Results of mathematics and its border areas
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
- 1.1 Kurt Reidemeister : Knot theory 1932
- 1,2 Karl Federhofer : Graphical Kinematics and Kinetostatics, 1932
- 1,3 MJO Strutt : Lamésche, Mathieusche and related functions in physics and technology, 1932
- 1,4 Kurt Hohenemser : The methods for the approximate solution of eigenvalue problems in elastokinetics, 1932
- 1.5 Harald Bohr : Almost Periodic Functions, 1932
- 2.1 Oswald Veblen : Projective Theory of Relativity, 1933
- 2.2 Tibor Radó : On the problem of Plateau, 1933
- 2,3 Andrei Kolmogorow : Basic Concepts of Probability Theory, 1933
- 2,4 Alexander Jakowlewitsch Chintschin : Asymptotic Laws of Probability Calculus, 1933
- 2.5 Cyrus MacDuffee : The theory of matrices, 1933
- 3.1 Tommy Bonnesen , Werner Fenchel : Theory of the convex body, 1934
- 3.2 Dirk Struik : Theory of linear connections, 1934
- 3,3 Heinrich Behnke , Peter Thullen : Theory of the functions of several complex variables, 1934
- 3,4 Arend Heyting : Basic mathematical research, intuitionism, proof theory, 1934
- 3,5 Oscar Zariski : Algebraic Surfaces, 1935
- 4.1 Max Deuring : Algebras 1935
- 4,2 Bartel Leendert van der Waerden : Groups of linear transformations, 1935
- 4.3 Wolfgang Krull : Ideal Theory, 1935
- 4,4 Jurjen Koksma : Diophantine Approximations, 1936
- 4,5 Constantin Caratheodory : Geometric Optics, 1937
- 5.1 Tibor Radó ; Subharmonic Functions, 1937
- 5.2 Eberhard Hopf : Ergodentheorie, 1937
- 5,3 Hans Ertel : Methods and Problems of Dynamic Meteorology 1938
- 5.4 Thoralf Skolem : Diophantine Equations, 1938
- 5,5 Béla Szőkefalvi-Nagy : Spectral representation of linear transformations of Hilbert's space, 1942
Second row volumes
- 1 Heinz Bachmann : Transfinite numbers 1955
- 2 Carlo Miranda : Equazioni alle derivate parziali di tipo ellittico, 1955, 2nd edition 1970: Partial differential equations of elliptic type
- 3 Ludwig Bieberbach : Analytical continuation, 1955
- 4 Pierre Samuel : Méthodes d'Algèbre Abstraite en Géométrie Algébrique, 1955, 2nd edition 1967
- 5 Jean Dieudonné : La géométrie des groupes classiques, 1955, 2nd edition 1963
- 6 Leonard Roth : Algebraic threefolds: with special regard to problems of rationality, 1955
- 7 Hans-Heinrich Ostmann : Additive Number Theory, Volume 1, 1956, 2nd edition 1968
- 8 Hans Wittich : Recent investigations into unambiguous analytical functions, 1956, 2nd edition 1968
- 9 Friedrich Hirzebruch : New topological methods in algebraic geometry, 1956, 2nd edition 1962
- 10 Michio Suzuki : Structure of a group and the structure of its lattice of subgroups, 1956
- 11 Hans-Heinrich Ostmann : Additive Number Theory, Volume 2, 1956
- 12 Mario Baldassarri : Algebraic Varieties, 1956
- 13 Beniamino Segre : Some properties of differentiable varieties and transformations: with special reference to the analytic and algebraic cases, 1957
- 14 HSM Coxeter , WOJ Moser : Generators and relations for discrete groups, 1957, 4th edition 1980
- 15 Karl Zeller : Theory of Limitation Processes, 1958, 2nd edition 1970
- 16 Lamberto Cesari : Asymptotic behavior and stability problems in ordinary differential equations, 1959, 2nd edition 1963
- 17 Francesco Severi : Il teorema di Riemann-Roch per curve, superficie e varietà: questioni collegate, 1958
- 18 James A. Jenkins : Univalent functions and conformal mapping, 1958, 2nd edition 1965
- 19 Ralph Boas , Robert Creighton Buck : Polynomial expansions of analytic functions, 1958, 2nd edition 1964
- 20 Richard Bruck : Survey of binary systems, 1958, 3rd edition 1971
- 21 Mahlon M. Day : Normed linear spaces, 1958, 2nd edition 1962
- 22 Wolfgang Hahn : Theory and application of the direct method by Lyapunow, 1959
- 23 Stefan Bergman : Integral operators in the theory of linear partial differential equations, 1961, 2nd edition 1969
- 24 Demetrios Kappos : Structural Theory of Probability Fields and Spaces, 1960
