MARC details
| 000 -LEADER |
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| fixed length control field |
02491nam a22003377a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
IIITD |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20250521171704.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
250514b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783031692123 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
IIITD |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.35 |
| Item number |
SCH-C |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Scheiderer, Claus |
| 245 ## - TITLE STATEMENT |
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| Title |
A course in real algebraic geometry : |
| Remainder of title |
positivity and sums of squares |
| Statement of responsibility, etc |
by Claus Scheiderer |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Switzerland : |
| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
©2024 |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xviii, 404 p. : |
| Other physical details |
ill. ; |
| Dimensions |
24 cm. |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Graduate Texts in Mathematics |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
1. Ordered fields |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
2. Positive polynomials and sums of squares |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
3. The real spectrum |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
4. Semialgebraic geometry |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
5. The archimedean property |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
6. Positive polynomials with zeros |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
7. Sums of squares on projective varities |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Title |
8. Sums of squares and optimization |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
This textbook is designed for a one-year graduate course in real algebraic geometry, with a particular focus on positivity and sums of squares of polynomials. The first half of the book features a thorough introduction to ordered fields and real closed fields, including the Tarski–Seidenberg projection theorem and transfer principle. Classical results such as Artin's solution to Hilbert's 17th problem and Hilbert's theorems on sums of squares of polynomials are presented in detail. Other features include careful introductions to the real spectrum and to the geometry of semialgebraic sets. The second part studies Archimedean positivstellensätze in great detail and in various settings, together with important applications. The techniques and results presented here are fundamental to contemporary approaches to polynomial optimization. Important results on sums of squares on projective varieties are covered as well. The last part highlights applications to semidefinite programming and polynomial optimization, including recent research on semidefinite representation of convex sets. Written by a leading expert and based on courses taught for several years, the book assumes familiarity with the basics of commutative algebra and algebraic varieties, as can be covered in a one-semester first course. Over 350 exercises, of all levels of difficulty, are included in the book.<br/>Collapse summary |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Geometry |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Koha item type |
Books |
| Source of classification or shelving scheme |
Dewey Decimal Classification |
