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The Art of the Intelligible

J. Bell
  • Kartonierter Einband
  • 268 Seiten
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A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their techn... Weiterlesen
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Beschreibung

A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of mathematics: the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Gödel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis - a new approach to the use of infinitesimals in the calculus - and of the philosophical thought of the great 20th century mathematician Hermann Weyl.
Readership: Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background.

Zusammenfassung
Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail.

Inhalt

Foreword. Acknowledgements. 1. Numerals and Notation. 2. The Mathematics of Ancient Greece. 3. The Development of the Number Concept. 4. The Evolution of Algebra, I. 5. The Evolution of Algebra, II. 6. The Evolution of Algebra, III. 7. The Development of Geometry, I. 8. The Development of Geometry, II. 9. The Calculus and Mathematical Analysis. 10. The Continuous and the Discrete. 11. The Mathematics of the Infinite. 12. The Philosophy of Mathematics. Appendices. Bibliography. Index of Names. Index of terms.

Produktinformationen

Titel: The Art of the Intelligible
Untertitel: An Elementary Survey of Mathematics in its Conceptual Development
Autor:
J. Bell
EAN: 9781402000072
ISBN: 1402000073
Format: Kartonierter Einband
Herausgeber: Springer Netherlands
Anzahl Seiten: 268
Gewicht: 434g
Größe: H240mm x B160mm x T14mm
Jahr: 2001
Auflage: 1999

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