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Real Algebraic Geometry

by Arnold, Vladimir I [author.].
Material type: materialTypeLabelBookPublisher: Heidelberg: Springer- Verlage, 2013Description: ix, 100p.ISBN: 9783642362422 (Pbk).Subject(s): Mathematics | Geometry, algebraic | Geometry | Mathematical physics | Mathematics | Algebraic Geometry | Mathematical Methods in Physics | Geometry | Mathematical Applications in the Physical SciencesDDC classification: 516.35 AR65R
Contents:
Publisher's Foreword -- Editors' Foreword -- Introduction -- 2 Geometry of Conic Sections -- 3 The Physics of Conic Sections and Ellipsoids -- 4 Projective Geometry -- 5 Complex Algebraic Curves -- 6 A Problem for School Pupils -- A Into How Many Parts do n Lines Divide the Plane?- Editors' Comments on Gudkov's Conjecture -- Notes.
Summary: This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).
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General Section 		516.35 AR65R (Browse shelf) Available 6936
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516.2 C547E Euclidean Geometry : 516.35 Al33 Algebraic Geometry : 516.35 Ar48G Grassmannian geometry of scattering amplitudes 516.35 AR65R Real Algebraic Geometry 516.35 B8A Algebraic geometry 516.35 D357C Computing in algebraic geometry 516.35 D35H Higher-Dimensional Algebraic Geometry

Publisher's Foreword -- Editors' Foreword -- Introduction -- 2 Geometry of Conic Sections -- 3 The Physics of Conic Sections and Ellipsoids -- 4 Projective Geometry -- 5 Complex Algebraic Curves -- 6 A Problem for School Pupils -- A Into How Many Parts do n Lines Divide the Plane?- Editors' Comments on Gudkov's Conjecture -- Notes.

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This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).

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