Real Algebraic Geometry
By: by Vladimir I. Arnold ; edited by Ilia Itenberg, Viatcheslav Kharlamov, Eugenii I. Shustin
Contributors: Itenberg, Ilia; Kharlamov, Viatcheslav; Shustin, Eugenii I.; SpringerLink (Online service)
Series: UNITEXT -- 66
Publisher: Springer Berlin Heidelberg; Imprint: Springer
Published: 2013
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 126
ISBN-13: 9783642362439
Subjects: Mathematical physics; Mathematical Applications in the Physical Sciences; Geometry; Mathematics; Algebraic Geometry; Mathematical Methods in Physics
Description: 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).
Table of contents: title: Publisher's Foreword; title: Editors' Foreword; title: Introduction; title: 2 Geometry of Conic Sections; title: 3 The Physics of Conic Sections and Ellipsoids; title: 4 Projective Geometry; title: 5 Complex Algebraic Curves; title: 6 A Problem for School Pupils; title: A Into How Many Parts do n Lines Divide the Plane?- Editors' Comments on Gudkov's Conjecture; title: Notes.