Arnold / Itenberg / Kharlamov Real Algebraic Geometry

2013
ISBN: 978-3-642-36243-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 66, 100 Seiten, eBook

Reihe: UNITEXT

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 16 th 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).

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Arnold, Vladimir I.

Itenberg, Ilia

Kharlamov, Viatcheslav

Shustin, Eugenii I.

Weitere Mitwirkende

Gould, Gerald G.

Inhaltsverzeichnis

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

Über Autor(innen)

Vladimir Arnold is one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. His first mathematical work, which he did being a third-year student, was the solution of the 13th Hilbert problem about superpositions of continuous functions. His early work on KAM (Kolmogorov, Arnold, Moser) theory solved some of the outstanding problems of mechanics that grew out of fundamental questions raised by Poincare and Birkhoff based on the discovery of complex motions in celestial mechanics. In particular, the discovery of invariant tori, their dynamical implications, and attendant resonance phenomena is regarded today as one of the deepest and most significant achievements in the mathematical sciences. Arnold has been the advisor to more than 60 PhD students, and is famous for his seminar which thrived on his ability to discover new and beautiful problems. He is known all over the world for his textbooks which include the classics Mathematical Methods of Classical Mechanics , and Ordinary Differential Equations , as well as the more recent Topological Methods m Hydrodynamics written together with Boris Khesin, and Lectures on Partial Differential Equations.