books tagged “math”

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The Annotated Flatland: A Romance of Many Dimensions
by Ian Stewart, Edwin Abbott Abbott

ISBN 0738205419 (0-7382-0541-9)
Hardcover, Perseus Books Group

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Book summary:
The product of an agreeably dotty cleric named Edwin Abbott Abbott and first published in 1884, Flatland distills all that the Victorian era knew of higher mathematics--and then some--into a witty, complex novel of ideas.
Ian Stewart, the author of the equally witty sequel, Flatterland--which adds to Abbott's store of science the key discoveries made since--does a superb job of explaining the original book's enigmas, allusions, ironies, implausibilities, and what Douglas Hofstadter would call "metamagical themas." Among other things, Stewart comments on Abbott's comments on such things as the nature/nurture controversy, the fourth dimension and beyond, the role of multidimensional spaces in economic systems, infinite series and perfect squares, celestial mechanics, and other matters close to the hearts of cosmologists and science buffs alike.
Stewart's notes make an entertaining and learned addition to an already classic bit of writing--one that has never been out of print since its first publication. For both devoted Abbott fans and newcomers to his work, this is the edition to have. --Gregory McNamee [via]
More editions of The Annotated Flatland: A Romance of Many Dimensions:
- The Annotated Flatland: A Romance of Many Dimensions: ISBN 0738205419 (0-7382-0541-9)
  Hardcover, Perseus Books Group
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Beautiful Mind: A Biography of John Forbes Nash, Jr., Winner of the Nobel Prize in Economics, 1994
by Sylvia Nasar

ISBN 0684853701 (0-684-85370-1)
Softcover, Simon & Schuster

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Book summary:
Stories of famously eccentric Princetonians abound--such as that of chemist Hubert Alyea, the model for The Absent-Minded Professor, or Ralph Nader, said to have had his own key to the library as an undergraduate. Or the "Phantom of Fine Hall," a figure many students had seen shuffling around the corridors of the math and physics building wearing purple sneakers and writing numerology treatises on the blackboards. The Phantom was John Nash, one of the most brilliant mathematicians of his generation, who had spiraled into schizophrenia in the 1950s. His most important work had been in game theory, which by the 1980s was underpinning a large part of economics. When the Nobel Prize committee began debating a prize for game theory, Nash's name inevitably came up--only to be dismissed, since the prize clearly could not go to a madman. But in 1994 Nash, in remission from schizophrenia, shared the Nobel Prize in economics for work done some 45 years previously.
Economist and journalist Sylvia Nasar has written a biography of Nash that looks at all sides of his life. She gives an intelligent, understandable exposition of his mathematical ideas and a picture of schizophrenia that is evocative but decidedly unromantic. Her story of the machinations behind Nash's Nobel is fascinating and one of very few such accounts available in print (the CIA could learn a thing or two from the Nobel committees). This highly recommended book is indeed "a story about the mystery of the human mind, in three acts: genius, madness, reawakening." --Mary Ellen Curtin [via]
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A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash
by Sylvia Nasar

ISBN 0743224574 (0-7432-2457-4)
Softcover, Simon & Schuster

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Book summary:
Stories of famously eccentric Princetonians abound--such as that of chemist Hubert Alyea, the model for The Absent-Minded Professor, or Ralph Nader, said to have had his own key to the library as an undergraduate. Or the "Phantom of Fine Hall," a figure many students had seen shuffling around the corridors of the math and physics building wearing purple sneakers and writing numerology treatises on the blackboards. The Phantom was John Nash, one of the most brilliant mathematicians of his generation, who had spiraled into schizophrenia in the 1950s. His most important work had been in game theory, which by the 1980s was underpinning a large part of economics. When the Nobel Prize committee began debating a prize for game theory, Nash's name inevitably came up--only to be dismissed, since the prize clearly could not go to a madman. But in 1994 Nash, in remission from schizophrenia, shared the Nobel Prize in economics for work done some 45 years previously.
Economist and journalist Sylvia Nasar has written a biography of Nash that looks at all sides of his life. She gives an intelligent, understandable exposition of his mathematical ideas and a picture of schizophrenia that is evocative but decidedly unromantic. Her story of the machinations behind Nash's Nobel is fascinating and one of very few such accounts available in print (the CIA could learn a thing or two from the Nobel committees). This highly recommended book is indeed "a story about the mystery of the human mind, in three acts: genius, madness, reawakening." --Mary Ellen Curtin [via]
More editions of A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash:
- A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash: ISBN 0743224574 (0-7432-2457-4)
  Softcover, Simon & Schuster
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Beyond Numeracy: Ruminations of a Numbers Man
by John Allen Paulos

