東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

A course in real algebraic geometry ...

Scheiderer, Claus.

Linked to FindBook

Google Book

Amazon

博客來

A course in real algebraic geometry = positivity and sums of squares /

Record Type:	Electronic resources : Monograph/item
Title/Author:	A course in real algebraic geometry/ by Claus Scheiderer.
Reminder of title:	positivity and sums of squares /
Author:	Scheiderer, Claus.
Published:	Cham :Springer International Publishing : : 2024.,
Description:	xviii, 404 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Ordered Fields -- 2 Positive Polynomials and Sums of Squares -- 3 The Real Spectrum -- 4 Semialgebraic Geometry -- 5 The Archimedean Property -- 6 Positive Polynomials with Zeros -- 7 Sums of Squares on Projective Varieties -- 8 Sums of Squares and Optimization -- Appendix A: Commutative Algebra and Algebraic Geometry -- Appendix B: Convex Sets in Real Infinite-Dimensional Vector Spaces.
Contained By:	Springer Nature eBook
Subject:	Geometry, Algebraic. -
Online resource:	https://doi.org/10.1007/978-3-031-69213-0
ISBN:	9783031692130

A course in real algebraic geometry = positivity and sums of squares /
Scheiderer, Claus.

A course in real algebraic geometrypositivity and sums of squares /[electronic resource] :by Claus Scheiderer. - Cham :Springer International Publishing :2024. - xviii, 404 p. :ill., digital ;24 cm. - Graduate texts in mathematics,v. 3032197-5612 ;. - Graduate texts in mathematics ;v. 303..

1 Ordered Fields -- 2 Positive Polynomials and Sums of Squares -- 3 The Real Spectrum -- 4 Semialgebraic Geometry -- 5 The Archimedean Property -- 6 Positive Polynomials with Zeros -- 7 Sums of Squares on Projective Varieties -- 8 Sums of Squares and Optimization -- Appendix A: Commutative Algebra and Algebraic Geometry -- Appendix B: Convex Sets in Real Infinite-Dimensional Vector Spaces.

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.

ISBN: 9783031692130

Standard No.: 10.1007/978-3-031-69213-0doiSubjects--Topical Terms:

532048
Geometry, Algebraic.

LC Class. No.: QA564

Dewey Class. No.: 516.35

A course in real algebraic geometry = positivity and sums of squares /
LDR:02837nmm a2200337 a 4500 001 2375288
003 DE-He213
005 20240912130300.0
006 m d
007 cr nn 008maaau
008 241231s2024 sz s 0 eng d
020 $a 9783031692130 $q (electronic bk.)
020 $a 9783031692123 $q (paper)
024 7 $a 10.1007/978-3-031-69213-0 $2 doi
035 $a 978-3-031-69213-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA564
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
090 $a QA564 $b .S318 2024
100 1 $a Scheiderer, Claus. $3 3607843
245 1 2 $a A course in real algebraic geometry $h [electronic resource] : $b positivity and sums of squares / $c by Claus Scheiderer.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2024.
300 $a xviii, 404 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 2197-5612 ; $v v. 303
505 0 $a 1 Ordered Fields -- 2 Positive Polynomials and Sums of Squares -- 3 The Real Spectrum -- 4 Semialgebraic Geometry -- 5 The Archimedean Property -- 6 Positive Polynomials with Zeros -- 7 Sums of Squares on Projective Varieties -- 8 Sums of Squares and Optimization -- Appendix A: Commutative Algebra and Algebraic Geometry -- Appendix B: Convex Sets in Real Infinite-Dimensional Vector Spaces.
520 $a 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.
650 0 $a Geometry, Algebraic. $3 532048
650 0 $a Algebra. $3 516203
650 1 4 $a Algebraic Geometry. $3 893861
650 2 4 $a Field Theory and Polynomials. $3 891077
650 2 4 $a Order, Lattices, Ordered Algebraic Structures. $3 896039
650 2 4 $a Convex and Discrete Geometry. $3 893686
650 2 4 $a Continuous Optimization. $3 1566748
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v v. 303. $3 3724713
856 4 0 $u https://doi.org/10.1007/978-3-031-69213-0
950 $a Mathematics and Statistics (SpringerNature-11649)