Results of mathematics and its border areas

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The results of mathematics and its border areas are a series of mathematical monographs by Springer Verlag . It began in 1932 with the volume Knotentheorie by Kurt Reidemeister . The second series (with a total of 101 volumes) began in 1955 with the volume Transfinite Numbers by Heinz Bachmann and the third series in 1983. The series was later given the English addition A series of modern surveys in mathematics .

Main part, story

It was founded in 1932 by the editors of the Zentralblatt für Mathematik , including Pawel Alexandrow , Wilhelm Blaschke , Richard Courant , Godfrey Harold Hardy , Gaston Julia , Tullio Levi-Civita , Rolf Nevanlinna , Bartel Leendert van der Waerden . Initially, with five articles per volume, they corresponded to a journal-like publication of large overview articles with a maximum length of 100 to 150 pages. In the time of National Socialism the numbers began to appear more irregular from 1936. The first series ended in 1942 (with the last number of the fifth volume).

After the Second World War, the company switched to publishing individual books ( booklets ). The following were named as editors in the first volume of the 2nd episode (published 1955): Lars Ahlfors (responsible for complex analysis), Reinhold Baer (group theory), Richard Courant , Joseph L. Doob (probability and statistics), Samuel Eilenberg (topology), Hans Rademacher , Friedrich Karl Schmidt , Beniamino Segre (algebraic geometry), Emanuel Sperner . Paul Halmos was responsible for analysis . Each of the editors could propose book projects in their field. 30 volumes had appeared by 1961. From 1961 Peter Hilton was the editor and the individual books were now published as volumes instead of booklets . In 1968 the editors were Paul Halmos, Reinhold Remmert , Peter Hilton, Béla Szőkefalvi-Nagy (with the help of Courant, Ahlfors, Baer, ​​Doob, Eilenberg, Rademacher, Sperner, B. Segre, Albrecht Dold , Martin Kneser , Michail Michailowitsch Postnikow , Friedrich L. Bauer , Gert Heinz Müller ). The last volume of the 2nd series (No. 101) was published in 1988. However, reprints also appeared later.

The third episode started in the 1970s with Reinhold Remmert as editor-in-chief, who had previously successfully founded the journal Inventiones Mathematicae and from there also introduced editors for the 3rd episode (such as Jacques Tits , Jean-Pierre Serre , Nicolaas Kuiper , Enrico Bombieri ). The first volume appeared in 1983. By 2017, 67 volumes had appeared in the third row. There is no editor-in-chief.

Well-known volumes were, for example, Algebras by Harald Bohr (1932), Algebras by Max Deuring (1935), Algebraic Surfaces by Oscar Zariski (1935), Theory of the Functions of Several Complex Variables by Heinrich Behnke and Peter Thullen (1934), Basic Concepts of Probability Calculus by Andrei Kolmogorow (1933), On the problem of Plateau by Tibor Radó (1933), Ideal theory by Wolfgang Krull (1935), Ergodic theory by Eberhard Hopf (1937), Diophantine approximations by Jurjen Koksma (1936), New topological methods in algebra Geometry by Friedrich Hirzebruch (1956), Generators and relations for discrete groups by HSM Coxeter and WOJ Moser (1957), Inequalities by Edwin F. Beckenbach and Richard Bellman , Geometric Invariant Theory (1965) by David Mumford , Finite Geometries (1968) by Peter Dembowski and Coding Theorems of Information Theory by Jacob Wolfowitz (1961).

The ISSN is 0071-1136 for the third episode.

Front row volumes

New editions of the volumes by Krull, Deuring, Zariski and Behnke / Thullen appeared in the second row

Second row volumes

Third row volumes

Web links

Individual evidence

  1. ^ History of the results , Springer Verlag
  2. Information in Deuring, Algebren, 1968 edition