. Campbell 270
Twenty-Five Analogies for Explaining Statistical Concepts, Roberto Behar, Pere Grima, and Lluís Marco-Almagro 288
College Admissions and the Stability of Marriage, David Gale and Lloyd S. Shapley 299
The Beauty of Bounded Gaps, Jordan Ellenberg 308
Contributors 315
Notable Writings 325
Acknowledgments 333
Credits 335