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Home > Mathematics and Science Textbooks > Mathematics > Geometry > Algebraic geometry > Real Algebraic Geometry: (36 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)
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Real Algebraic Geometry: (36 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)

Real Algebraic Geometry: (36 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)


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About the Book

This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Geometrie algebrique reelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.

Table of Contents:
1. Ordered Fields, Real Closed Fields.- 2. Semi-algebraic Sets.- 3. Real Algebraic Varieties.- 4. Real Algebra.- 5. The Tarski-Seidenberg Principle as a Transfer Tool.- 6. Hilbert’s 17th Problem. Quadratic Forms.- 7. Real Spectrum.- 8. Nash Functions.- 9. Stratifications.- 10. Real Places.- 11. Topology of Real Algebraic Varieties.- 12. Algebraic Vector Bundles.- 13. Polynomial or Regular Mappings with Values in Spheres.- 14. Algebraic Models of C? Manifolds.- 15. Witt Rings in Real Algebraic Geometry.- Index of Notation.

Review :
"Wie schon das franzosische Original, so ist auch die englische Version sehr sorgfaltig verfasst. Beim Vergleich zwischen beiden stosst man immer wieder auf Stellen, wo der ursprungliche Text nicht nur einfach ubersetzt, sondern im Interesse einer noch klareren Darstellung auch neu konzipiert worden ist. Kein Zweifel, dass die neue Fassung auch weiterhin die Rolle einer Standradreferenz spielen wird." DMV Jahresbericht, 103. Band, Heft 2, Juli 2001


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Product Details
  • ISBN-13: 9783540646631
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 430
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 3540646639
  • Publisher Date: 19 Aug 1998
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: 36 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics


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Real Algebraic Geometry: (36 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)
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