ISBN 067973807X (0-679-73807-X)
Softcover, Random House Inc

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Book summary:
Beyond Numeracy by bestselling author John Allen Paulos is, according to the introduction, "in part a dictionary, in part a collection of short mathematical essays, and in part the ruminations of a numbers man." This book is genuinely different from other books on mathematics intended for a wide audience as the essay topics are indisputably diverse. (Titles include "Human Consciousness, Its Fractal Nature" and "Mathematics in Ethics.") Furthermore, Paulos's unique sense of humor and ability to intelligently editorialize are delightful--especially in a book on such a dry subject. [via]
More editions of Beyond Numeracy: Ruminations of a Numbers Man:
- Beyond Numeracy: Ruminations of a Numbers Man: ISBN 0394586409 (0-394-58640-9)
  Hardcover, Knopf Publishing Group
- Beyond Numeracy: Ruminations of a Numbers Man: ISBN 067973807X (0-679-73807-X)
  Softcover, Random House Inc
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Calculus and Analytic Geometry
by George B. Thomas, Ross L. Finney

ISBN 0201712164 (0-201-71216-4)
Hardcover, Addison-Wesley

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Book summary:
George Thomas' clear, precise calculus text with superior applications defined the modern-day, three-semester or four-quarter calculus course. The ninth edition of this proven text has been carefully revised to give students the solid base of material they will need to succeed in math, science, and engineering programs. This edition includes recent innovations in teaching and learning that involve technology, projects, and group work. [via]
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Calculus and Analytic Geometry: Alternate Edition
by Ross L. Finney, George D. Thomas

ISBN 0321193636 (0-321-19363-6)
Hardcover, Addison-Wesley

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Book summary:
George Thomas' clear precise calculus text with superior applications defined the modern-day calculus course. This proven text gives students the solid base of material they will need to succeed in math, science, and engineering programs. [via]
More editions of Calculus and Analytic Geometry: Alternate Edition:
- Calculus and Analytic Geometry: Alternate Edition: ISBN 0321193636 (0-321-19363-6)
  Hardcover, Addison-Wesley
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Chaos
by James Gleick

ISBN 0140092501 (0-14-009250-1)
Softcover, Penguin Group USA

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Book summary:
Few writers distinguish themselves by their ability to write about complicated, even obscure topics clearly and engagingly. James Gleick, a former science writer for the New York Times, resides in this exclusive category. In Chaos, he takes on the job of depicting the first years of the study of chaos--the seemingly random patterns that characterize many natural phenomena.
This is not a purely technical book. Instead, it focuses as much on the scientists studying chaos as on the chaos itself. In the pages of Gleick's book, the reader meets dozens of extraordinary and eccentric people. For instance, Mitchell Feigenbaum, who constructed and regulated his life by a 26-hour clock and watched his waking hours come in and out of phase with those of his coworkers at Los Alamos National Laboratory.
As for chaos itself, Gleick does an outstanding job of explaining the thought processes and investigative techniques that researchers bring to bear on chaos problems. Rather than attempt to explain Julia sets, Lorenz attractors, and the Mandelbrot Set with gigantically complicated equations, Chaos relies on sketches, photographs, and Gleick's wonderful descriptive prose. [via]
More editions of Chaos:
- Chaos: ISBN 0670811785 (0-670-81178-5)
  Hardcover, Penguin Group USA
- Chaos: ISBN 0140092501 (0-14-009250-1)
  Softcover, Penguin Group USA
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The Code Book for Young People
by Simon Singh

ISBN 0385730624 (0-385-73062-4)
Softcover, Random House Children's Books

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Book summary:
Calling upon accounts of political intrigue and tales of life and death, author Simon Singh tells history's most fascinating story of deception and cunning: the science of cryptography--the encoding and decoding of private information. Based on The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography, this version has been abridged and slightly simplified for a younger audience. None of the appeal for curious problem-solving minds has been lost, though. From Julius Caesar to the 10th-century Arabs; from Mary Queen of Scots to "Alice and Bob"; from the Germans' Enigma machine to the Navajo code talkers in World War II, Singh traces the use of code to protect--and betray--secrecy. Moving right into the present, he describes how the Information Age has provided a whole new set of challenges for cryptographers. How private are your e-mail communications? How secure is sending your credit card information over the Internet? And how much secrecy will the government tolerate? Complex but highly accessible, The Code Book will make readers see the past--and the future--in a whole new light. (Ages 14 and older) [via]
More editions of The Code Book for Young People:
- The Code Book for Young People: ISBN 0385730624 (0-385-73062-4)
  Softcover, Random House Children's Books
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The Code Book : The Evolution of Secrecy from Mary, Queen of Scots to Quantum Cryptography
by Simon Singh

ISBN 0385495315 (0-385-49531-5)
Hardcover, Doubleday Publishing

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Book summary:
People love secrets, and ever since the first word was written, humans have written coded messages to each other. In The Code Book, Simon Singh, author of the bestselling Fermat's Enigma, offers a peek into the world of cryptography and codes, from ancient texts through computer encryption. Singh's compelling history is woven through with stories of how codes and ciphers have played a vital role in warfare, politics, and royal intrigue. The major theme of The Code Book is what Singh calls "the ongoing evolutionary battle between codemakers and codebreakers," never more clear than in the chapters devoted to World War II. Cryptography came of age during that conflict, as secret communications became critical to either side's success.

