Basics of mathematical Sciences

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The basic doctrines of the mathematical sciences (originally the basic doctrines of the mathematical sciences in individual presentations with special consideration of the areas of application ) are a traditional and respected series of mathematical monographs and textbooks published by Springer Verlag . They have been published since 1921 under the editorship of Richard Courant , who at that time was the advisor to Springer Verlag for the mathematics division and was backed by David Hilbert in Göttingen, the leading German mathematician. The transition of the leading role of the German mathematics publishers from Teubner to Springer is also reflected in the development. Because of the yellow color of its bindings, it is also called the yellow series .


The best-known volumes from the early years include the lectures on functional theory by Adolf Hurwitz and Courant, the lectures on mathematical physics by Courant and Hilbert, the two-volume algebra by Bartel Leendert van der Waerden , Ludwig Bieberbach's theory of differential equations, several lecture volumes by Felix Klein ( including his history of mathematics in the 19th century , elementary mathematics from a higher point of view or higher geometry ), the descriptive geometry by David Hilbert and Stefan Cohn-Vossen , the lectures on differential geometry by Wilhelm Blaschke or Konrad Knopp's infinite series. Here Abraham Fraenkel published the introduction to set theory , David Hilbert and Paul Bernays published the fundamentals of mathematics , the tasks and theorems from analysis by George Pólya and Gábor Szegő , the topology by Pawel Alexandrow and Heinz Hopf , the Foundations of Potential Theory by Oliver Kellogg , the theory of groups of finite order by Andreas Speiser , the absolute differential calculus by Tullio Levi-Civita , the Ricci calculus by Jan Schouten , the geometry lectures by Moritz Pasch and John von Neumann Mathematical Foundations of Quantum Mechanics . Besides Courant, co-editors in the early years were Max Born , Carl Runge , Blaschke (in 1935 Courant, Blaschke, van der Waerden and Friedrich Karl Schmidt ).

After the Second World War, the authorship became considerably international and most of the texts appeared in English. In addition, the individual volumes are mostly special monographs and less textbooks, for which Springer Verlag has other series such as Graduate Texts in Mathematics .

Well-known monographs and textbooks in the series after 1945 were Carl Ludwig Siegel , Jürgen Moser Lectures on Celestial Mechanics , Lars Hörmander Analysis of Linear Partial Differential Operators (4 volumes), Herbert Federer Geometric Measure Theory , Jürgen Neukirch Algebraic Number Theory , John Horton Conway and Neil Sloane Sphere packings, lattices and groups , Henry McKean and Kiyoshi Ito Diffusion processes and their sample paths , André Weil Basic Number Theory , Igor Schafarewitsch Basic Algebraic Geometry and Topological Vector Spaces by Gottfried Köthe .

Works on physics also appeared in the series, for example the textbook on the theory of relativity by Arthur Eddington and the mathematical tools of the physicist by Erwin Madelung before the war and then the computational methods of quantum theory by Siegfried Flügge .

In 1968, Beno Eckmann and Bartel Leendert van der Waerden were the editors and co-editors were Joseph Doob , Erhard Heinz , Friedrich Hirzebruch , Eberhard Hopf , Heinz Hopf , Wilhelm Maak , Saunders MacLane , Wilhelm Magnus , David Mumford , Michail Michailowitsch Postnikow , Friedrich Karl Schmidt , Dana Scott , Karl Stein .

The editors in 2013 were: Alain Chenciner , John Coates , SRS Varadhan (editor-in-chief) and for the individual series Marcel Berger , Pierre de la Harpe , Nigel Hitchin , Antti Kupiainen , Gilles Lebeau , Fang-Hua Lin , Shigefumi Mori , Ngô Bảo Châu , Marina Ratner , Denis Serre , Neil Sloane , Anatoli Moissejewitsch Werschik (Vershik) and Michel Waldschmidt . In 2018 the same except for Ratner and Berger, who have since passed away.

Around 350 volumes had appeared by 2013.

List of all volumes

Some of the volumes are English translations (mostly with revision) of volumes previously published in German in the series.


Volker Remmert / Ute Schneider : A Discipline and its Publishers - Disciplinary Culture and the Publication of Mathematics in Germany, 1871–1949, Bielefeld 2010 [Mainzer Historische Kulturwissenschaften 4]

Web links

Individual evidence

  1. 2013 according to the publisher only in English