- 25 Roman Sikorski : Boolean Algebras, 1960, 2nd edition 1964
- 26 Hans Künzi : Quasi-conformal illustrations, 1960
- 27 Robert Schatten : Norm ideals of completely continuous operators, 1960
- 28 Kiyoshi Noshiro : Cluster Sets, 1960
- 29 Konrad Jacobs : Newer Methods and Results of Ergodic Theory 1960
- 30 Edwin Beckenbach , Richard Bellman : Inequalities, 1961, 2nd edition 1965
- 31 Jacob Wolfowitz : Coding theorems of information theory, 1961, 3rd edition 1978
- 32 Corneliu Constantinescu , Aurel Cornea : Ideal margins of Riemann surfaces, 1963
- 33 Pierre Conner , Edwin Floyd : Differentiable periodic maps, 1964
- 34 David Mumford : Geometric Invariant Theory, 1965, 2nd edition 1982, 3rd edition 1994
- 35 Peter Gabriel , M. Zisman: Calculus of fractions and homtopy theory, 1967
- 36 Calvin Richard Putnam : Commutation properties of Hilbert space operators and related topics, 1967
- 37 Hanna Neumann : Varieties of Groups, 1967
- 38 Ralph Boas : Integrability theorems for trigonometric transforms, 1967
- 39 Béla Szőkefalvi-Nagy : Spectral representation of linear transformations of Hilbert's space, 1967
- 40 George Seligman : Modular Lie Algebras, 1967
- 41 Max Deuring : Algebras, 2nd edition 1967
- 42 Kurt Schütte : Complete Systems of Modal and Intuitionist Logic, 1968
- 43 Raymond Smullyan : First order logic, 1968 (Dover reprinted 1995)
- 44 Peter Dembowski : Finite Geometries, 1968
- 45 Juri Linnik : Ergodic properties of algebraic fields, 1968
- 46 Wolfgang Krull : Ideal Theory, 2nd edition 1968
- 47 Leopoldo Nachbin : Topology on spaces of holomorphic mappings, 1969
- 48 A. Ionescu Tulcea , Cassius Ionescu Tulcea : Topics in the theory of lifting 1969
- 49 Charles A. Hayes , Christian Y. Pauc : Derivation and Martingales, 1970
- 50 Jean-Pierre Kahane : Séries de Fourier absolument convergentes, 1970
- 51 Heinrich Behnke , Peter Thullen : Theory of the functions of several complex variables, 2nd edition, Ed. Reinhold Remmert
- 52 Herbert Wilf : Finite sections of some classical inequalities, 1970
- 53 Jean-Pierre Ramis : Sous-ensembles analytiques d'une variété banachique complexe, 1970
- 54 Herbert Busemann : Recent synthetic differential geometry, 1970
- 55 Wolfgang Walter : Differential and integral inequalities, 1970
- 56 Antonie Frans Monna : Analysis non-archimédienne, 1970
- 57 Erik Alfsen : Compact convex sets and boundary integrals, 1971
- 58 Silvio Greco , Paolo Salmon : Topics in m-adic topologies, 1971
- 59 Santiago López de Medrano : Involutions on manifolds, 1971
- 60 Shōichirō Sakai : C * -algebras and W * -algebras, 1971
- 61 Oscar Zariski : Algebraic Surfaces, 2nd edition 1971, with appendices by SS Abhyankar , Joseph Lipman and David Mumford
- 62, 63 Derek JS Robinson : Finiteness conditions and generalized soluble groups, Part 1, 2, 1972
- 64 Monique Hakim : Topos annelés et schémas relatifs, 1972
- 65 William Browder : Surgery on simply-connected manifolds, 1972
- 66 Albrecht Pietsch : Nuclear locally convex spaces, 1972
- 67 Claude Dellacherie : Capacités et processus stochastiques, 1972
- 68 MS Raghunathan : Discrete subgroups of Lie groups, 1972
- 69 Colin Rourke , Brian J. Sanderson : Introduction to piecewise-linear topology, 1972
- 70 Shoshichi Kobayashi : Transformation groups in differential geometry, 1972
- 71 Jean Claude Tougeron : Idéaux de fonctions différentiables, 1972
- 72 Iossif Iljitsch Gichman , Anatoli Skorochod : Stochastic differential equations, 1972
- 73 John Milnor : Symmetric bilinear forms, 1973
- 74 Robert Fossum : The divisor class group of a Krull domain, 1973
- 75 Tonny Springer : Jordan algebras and algebraic groups, 1973
- 76 Bertram Wehrfritz : Infinite linear groups: an account of the group-theoretical properties of infinite groups of matrices, 1973
- 77 Heydar Radjavi , Peter Rosenthal : Invariant Subspaces, 1973
- 78 János Bognár : Indefinite inner product spaces, 1974