Confronted with the prospect of defeat, the Allied cryptanalysts had worked night and day to penetrate German ciphers. It would appear that fear was the main driving force, and that adversity is one of the foundations of successful codebreaking.
In the information age, the fear that drives cryptographic improvements is both capitalistic and libertarian--corporations need encryption to ensure that their secrets don't fall into the hands of competitors and regulators, and ordinary people need encryption to keep their everyday communications private in a free society. Similarly, the battles for greater decryption power come from said competitors and governments wary of insurrection. The Code Book is an excellent primer for those wishing to understand how the human need for privacy has manifested itself through cryptography. Singh's accessible style and clear explanations of complex algorithms cut through the arcane mathematical details without oversimplifying. Can't get enough crypto? Try solving the Cipher Challenge in the back of the book--$15,000 goes to the first person to crack the code! --Therese Littleton [via]
More editions of The Code Book : The Evolution of Secrecy from Mary, Queen of Scots to Quantum Cryptography:
- The Code Book : The Evolution of Secrecy from Mary, Queen of Scots to Quantum Cryptography: ISBN 0385495315 (0-385-49531-5)
  Hardcover, Doubleday Publishing
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The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography
by Simon Singh

ISBN 0385495323 (0-385-49532-3)
Softcover, Random House Inc

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Book summary:
People love secrets. Ever since the first word was written, humans have sent coded messages to each other. In The Code Book, Simon Singh, author of the bestselling Fermat's Enigma, offers a peek into the world of cryptography and codes, from ancient texts through computer encryption. Singh's compelling history is woven through with stories of how codes and ciphers have played a vital role in warfare, politics, and royal intrigue. The major theme of The Code Book is what Singh calls "the ongoing evolutionary battle between codemakers and codebreakers," never more clear than in the chapters devoted to World War II. Cryptography came of age during that conflict, as secret communications became critical to both sides' success.

Confronted with the prospect of defeat, the Allied cryptanalysts had worked night and day to penetrate German ciphers. It would appear that fear was the main driving force, and that adversity is one of the foundations of successful codebreaking.
In the information age, the fear that drives cryptographic improvements is both capitalistic and libertarian--corporations need encryption to ensure that their secrets don't fall into the hands of competitors and regulators, and ordinary people need encryption to keep their everyday communications private in a free society. Similarly, the battles for greater decryption power come from said competitors and governments wary of insurrection.
The Code Book is an excellent primer for those wishing to understand how the human need for privacy has manifested itself through cryptography. Singh's accessible style and clear explanations of complex algorithms cut through the arcane mathematical details without oversimplifying. --Therese Littleton [via]
More editions of The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography:
- The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography: ISBN 0756754739 (0-7567-5473-9)
  Hardcover, Diane Pub Co
- The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography: ISBN 0385495323 (0-385-49532-3)
  Softcover, Random House Inc
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E: The Story of a Number
by Eli Maor

ISBN 0691058547 (0-691-05854-7)
Softcover, Princeton Univ Pr

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Book summary:
Until about 1975, logarithms were every scientist's best friend. They were the basis of the slide rule that was the totemic wand of the trade, listed in huge books consulted in every library. Then hand-held calculators arrived, and within a few years slide rules were museum pieces.
But e remains, the center of the natural logarithmic function and of calculus. Eli Maor's book is the only more or less popular account of the history of this universal constant. Maor gives human faces to fundamental mathematics, as in his fantasia of a meeting between Johann Bernoulli and J.S. Bach. e: The Story of a Number would be an excellent choice for a high school or college student of trigonometry or calculus. --Mary Ellen Curtin [via]
More editions of E: The Story of a Number:
- E: The Story of a Number: ISBN 0691033900 (0-691-03390-0)
  Hardcover, Princeton Univ Pr
- E: The Story of a Number: ISBN 0691058547 (0-691-05854-7)
  Softcover, Princeton Univ Pr
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Elementary Differential Equations
by William E. Boyce

ISBN 0471135828 (0-471-13582-8)
Softcover, John Wiley & Sons Inc

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Book summary:
This revision of Boyce and DiPrima's text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Like previous editions, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. A perennial best seller designed for engineers and scientists who need to use Elementary Differential Equations in their work and studies.The CD-ROM includes: The award-winning ODE Architect software. The software's 14 modules enable you to build and solve your own ODEs, and to use simulations and multimedia to develop detailed mathematical models and concepts in a truly interactive environment, and the ODE Architect Companion. The Companion extends the ideas featured in each multimedia module. The web-based learning tools include: Review and Study Guidelines. The Chapter Review Guidelines will help you prepare for quizzes and exams; Online Review Quizzes. The quizzes enable you to test your knowledge of key concepts and provide diagnostic feedback that references appropriate sections in the text; PowerPoint Slides. You can print these slides out for in-class note taking; and, getting started with ODE Architect. This guide will help you get up-and-running with ODE Architect's simulations and multimedia. [via]
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Elementary Differential Equations and Boundary Value Problems
by William E. Boyce, Richard C. Diprima

ISBN 0471078956 (0-471-07895-6)
Hardcover, Wiley

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Book summary:
This book covers all the essential topics on differential equations, including series solutions, Laplace transforms, systems of equations, numerical methods and phase plane methods. Clear explanations are detailed with many current examples. [via]
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Elementary Differential Equations and Boundary Value Problems
by Richard C. Diprima, William Boyce, Charles W. Haines

ISBN 0471433403 (0-471-43340-3)
Softcover, John Wiley & Sons Inc

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Book summary:
This revision of Boyce & DiPrima's market-leading text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Like previous editions, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences.

