Ergebnisse der Mathematik und ihrer Grenzgebiete
Encyclopedia
Ergebnisse der Mathematik und ihrer Grenzgebiete/A Series of Modern Surveys in Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 is a series of scholarly monographs published by Springer-Verlag. The title literally means "Results in mathematics and related areas". Most of the books were published in German or English, but there were a few in French and Italian. There have been several sequences, or Folge: the original series, neue Folge, 3.Folge. Some of the most significant mathematical monographs of 20th century appeared in this series.

Scope

The publisher's description states:
Ergebnisse der Mathematik und ihrer Grenzgebiete, now in its third sequence, aims to provide summary reports, on a high level, on important topics of mathematical research. Each book is designed as a reliable reference covering a significant area of advanced mathematics, spelling out related open questions, and incorporating a comprehensive, up-to-date bibliography.

The original series

The series started in 1932 with publication of Knotentheorie by Kurt Reidemeister
Kurt Reidemeister
Kurt Werner Friedrich Reidemeister was a mathematician born in Braunschweig , Germany.He received his doctorate in 1921 with a thesis in algebraic number theory at the University of Hamburg under the supervision of Erich Hecke. In 1923 he was appointed assistant professor at the University of Vienna...

 as Band 1, 1. There seems to have been double numeration in this sequence.

neue Folge

This sequence started in 1950 with publication of Transfinite Zahlen by Heinz Bachmann. The volumes are consecutively numbered, designated as either Band or Heft. Total of 100 volumes were published, often, in multiple editions, but preserving the original numbering within the series.

The ISSN for this sequence is 0071-1136. As of February 2008, the following persons are listed at the Springer website as the editors of the defunct 2.Folge:
  • P. R. Halmos
    Paul Halmos
    Paul Richard Halmos was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis . He was also recognized as a great mathematical expositor.-Career:Halmos obtained his B.A...

    , P. J. Hilton
    Peter Hilton
    Peter John Hilton was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during the Second World War.-Life:Hilton was born in London, and educated at St Paul's School...

    , R. Remmert, B. Szökefalvi-Nagy.

3. Folge

This sequence started in 1983 with publication of Galois module structure of algebraic integers by Albrecht Fröhlich. Publication of volume 52 is announced for April 2008.

As of February 2008, the editors are:
  • Editor-in-chief: R. Remmert
  • Series Editors: M. Gromov, J. Jost, J. Kollar, G. Laumon, H. W. Lenstra
    Hendrik Lenstra
    Hendrik Willem Lenstra, Jr. is a Dutch mathematician.-Biography:Lenstra received his doctorate from the University of Amsterdam in 1977 and became a professor there in 1978...

    , J. Tits
    Jacques Tits
    Jacques Tits is a Belgian and French mathematician who works on group theory and geometry and who introduced Tits buildings, the Tits alternative, and the Tits group.- Career :Tits received his doctorate in mathematics at the age of 20...

    , D. Zagier
    Don Zagier
    Don Bernard Zagier is an American mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany, and a professor at the Collège de France in Paris, France.He was born in Heidelberg, Germany...

    , G. M. Ziegler
    Günter M. Ziegler
    Günter M. Ziegler is a German mathematician. Ziegler is known for his research in discrete mathematics and geometry, and particularly on the combinatorics of polytopes.- Biography :...

    .
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