- 79 Anatoli Skorochod : Integration in Hilbert Space, 1974
- 80 Frank Featherstone Bonsall , John Duncan : Complete normed algebras, 1973
- 81 John Crossley , Anil Nerode : Combinatorial functors, 1974
- 82 Valentin Vladimirowitsch Petrov (Valentin V. Petrov): Sums of independent random variables, 1975
- 83 Russell C. Walker : The Stone-Čech compactification, 1974
- 84 James Howard Wells , Lynn R. Williams : Embeddings and extensions in analysis, 1975
- 85 Wu Yi Hsiang : Cohomology theory of topological transformation groups, 1975
- 86 Alexander Olewski : Fourier series with respect to general orthogonal systems, 1975
- 87 Christian Berg , Gunnar Forst : Potential theory on locally compact Abelian groups, 1975
- 88 André Weil : Elliptic functions according to Kronecker and Eisenstein, 1976
- 89 Roger Lyndon , Paul E. Schupp : Combinatorial group theory, 1977
- 90 Robert E. Edwards , Garth Gaudry : Littlewood-Paley and multiplier theory, 1977
- 91 Robert Gunning : Riemann surfaces and generalized theta functions, 1976
- 92 Joram Lindenstrauss , Lior Tzafriri : Classical Banach spaces 1: Sequence spaces, 1977
- 93 Arthur Besse : Manifolds all of whose geodesics are closed, 1978
- 94 Herbert Heyer : Probability measures on locally compact groups 1977
- 95 Sergei Adjan : The Burnside problem and identities in groups, 1979
- 96 Paul Halmos , VS Sunder : Bounded integral operators on L2 spaces, 1978
- 97 Joram Lindenstrauss , Lior Tzafriri : Classical Banach spaces 2: Function spaces, 1979
- 98 Sibylla Prieß-Crampe : Arranged structures: groups, bodies, projective planes, 1983
- 99 Bruce L. Reinhart : Differential geometry of foliations: the fundamental integrability problem, 1983
- 100 Hans Petersson : Module functions and square forms, 1982
- 101 Ramesh Gangolli , VS Varadarajan : Harmonic analysis of spherical functions on real reductive groups, 1988
Third row volumes
- 1 Albrecht Fröhlich : Galois module structure of algebraic integers, 1983
- 2 William Fulton : Intersection theory, 1983
- 3 Jens Carsten Jantzen : Enveloping algebras of semi-simple Lie algebras, 1983
- 4 Wolf Barth , Klaus Hulek Chris AM Peters , Antonius Van de Ven : Compact complex surface, 1984, 2nd edition 2004
- 5 Kurt Strebel : Quadratic differentials, 1984
- 6 Michael J. Beeson : Foundations of constructive mathematics: metamathematical studies, 1985
- 7 Allan Pinkus : n-widths in approximation theory, 1986
- 8 Ricardo Mañé : Ergodic theory and differentiable dynamics 1987
- 9 Michail Leonidowitsch Gromow : Partial differential relations, 1986
- 10 Arthur Besse : Einstein manifolds, 1987
- 11 Michael D. Fried , Moshe Jarden : Field arithmetic, 1986
- 12 Jacek Bochnak , Michel Coste , Marie-Francoise Roy : Géométrie algébrique réelle, 1987
- 13 Eberhard Freitag , Reinhardt Kiehl : Etale cohomology and the Weil conjecture 1988
- 14 Mark Goresky , Robert MacPherson : Stratified Morse Theory, 1988
- 15 Tadao Oda : Convex bodies and algebraic geometry: an introduction to the theory of toric varieties, 1988
- 16 Gerard van der Geer : Hilbert modular surfaces, 1988
- 17 Grigori Alexandrowitsch Margulis : Discrete subgroups of semisimple Lie groups, 1991
- 18 Andries Evert Brouwer , Arjeh Cohen , Arnold Neumaier : Distance-regular graphs, 1989
- 19 Ivar Ekeland : Convexity methods in Hamiltonian mechanics, 1990
- 20 Alexei Kostrikin : Around Burnside, 1990
- 21 Siegfried Bosch , Werner Lütkebohmert , Michel Raynaud : Néron models, 1990
- 22 Gerd Faltings , Ching-Li Chai : Degeneration of abelian varieties, 1990
- 23 Michel Ledoux , Michel Talagrand : Probability in Banach spaces: isoperimetry and processes, 1991, 2nd edition 2010
- 24 Vladimir F. Lazutkin : KAM theory and semiclassical approximations to eigenfunctions, 1993
- 25 Welington de Melo , Sebastian van Strien : One-dimensional dynamics, 1993
- 26 Seppo Rickman : Quasiregular mappings, 1993