Student Solutions Manual:
Created as an integral learning aid to Boyce and DiPrima's Elementary Differntial Equations, 8E, this Solutions Manual provides worked out answers to select problems in the text. Using the Solutions Manual as you work your way through the course will ensure that you are doing the work right all along. [via]
More editions of Elementary Differential Equations and Boundary Value Problems:
- Elementary Differential Equations and Boundary Value Problems: ISBN 0471433403 (0-471-43340-3)
  Softcover, John Wiley & Sons Inc
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Elementary Differential Equations With Boundary Value Problems: Course Advantage Edition
by William E. Boyce, Richard C. Diprima

ISBN 0471307890 (0-471-30789-0)
Hardcover, John Wiley & Sons Inc

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Book summary:
Boyce & DiPrima's market-leading text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. A reorganized structure helps to make concepts even clearer and easier to understand. An abundance of new problems have been added to the problem sets, with special attention paid to incorporating computer technology.
Like previous editions, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. The text is intended for a sophomore/junior level course in Ordinary Differential Equations that is taught in departments of mathematics and engineering with a calculus prerequisite.Take advantage of a valuable opportunity
When you purchase this new Course Advantage Edition of Boyce & Diprima's Elementary Differential Equations and Boudary Value Problems, 7/e, you'll have all the resources you need to succeed in your course. The Course Advantage Edition gives you a CD-ROM with powerful ODE Architect modeling software and a special registration password that connects you to an array of Web-based Learning tools.
The CD-ROM includes:
- The award-winning ODE Architect software. The software's 14 modules enable you to build and solve your own ODEs, and to use simulations and multimedia to develop detailed mathematical models and concepts in a truly interactive environment.
- The ODE Architect Companion. The Companion extends the ideas featured in each multimedia module.
- Student solutions Manual. This electronic solutions manual contains selected problems from th textbook.
- An electronic version of the entire Seventh Edition. The electronic version of the text features hyperlinks for navigation, as well as hyperlinks to the ODE Architect software and the Student Solutions Manual.
The Web-based learning tools include:
- Review & Study Outlines. The Chapter Review Outlines will help you prepare for quizzes and exams.
- Online Review Quizzes. The quizzes enable you to test your knowledge of key concepts and provide diagnostic feedback that references appropriate sections in the text.
- PowerPoint Slides. You can print these slides out for in-class note taking.
- Getting Started with ODE Architect. This guide will help you get up-and-running with ODE Architect's simulations and multimedia.
[via]
More editions of Elementary Differential Equations With Boundary Value Problems: Course Advantage Edition:
- Elementary Differential Equations With Boundary Value Problems: Course Advantage Edition: ISBN 0471307890 (0-471-30789-0)
  Hardcover, John Wiley & Sons Inc
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Everything and More: A Compact History of Infinity
by David Foster Wallace

ISBN 0393326292 (0-393-32629-2)
Softcover, W W Norton & Co Inc

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Book summary:
Before discussing the merits of David Foster Wallace's Everything and More: A Compact History of Infinity, it is essential to define what the book is not. This volume in the "Great Discoveries" series is not a history of the personalities and social conditions that led to the "discovery" of infinity. Nor is it a narrative fixated on the cultish fear of--and obsession with--the infinite that has seemingly driven mathematicians insane over the centuries. Rather, Everything and More is a surprisingly rigorous march through the 2000 plus years of mathematical research that began with Aristotle; continued through Galileo, Isaac Newton, G.W. Leibniz, Karl Weierstrass, and J.W.R. Dedekind; and culminated in Georg Cantor and his Set Theory. The task Wallace (author of the bestseller Infinite Jest and other fiction) has set himself is enormously challenging: without radically compromising the complexity of the philosophy, metaphysics, or mathematics that underlies the evolving concept of infinity, present the material to a lay audience in a manner that is entertaining. To propel his narrative, Wallace even develops a style that mirrors the mathematical language he probes. One difficulty in his focus on concepts and not a strict human chronology, though, is that his structure is dependent on frequent digressions (especially early on). Patience is required. Wallace demands that his reader walk through the equations, study the graphs and charts, and relearn college-level concepts to follow along on the exploration. Indeed, after one wrenching dip into Zenos paradoxes, Wallace spouts at his imagined complaining audience: "Deal." But the book should be deemed a success. If one grants him the attention he requires, Wallace has made the trip richly rewarding. --Patrick OKelley [via]
More editions of Everything and More: A Compact History of Infinity:
- Everything and More: A Compact History of Infinity: ISBN 0393003388 (0-393-00338-8)
  Hardcover, Norton & Company, Incorporated, W. W.
- Everything And More: A Compact History Of Infinity: ISBN 0393326292 (0-393-32629-2)
  Softcover, W W Norton & Co Inc
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Fermat's Enigma
by Simon Singh

