The World of Mathematics, Volume 3

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Overview

Vol. 3 of a monumental 4-volume set covers such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the unreasonableness of mathematics, the vocabulary of mathematics, and mathematics as an art. Specific contributions by Jacob Bernoulli, George Bernard Shaw, Bertrand Russell, Hans Hahn, Ernst Mach, Hermann Weyl, George Boole, Alfred Tarski, and many others. Informative commentary by noted mathematics scholar James R. Newman precedes ...

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Paperback (Unabridged Edition, Parts VIII-XVII)
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Overview

Vol. 3 of a monumental 4-volume set covers such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the unreasonableness of mathematics, the vocabulary of mathematics, and mathematics as an art. Specific contributions by Jacob Bernoulli, George Bernard Shaw, Bertrand Russell, Hans Hahn, Ernst Mach, Hermann Weyl, George Boole, Alfred Tarski, and many others. Informative commentary by noted mathematics scholar James R. Newman precedes each essay. Numerous figures.

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Editorial Reviews

Booknews
Presents 33 essays on such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the mathematical way of thinking, the unreasonableness of mathematics, and mathematics as an art. A reprint of volume 3 of the four-volume edition originally published by Simon and Schuster in 1956. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780486411514
  • Publisher: Dover Publications
  • Publication date: 9/18/2000
  • Series: Dover Books on Mathematics Series
  • Edition description: Unabridged Edition, Parts VIII-XVII
  • Pages: 624
  • Sales rank: 1,186,886
  • Product dimensions: 5.35 (w) x 8.38 (h) x 1.10 (d)

Meet the Author

James R. Newman's World of Mathematics
James R. Newman (1907–1966) was a rare mathematician who was also a lawyer who held several administrative positions in the United States government during and after World War II, including Chief Intelligence Officer at the US Embassy in London. His mammoth four-volume World of Mathematics was first published in 1956 and reprinted by Dover in 2000. It represented the culmination of a fifteen-year effort by Newman, in his later years as a member of the Editorial Board of Scientific American, to assemble in one publication what he considered the most important essays in the field. It's the book that has introduced generations of students to the range and extent of mathematical literature.

In the Author's Own Words:
"The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing."

"The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked." ― James R. Newman

Critical Acclaim for The World of Mathematics:
"Others with bigger and now whetted appetites will no doubt regard this book as a generous hors d’oeuvre and obtain additional fare by pursuing the numerous recommendations made by the author." ― Morris Kline, New York Herald Tribune Book Review

"Promises to be the most frequently used reference book on mathematics, as well as a delight to readers with a wide range of backgrounds." ― J.G. Kemeny, The New York Times

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Table of Contents

VOLUME THREE
PART VIII: Statistics and the Design of Experiments
  An Ingenious Army Captain and a Generous and Many-sided Man: Commentary
  1. Foundations of Vital Statistics by JOHN GRAUNT
  2. First Life Insurance Tables by EDMUND HALLEY
  Commentary
  3. The Law of Large Numbers by JACOB BERNOULLI
  Statistics and the Lady with a Fine Palate: Commentary
  4. Sampling and Standard Error by L. C. Tippett
  5. On the Average and Scatter by M. J. MORONEY
  6. Mathematics of a Lady Tasting Tea by SIR RONALD. A FISHER
  The Scientific Aptitude of George Bernard Shaw: Commentary
  7. The Vice of Gambling and the Virtue of Insurance by GEORGE BERNARD SHAW
PART IX: The Supreme Art of Abstraction: Group Theory
  Certain Important Abstractions: Commentary
  1. The Group Concept by CASSIUS J. KEYSER
  2. The Theory of Groups by SIR ARTHUR STANLEY EDDINGTON
PART X: Mathematics of Infinity
1. Mathematics and the Metaphysicians by BERTRAND RUSSELL
Hans Han: Commentary
2. Infinity by HANS HAHN
PART XI: Mathematical Truth and the Structure of Mathematics
  The Foundations of Mathematics: Commentary
  1. On the Nature of Mathematical Truth by CARL G. HEMPEL
  2. Geometry and Empirical Science by CARL G. HEMPEL
  3. The Axiomatic Method by RAYMOND L. WILDER
  4. Goedel's Proof by ERNEST NAGEL AND JAMES R. NEWMAN
  5. A Mathematical Science by OSWALD VEBLEN and JOHN WESLEY YOUNG
  6. Mathematics and the World by DOUGLAS GASKING
  7 Mathematics Postulates and Human Understanding by RICHARD VON MISES

PART XII: THE MATHEMATICAL Way of Thinking
  An Eristic Controversy: Commentary
  1. The Study That Knows Nothing of Observation by JAMES JOSEPH SYLVESTER
  Charles Sanders Peirce: Commentary
  2. The Essence of Mathematics by CHARLES SANDERS PEIRCE
  Ernst Mach: Commentary
  3. The Economy of Science by ERNST MACH
  Norman Robet Campbell: Commentary
  4. Measurement by NORMAN CAMPBELL
  5. Numerical Laws and the Use of Mathematics in Science by NORMAN CAMPBELL
  Hermann Weyl: Commentary
  6. The Mathematical Way of Thinking by HERMANN WEYL
PART XIII: Mathematics and Logic
  "Symbolic Logic, George Boole and a Horrible Dream: Commentary "
  1. Mathematical Analysis of Logic by GEORGE BOOLE
  2. History of Symbolic Logic by CLARENCE IRVING LEWIS and COOPER HAROLD LANGFORD
  3. "Symbolic Notation, Haddocks' Eyes and the Dog-Walking Ordinance by ERNEST NAGEL"
  4. Symbolic Logic by ALFRED TARSKI
PART XIV: The Unreasonableness of Mathematics
  The Importance of Being Absurd: Commentary
  1. Paradox Lost and Paradox Regained by EDWARD KASNER AND JAMES R. NEWMAN
  2. The Crisis in Intuition by HANS HAHN
PART XV: How to Solve It
  The Tears of Mathematics: Commentary
  1. How to Solve It by G. POLYA
PART XVI: The Vocabulary of Mathemtics
  Double Infinite Rapport and Other Mathematical Jargon: Commentary
  1. New Names for Old by EDWARD KASNER AND JAMES R. NEWMAN
PART XVII: Mathematics as an Art
  John William Navin Sullivan: Commentary
  1. Mathematics as an Art by JOHN WILLIAM NAVIN SULLIVAN
INDEX

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