- 27 Robert Friedman , John W. Morgan : Smooth four-manifolds and complex surfaces, 1994
- 28 Victor Havin , Burglind Jöricke : The uncertainty principle in harmonic analysis, 1993
- 29 Anthony Joseph : Quantum groups and their primitive ideals, 1995
- 30 Eckart Viehweg : Quasi-projective moduli for polarized manifolds, 1995
- 31 Waleri Kozlow : Symmetries, topology and resonances in Hamiltonian mechanics
- 32 János Kollár : Rational curves on algebraic varieties, 1996
- 33 Carlos Andrada , Ludwig Bröcker , Jesús M. Ruiz : Constructible sets in real geometry, 1996
- 34 David Goss : Basic structures of function field arithmetic, 1996
- 35 Michael Struwe : Variational methods: applications to nonlinear partial differential equations and Hamiltonian systems, 3rd edition 2000
- 36 Jacek Bochnak , Michel Coste , Marie-Francoise Roy : Real algebraic geometry, 1998
- 37 Mariano Giaquinta , Giuseppe Modica , Jiří Souček : Cartesian currents in the calculus of variations 1, 1998
- 38 Mariano Giaquinta , Giuseppe Modica , Jiří Souček : Cartesian currents in the calculus of variations 2: Variational integrals, 1998
- 39 Gérard Laumon , Laurent Moret-Bailly : Champs algébriques, 2000
- 40 Luis Ribes , Pavel Zalesskii : Profinite groups, 2000, 2nd edition 2010
- 41 Igor Nikolaev : Foliations on surfaces, 2001
- 42 Reinhardt Kiehl , Rainer Weissauer : Weil conjectures, perverse sheaves and l'adic Fourier transform, 2001
- 43 George Greaves : Sieves in number theory, 2001
- 44 Wolfgang Lück : L2-invariants: theory and applications to geometry and K-theory, 2002
- 45 Thomas Kappeler , Jürgen Pöschel : KdV & KAM, 2003
- 46 Michel Talagrand : Spin glasses: a challenge for mathematicians; cavity and mean field models, 2003
- 47 Mark Adler , Pierre van Moerbeke , Pol Vanhaecke : Algebraic integrability, Painlevé geometry and Lie algebras, 2004
- 48, 49 Robert Lazarsfeld : Positivity in algebraic geometry, part 1,2, 2004
- 50 Sergey Neshveyev , Erling Størmer : Dynamic entropy in operator algebras, 2006
- 51 Boris Khesin , Robert Wendt : The geometry of infinite-dimensional groups, 2009
- 52 Chris AM Peters , Joseph Steenbrink : Mixed Hodge Structures, 2009
- 53 Vítor Araújo , Maria José Pacifico : Three-dimensional flows, 2010
- 54,55 Michel Talagrand : Mean field models for spin glasses, part 1,2, 2011
- 56 Franc Forstnerič : Stein manifolds and holomorphic mappings: the homotopy principle in complex analysis, 2011, 2nd edition 2017
- 57 Francis Buekenhout , Arjeh Cohen : Diagram geometry: related to classical groups and buildings, 2013
- 58 Eckhard Meinrenken : Clifford algebras and Lie theory, 2013
- 59 Frédéric Paugam : Towards the mathematics of quantum field theory, 2014
- 60 Michel Talagrand : Upper and lower bounds for stochastic processes: modern methods and classical problems, 2014
- 61 Werner Lütkebohmert : Rigid geometry of curves and their Jacobians, 2016
- 62 Yves Benoist , Jean-François Quint : Random walks on reductive groups, 2016
- 63 Tuomas Hytönen , Jan van Neerven , Mark Veraar , Lutz Weis : Analysis in Banach spaces, Volume 1: Martingales and Littlewood-Paley theory, 2016
- 64 Nihat Ay , Jürgen Jost , Hông Vân Lê , Lorenz Schwachhöfer : Information Geometry, 2016
- 65 Annette Huber , Stefan Müller-Stach : Periods and Nori motives, 2017 (with contributions by Benjamin Friedrich, Jonas von Wangeheim)
- 66 Luis Ribes : Profinite graphs and groups, 2017
- 67 Tuomas Hytönen , Jan van Neerven , Mark Veraar , Lutz Weis : Analysis in Banach spaces, Volume 2: Probabilistic methods and operator theory, 2017
- 68 Viviane Baladi : Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps, 2018
- 69 Gaetan Chevenier , Jean Lannes : Automorphic Forms and Even Unimodular Lattices, 2019
- 70 Matthias Schütt , Tetsuji Shioda : Mordell-Weil Lattices, 2019
Web links
Individual evidence
- ^ History of the results , Springer Verlag
- ↑ Information in Deuring, Algebren, 1968 edition