ISBN 0385493622 (0-385-49362-2)
Softcover, Random House Inc

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Book summary:
When Andrew Wiles of Princeton University announced a solution of Fermat's last theorem in 1993 it electrified the world of mathematics. After a flaw was discovered in the proof, Wiles had to work for another year--he had already labored in solitude for seven years--to establish that he had solved the 350-year-old problem. Simon Singh's book is a lively, comprehensible explanation of Wiles's work and of the star-, trauma-, and wacko-studded history of Fermat's last theorem. Fermat's Enigma contains some problems that offer a taste for the math, but it also includes limericks to give a feeling for the goofy side of mathematicians. [via]
More editions of Fermat's Enigma:
- Fermat's Enigma: ISBN 0613181050 (0-613-18105-0)
  Hardcover, Bt Bound
- Fermat's Enigma: ISBN 0385493622 (0-385-49362-2)
  Softcover, Random House Inc
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Fermat's Enigma: The Quest to Solve the World's Greatest Mathematical Problem
by Simon Singh

ISBN 0802713319 (0-8027-1331-9)
Hardcover, Walker & Company

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Book summary:
When Andrew Wiles of Princeton University announced a solution of Fermat's last theorem in 1993 it electrified the world of mathematics. After a flaw was discovered in the proof, Wiles had to work for another year--he had already labored in solitude for seven years--to establish that he had solved the 350-year-old problem. Simon Singh's book is a lively, comprehensible explanation of Wiles's work and of the star-, trauma-, and wacko-studded history of Fermat's last theorem. Fermat's Enigma contains some problems that offer a taste for the math, but it also includes limericks to give a feeling for the goofy side of mathematicians. [via]
More editions of Fermat's Enigma: The Quest to Solve the World's Greatest Mathematical Problem:
- Fermat's Enigma: The Quest to Solve the World's Greatest Mathematical Problem: ISBN 0802713319 (0-8027-1331-9)
  Hardcover, Walker & Company
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Fermat's Last Theorem: The Story of a Riddle That Confounded the World's Greatest Minds for 358 Years
by Simon Singh

ISBN 1857026691 (1-85702-669-1)
Hardcover, Fourth Estate

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Book summary:
In 1963, a schoolboy browsing in his local library stumbled across a great mathematical problem: Fermat's Last Theorem, a puzzle that every child can now understand, but which has baffled mathematicians for over 300 years. Aged just ten, Andrew Wiles dreamed he would crack it. Many people had tried before Wiles and failed, including an 18th-century philanderer who was killed in a duel. An 18th-century Frenchwoman made a major breakthrough in solving the riddle, but she had to attend maths lectures at the Ecole Polytechnique disguised as a man. This is the story of the puzzle that has confounded mathematicians since the 17th century. The solution of the Theorem is one of the most important mathematical developments of the 20th century. [via]
More editions of Fermat's Last Theorem: The Story of a Riddle That Confounded the World's Greatest Minds for 358 Years:
- Fermat's Last Theorem: The Story of a Riddle That Confounded the World's Greatest Minds for 358 Years: ISBN 1857026691 (1-85702-669-1)
  Hardcover, Fourth Estate
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Flatland
by Edwin Abbott Abbott

ISBN 1406503436 (1-4065-0343-6)
Softcover, Dodo Pr

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Book summary:
Flatland is one of the very few novels about math and philosophy that can appeal to almost any layperson. Published in 1880, this short fantasy takes us to a completely flat world of two physical dimensions where all the inhabitants are geometric shapes, and who think the planar world of length and width that they know is all there is. But one inhabitant discovers the existence of a third physical dimension, enabling him to finally grasp the concept of a fourth dimension. Watching our Flatland narrator, we begin to get an idea of the limitations of our own assumptions about reality, and we start to learn how to think about the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England. [via]
More editions of Flatland:
Flatland : A Romance of Many Dimensions
by Edwin A. Abbot

ISBN 1419120026 (1-4191-2002-6)
Softcover, Kessinger Pub Co

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Book summary:
Flatland is one of the very few novels about math and philosophy that can appeal to almost any layperson. Published in 1880, this short fantasy takes us to a completely flat world of two physical dimensions where all the inhabitants are geometric shapes, and who think the planar world of length and width that they know is all there is. But one inhabitant discovers the existence of a third physical dimension, enabling him to finally grasp the concept of a fourth dimension. Watching our Flatland narrator, we begin to get an idea of the limitations of our own assumptions about reality, and we start to learn how to think about the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England. [via]
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Flatland
by A. Square

ISBN 1883938775 (1-883938-77-5)
Softcover, Dry Bones Pr

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More editions of Flatland:
- Flatland: ISBN 1883938775 (1-883938-77-5)
  Softcover, Dry Bones Pr
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Flatland: A Journey of Many Dimensions
by Edwin A. Abbott, Dionys Burger

