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Overview
Vol. 3 of a monumental 4volume 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.
Product Details
ISBN13:  9780486411514 

Publisher:  Dover Publications 
Publication date:  09/18/2000 
Series:  Dover Books on Mathematics Series 
Edition description:  Unabridged Edition, Parts VIIIXVII 
Pages:  624 
Sales rank:  847,619 
Product dimensions:  5.35(w) x 8.38(h) x 1.10(d) 
About 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 fourvolume World of Mathematics was first published in 1956 and reprinted by Dover in 2000. It represented the culmination of a fifteenyear 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
Read an Excerpt
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 fourvolume World of Mathematics was first published in 1956 and reprinted by Dover in 2000. It represented the culmination of a fifteenyear 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
First Chapter
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 fourvolume World of Mathematics was first published in 1956 and reprinted by Dover in 2000. It represented the culmination of a fifteenyear 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
Table of Contents
PART VIII: Statistics and the Design of Experiments
An Ingenious Army Captain and a Generous and Manysided 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 DogWalking 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
Reading Group Guide
VOLUME THREE
PART VIII: Statistics and the Design of Experiments
An Ingenious Army Captain and a Generous and Manysided 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 DogWalking 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
Interviews
VOLUME THREE
PART VIII: Statistics and the Design of Experiments
An Ingenious Army Captain and a Generous and Manysided 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 DogWalking 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
Recipe
PART VIII: Statistics and the Design of Experiments
An Ingenious Army Captain and a Generous and Manysided 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 DogWalking 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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