The Legacy of Niels Henrik Abel (eBook, PDF)

The Abel Bicentennial, Oslo, 2002
Redaktion: Laudal, Olav Arnfinn; Piene, Ragni

• Format: PDF

Produktbeschreibung

Abel's influence on modern mathematics is substantial. This is seen in many ways, but maybe clearest in the number of mathematical terms containing the adjective Abelian. In algebra, algebraic and complex geometry, analysis, the theory of differential and integral equations, and function theory there are terms like Abelian groups, Abelian varieties, Abelian integrals, Abelian functions. A number of theorems are attributed to Abel. The famous Addition Theorem of Abel, proved in his Paris Mémoire, stands out, even today, as a mathematical landmark.

This book, written by some of the foremost specialists in their fields, contains important survey papers on the history of Abel and his work in several fields of mathematics. The purpose of the book is to combine a historical approach to Abel with an overview of his scientific legacy as perceived at the beginning of the 21st century.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 784
• Erscheinungstermin: 28. Juni 2011
• Englisch
• ISBN-13: 9783642189081
• Artikelnr.: 53135577

Inhaltsangabe

The Legacy of Niels Henrik Abel.- Opening address The Abel Bicentennial Conference University of Oslo, June 3, 2002.- The Life of Niels Henrik Abel.- The Work of Niels Henrik Abel.- The Legacy of Abel in Algebraic Geometry.- Solving Quintics by Radicals.- From Abel to Kronecker: Episodes from 19th Century Algebra.- On the History of the Artin Reciprocity Law in Abelian Extensions of Algebraic Number Fields: How Artin was Led to his Reciprocity Law.- The Italian School of Algebraic Geometry and Abel's Legacy.- From Abel's Heritage: Transcendental Objects in Algebraic Geometry and Their Algebraization.- What is Abel's Theorem Anyway?.- On Abel's Hyperelliptic Curves.- Formal Deformation of Chow Groups.- An Analogue of Abel's Theorem.- Arithmetic Questions Related to Rationally Connected Varieties.- Hyperbolicity in Complex Geometry.- Abel-Radon Transform and Applications.- Abel Transform and Integral Geometry.- Abel's Inverse Problem and Inverse Scattering.- Residues and D-modules.- Algebraic Equations and Hypergeometric Series.- Dirichlet Series and Functional Analysis.- Real Multiplication and Noncommutative Geometry.- On the Quantum Cohomology of Homogeneous Varieties.- Quantum Principal Bundles up to Homotopy Equivalence.- Non-commutative Crepant Resolutions.- Closed String Operators in Topology Leading to Lie Bialgebras and Higher String Algebra.

Rezensionen

From the reviews:

" [... ] The result is a massive book with a lot of interesting material in it. About half of this material should be accessible to a wide audience; the other half will be of interest mostly to specialists.

With the book comes a CD-ROM containing still more material related to Abel and to the conference. [...]

It's a delightful package, particularly for those of us who are interested in the history of mathematics and/or in number theory, algebraic geometry, and complex function theory. Just the images on the CD would make me want to have a copy. Given the size of this book and the extras on the CD, this isn't even very expensive; no library should be without a copy."

Fernando Q. Gouvêa, MAA Online (for complete review see "Briefly noted" at http://www.maa.org/reviews)

"The core of the book consists of contributions presented at the Abel bicentennial conference held at the University of Oslo ... . The book contains a huge amount of information of historical and mathematical nature. It can be recommended not only to those working in fields having roots in one of Abel's versatile contributions to mathematics but also to anybody who likes to read how ideas can influence the future development." (EMS Newsletter, June, 2005)