ISBN 0062732765 (0-06-273276-5)
Softcover, Harper Resource

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Book summary:
Unless you're a mathematician, the chances of you reading any novels about geometry are probably slender. But if you read only two in your life, these are the ones. Taken together, they form a couple of accessible and charming explanations of geometry and physics for the curious non-mathematician. Flatland, which is also available under separate cover, was published in 1880 and imagines a two-dimensional world inhabited by sentient geometric shapes who think their planar world is all there is. But one Flatlander, a Square, discovers the existence of a third dimension and the limits of his world's assumptions about reality and comes to understand the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England. The further mathematical fantasy, Sphereland, published 60 years later, revisits the world of Flatland in time to explore the mind-bending theories created by Albert Einstein, whose work so completely altered the scientific understanding of space, time, and matter. Among Einstein's many challenges to common sense were the ideas of curved space, an expanding universe and the fact that light does not travel in a straight line. Without use of the mathematical formulae that bar most non-scientists from an understanding of Einstein's theories, Sphereland gives lay readers ways to start comprehending these confusing but fundamental questions of our reality. [via]
More editions of Flatland: A Journey of Many Dimensions:
- Flatland: A Journey of Many Dimensions: ISBN 0062732765 (0-06-273276-5)
  Softcover, Harper Resource
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Godel's Proof
by Ernest Nagel, Douglas R. Hofstadter, James Roy Newman

ISBN 0814758169 (0-8147-5816-9)
Hardcover, New York Univ Pr

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Book summary:
'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.'  The Guardian

In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from maths to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godels theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, Godels Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.

Kurt Godel (1906 1978) Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J.
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Godel, Escher, Bach: An Eternal Golden Braid
by Douglas R. Hofstadter

ISBN 0465026567 (0-465-02656-7)
Softcover, Basic Books

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Book summary:
As stated in the Scientific American, "Every few decades an unknown author brings out a boof of such depth, clarity range, wit beauty and originality that it is recognized at once as a major literary event - this is such a work." [via]
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The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
by Mario Livio

ISBN 0767908163 (0-7679-0816-3)
Softcover, Bantam Dell Pub Group

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Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!

The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist. [via]
More editions of The Golden Ratio: The Story of Phi, the World's Most Astonishing Number:
- The Golden Ratio : The Story of Phi, the World's Most Astonishing Number: ISBN 0767908155 (0-7679-0815-5)
  Hardcover, Broadway Books
- The Golden Ratio: The Story of Phi, the World's Most Astonishing Number: ISBN 0767908163 (0-7679-0816-3)
  Softcover, Bantam Dell Pub Group
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History of Pi
by Peter Beckmann

ISBN 0312381859 (0-312-38185-9)
Softcover, St Martins Pr

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Book summary:
The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.
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How to Lie With Statistics
by Darrell Huff

ISBN 039309426X (0-393-09426-X)
Softcover, W W Norton & Co Inc

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Book summary:
"There is terror in numbers," writes Darrell Huff in How to Lie with Statistics. And nowhere does this terror translate to blind acceptance of authority more than in the slippery world of averages, correlations, graphs, and trends. Huff sought to break through "the daze that follows the collision of statistics with the human mind" with this slim volume, first published in 1954. The book remains relevant as a wake-up call for people unaccustomed to examining the endless flow of numbers pouring from Wall Street, Madison Avenue, and everywhere else someone has an axe to grind, a point to prove, or a product to sell. "The secret language of statistics, so appealing in a fact-minded culture, is employed to sensationalize, inflate, confuse, and oversimplify," warns Huff.
Although many of the examples used in the book are charmingly dated, the cautions are timeless. Statistics are rife with opportunities for misuse, from "gee-whiz graphs" that add nonexistent drama to trends, to "results" detached from their method and meaning, to statistics' ultimate bugaboo--faulty cause-and-effect reasoning. Huff's tone is tolerant and amused, but no-nonsense. Like a lecturing father, he expects you to learn something useful from the book, and start applying it every day. Never be a sucker again, he cries!

Even if you can't find a source of demonstrable bias, allow yourself some degree of skepticism about the results as long as there is a possibility of bias somewhere. There always is.
Read How to Lie with Statistics. Whether you encounter statistics at work, at school, or in advertising, you'll remember its simple lessons. Don't be terrorized by numbers, Huff implores. "The fact is that, despite its mathematical base, statistics is as much an art as it is a science." --Therese Littleton [via]
More editions of How to Lie With Statistics:
- How to Lie With Statistics: ISBN 0393310728 (0-393-31072-8)
  Softcover, W W Norton & Co Inc
- How to Lie With Statistics: ISBN 039309426X (0-393-09426-X)
  Softcover, W W Norton & Co Inc
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How to Solve It: A New Aspect of Mathematical Method
by George Polya, John Horton Conway

ISBN 069111966X (0-691-11966-X)
Softcover, Princeton Univ Pr

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Book summary:
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight.
In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.
[via]
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Innumeracy
by John Allen Paulos

