Course in Real Algebraic Geometry

Positivity and Sums of Squares

AvClaus Scheiderer

Inbunden, Engelska, 2024

Del 303 i serien Graduate Texts in Mathematics

747 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2024-09-13
Mått:155 x 235 x 27 mm
Vikt:832 g
Format:Inbunden
Språk:Engelska
Serie:Graduate Texts in Mathematics
Antal sidor:404
Förlag:Springer International Publishing AG
ISBN:9783031692123

Utforska kategorier

Optimering inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Mer om författaren

Claus Scheiderer is Professor for Geometry at Konstanz University (Germany). Among his main mathematical interests are real algebraic geometry, convex algebraic geometry and linear algebraic groups.

Innehållsförteckning

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.