ISBN 0809058405 (0-8090-5840-5)
Softcover, Farrar Straus & Giroux

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This is the book that made "innumeracy" a household word, at least in some households. Paulos admits that "at least part of the motivation for any book is anger, and this book is no exception. I'm distressed by a society which depends so completely on mathematics and science and yet seems to indifferent to the innumeracy and scientific illiteracy of so many of its citizens."
But that is not all that drives him. The difference between our pretensions and reality is absurd and humorous, and the numerate can see this better than those who don't speak math. "I think there's something of the divine in these feelings of our absurdity, and they should be cherished, not avoided."
Paulos is not entirely successful at balancing anger and absurdity, but he tries. His diatribes against astrology, bad math education, Freud, and willful ignorance are leavened with jokes, mathematical or the sort (he claims) favored by the numerate.
It remains to be seen if Innumeracy will indeed be able, as Hofstadter hoped, to "help launch a revolution in math education that would do for innumeracy what Sabin and Salk did for polio"--but many of the improvements Paulos suggested have come to pass within 10 years. Only time will tell if the generation raised on these new principles is more resistant to innumeracy--and need only worry about being incomputable. --Mary Ellen Curtin [via]
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Introduction to Differential Equations
by William E. Boyce, Richard C. Diprima

ISBN 0471093386 (0-471-09338-6)
Hardcover, J. Wiley

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- Introduction to Differential Equations: ISBN 0471093386 (0-471-09338-6)
  Hardcover, J. Wiley
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The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth
by Paul Hoffman

ISBN 0786884061 (0-7868-8406-1)
Softcover, Hyperion Books

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Book summary:
Paul Erdös was an amazing and prolific mathematician whose life as a world-wandering numerical nomad was legendary. He published almost 1500 scholarly papers before his death in 1996, and he probably thought more about math problems than anyone in history. Like a traveling salesman offering his thoughts as wares, Erdös would show up on the doorstep of one mathematician or another and announce, "My brain is open." After working through a problem, he'd move on to the next place, the next solution.
Hoffman's book, like Sylvia Nasar's biography of John Nash, A Beautiful Mind, reveals a genius's life that transcended the merely quirky. But Erdös's brand of madness was joyful, unlike Nash's despairing schizophrenia. Erdös never tried to dilute his obsessive passion for numbers with ordinary emotional interactions, thus avoiding hurting the people around him, as Nash did. Oliver Sacks writes of Erdös: "A mathematical genius of the first order, Paul Erdös was totally obsessed with his subject--he thought and wrote mathematics for nineteen hours a day until the day he died. He traveled constantly, living out of a plastic bag, and had no interest in food, sex, companionship, art--all that is usually indispensable to a human life."
The Man Who Loved Only Numbers is easy to love, despite his strangeness. It's hard not to have affection for someone who referred to children as "epsilons," from the Greek letter used to represent small quantities in mathematics; a man whose epitaph for himself read, "Finally I am becoming stupider no more"; and whose only really necessary tool to do his work was a quiet and open mind. Hoffman, who followed and spoke with Erdös over the last 10 years of his life, introduces us to an undeniably odd, yet pure and joyful, man who loved numbers more than he loved God--whom he referred to as SF, for Supreme Fascist. He was often misunderstood, and he certainly annoyed people sometimes, but Paul Erdös is no doubt missed. --Therese Littleton [via]
More editions of The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth:
- The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth: ISBN 0786863625 (0-7868-6362-5)
  Hardcover, Hyperion Books
- The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth: ISBN 0786884061 (0-7868-8406-1)
  Softcover, Hyperion Books
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Math Curse
by Lane Smith, Jon Scieszka

ISBN 0670861944 (0-670-86194-4)
Hardcover, Penguin Group USA

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Book summary:
Did you ever wake up to one of those days where everything is a problem? You have 10 things to do, but only 30 minutes till the bus leaves. Is there enough time? You have 3 shirts and 2 pairs of pants -- can you make 1 good outfit? Don't worry -- it's just the Math Curse striking! An amusing book about dealing with numbers in everyday life. [via]
More editions of Math Curse:
- Math Curse: ISBN 0670861944 (0-670-86194-4)
  Hardcover, Penguin Group USA
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Metamagical Themas: Questing for the Essence of Mind and Pattern
by Douglas R. Hofstadter

ISBN 0465045669 (0-465-04566-9)
Softcover, Perseus Books

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Book summary:
An interlocked collection of literary, scientific, and artistic studies. [via]
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A New Kind of Science
by Stephen Wolfram

ISBN 1579550088 (1-57955-008-8)
Hardcover, Wolfram Media Inc

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Book summary:
Physics and computer science genius Stephen Wolfram, whose Mathematica computer language launched a multimillion-dollar company, now sets his sights on a more daunting goal: understanding the universe. A New Kind of Science is a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modelling complex systems.
On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple non-mathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day.
Wolfram wrote the book in a distinct style meant to make it easy to read, even for non-techies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton [via]
More editions of A New Kind of Science:
- A New Kind of Science: ISBN 1579550088 (1-57955-008-8)
  Hardcover, Wolfram Media Inc
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Students Solution Manual for Calculus
by William E. Boyce, Richard C. Diprima

ISBN 0471854506 (0-471-85450-6)
Softcover, John Wiley & Sons Inc

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Book summary:
Provides clear, well organized presentation of calculus with applications to engineering and the sciences. Emphasizes the methods and applications of the calculus with some coverage of relevant theory, including functions, limits, continuity, differentiation, integrations in higher dimensions, and line and surface integrals. Pays particular attention to those aspects of calculus that are important in developing effective problem solving methods--often involving estimating errors or constructing numerical approximations. Supplies more thorough treatment of some major topics than most books, such as: comparison tests for improper integrals; use of power series representations for functions; and the relation between linear approximations and differentiation. Also covers elementary transcendental functions, infinite series, Taylor's approximation, polar coordinates, and vectors and three dimensional geometry. [via]
More editions of Students Solution Manual for Calculus:
- Students Solution Manual for Calculus: ISBN 0471854506 (0-471-85450-6)
  Softcover, John Wiley & Sons Inc
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A Tour of the Calculus
by David Berlinski

ISBN 0679747885 (0-679-74788-5)
Softcover, Random House Inc

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In its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the world and perhaps its greatest meditation on the theme of continuity. Charts and graphs throughout. [via]
More editions of A Tour of the Calculus:
- A Tour of the Calculus: ISBN 0679426450 (0-679-42645-0)
  Hardcover, Knopf Publishing Group
- A Tour of the Calculus: ISBN 0679747885 (0-679-74788-5)
  Softcover, Random House Inc
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Zero: The Biography of a Dangerous Idea
by Charles Seife, Matt Zimet

ISBN 0140296476 (0-14-029647-6)
Softcover, Penguin Group USA

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Book summary:
The seemingly impossible Zen task--writing a book about nothing--has a loophole: people have been chatting, learning, and even fighting about nothing for millennia. Zero: The Biography of a Dangerous Idea, by noted science writer Charles Seife, starts with the story of a modern battleship stopped dead in the water by a loose zero, then rewinds back to several hundred years BCE. Some empty-headed genius improved the traditional Eastern counting methods immeasurably by adding zero as a placeholder, which allowed the genesis of our still-used decimal system. It's all been uphill from there, but Seife is enthusiastic about his subject; his synthesis of math, history, and anthropology seduces the reader into a new fascination with the most troubling number.
Why did the Church reject the use of zero? How did mystics of all stripes get bent out of shape over it? Is it true that science as we know it depends on this mysterious round digit? Zero opens up these questions and lets us explore the answers and their ramifications for our oh-so-modern lives. Seife has fun with his format, too, starting with chapter 0 and finishing with an appendix titled "Make Your Own Wormhole Time Machine." (Warning: don't get your hopes up too much.) There are enough graphs and equations to scare off serious numerophobes, but the real story is in the interactions between artists, scientists, mathematicians, religious and political leaders, and the rest of us--it seems we really do have nothing in common. --Rob Lightner [via]
More editions of Zero: The Biography of a Dangerous Idea:
- Zero : The Biography of a Dangerous Idea: ISBN 067088457X (0-670-88457-X)
  Hardcover, Penguin Group (USA) Incorporated
- Zero: The Biography of a Dangerous Idea: ISBN 0140296476 (0-14-029647-6)
  Softcover, Penguin Group USA

Spanish

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Gdel, Escher, Bach
by D.R. Hofstadter

ISBN 8472234592 (84-7223-459-2)
Softcover, Tusquets Editor

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Book summary:
¿Puede un sistema comprenderse a sí mismo ? Si esta pregunta se refiere a la mente humana, entonces nos encontramos ante una cuestión clave del pensamiento científico. Y de la filosofía. Y del arte. Investigar este misterio es una aventura que recorre la matemática, la física, la biología, la psicología y, muy especialmente, el lenguaje. Douglas R. Hofstadter, joven y ya célebre científico, nos abre la puerta del enigma con la belleza y la alegría creadora de su estilo. Sorprendentes paralelismos ocultos entre los grabados de Escher y la música de Bach nos remiten a las paradojas clásicas de los antiguos griegos y a un teorema de la lógica matemática moderna que ha estremecido el pensamiento del siglo XX : el de Kurt Gödel. Todo lenguaje, todo sistema formal, todo programa de ordenador, todo proceso de pensamiento, llegan, tarde o temprano, a la situación límite de la autorreferencia : de querer expresarse sobre sí mismos. Surge entonces la emoción del infinito, como dos espejos enfrentados y obligados a reflejarse mutua e indefinidamente. Gödel, Escher, Bach: un Eterno y Grácil Bucle, es una obra de arte escrita por un sabio. Versa sobre los misterios del pensamiento e incluye, ella misma, sus propios misterios. / Winner of the Pulitzer Prize, this book applies Godel's seminal contribution to modern Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel.mathematics to the study of the human mind and the development of artificial intelligence. [via]
More editions of Gdel, Escher, Bach:
- Gdel, Escher, Bach: ISBN 8472234592 (84-7223-459-2)
  Softcover, Tusquets Editor
Una Mente Prodigiosa / A Beautiful Mind
by Sylvia Nasar, Ricard Martinez Muntada

ISBN 8497934393 (84-9793-439-3)
Softcover, Debolsillo

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- Una Mente Prodigiosa / A Beautiful Mind: ISBN 8497934393 (84-9793-439-3)
  Softcover, Debolsillo

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