Georg Aumann

Born in Munich, George Aumann initially considered a career as a civil servant.{{cite web |url=http://badw.de/fileadmin/nachrufe/Aumann%20Georg.pdf |title= Obituary Aumann Georg (Yearbook 1981, Otto Haupt) (German:Nachruf Aumann Georg (Jahrbuch 1981, Otto Haupt)) |publisher=Bayerische Akademie der Wissenschaften |access-date=7 March 2017}} From 1925, Aumann studied mathematics and physics at the Ludwig-Maximilian-University of Munich, among others with Professor Constantin Carathéodory and Professor Heinrich Tietze. He was promoted in 1931 to Doctor of Philosophy with a thesis titled: contributions to the theory of decomposition spaces (German:Beiträge zur Theorie der Zerlegungsräume){{mathgenealogy|id=36548}} In 1933 he habilitated twice, at the Technical University of Munich, and at the University of Munich (with different degrees of postdoctoral dissertation). In 1934–35 he was appointed a Rockefeller scholar at the Institute for Advanced Study in Princeton N.J. In 1936 he became an extraordinary professor at the Goethe University in Frankfurt. At the beginning of the war, he was conscripted for military service Appeals to a full professorship failed several times because he was regarded as politically unreliable among the Nazis Ministry of Education. In all these years his wife was an indispensable, prudent and energetic support to him.

In 1949 he became full professor at the University of Würzburg and in 1950 at the University of Munich. In 1960 he moved to a professorship at the Technical University of Munich. After the war, he received an apology.

In 1954 he published Real Functions, a nine-chapter textbook on real analysis. In a review, Paul Halmos said "The quality, quantity, organization, and exposition of its contents, together with the fact that much of the material in it has not been available hitherto in book form, serve to make it a recommended part of the library of every modern analyst."{{mr|id=0061652}} The text was re-printed in 1969.{{mr|id=0257287}}

He also dealt with conformal illustrations, properties of complex polynomials, band theory and cluster theory. Aumann also wrote a three-dimensional analysis textbook with Otto Haupt and a three-volume mathematics textbook for engineers.{{citation needed|date=January 2020}}

In 1958 Aumann became a full member of the Bavarian Academy of Sciences{{cite web |url=http://badw.de/data/footer-navigation/personentreffer.html?tx_badwdb_badwperson%5Bper_id%5D=69&tx_badwdb_badwperson%5BpartialType%5D=BADWPersonDetailsPartial&tx_badwdb_badwperson%5Baction%5D=show&tx_badwdb_badwperson%5Bcontroller%5D=BADWPerson&cHash=6156ee06cf1b54cb46ed28b6c607e18d |title= Prof. Dr. Georg Aumann |publisher= Bayerische Akademie der Wissenschaften |date=2017 |website=Bavarian Academy of Sciences |access-date=3 March 2017}}

In 1977 the University of Erlangen awarded Aumann an Honorary Doctor of Science degree, Doctor rerum naturalium honoris causa.

In 1970 Aumann contributed to the theory of binary relations with a generalization of the set membership relation ∈. The elements of a universe U form the domain of this relation while the range is the power set on U, denoted P(U). A contact relation C with this domain and range is expressed in terms of the calculus of relations using compositions:

:$C^T\; \backslash bar\{C\}\; \backslash \; \backslash subseteq\; \backslash \; \backslash ni\; \backslash bar\{C\}\; ,$ where C^T is the converse of C, $\backslash ni$ is the converse of set membership, and $\backslash bar\{C\}$ is the complementary relation to C.G. Aumann (1970) Kontakt-Relationen, Sitzungbericht der Bayer, Akademie der Wissenschaften, Math-Nat Klasse {{mr|id=0309040}}G. Aumann (1974) AD ARTEM ULTIMAM : Eine Einfuhrung in die Gedankenwelt der Mathematik, R. Oldenbourg, {{ISBN|3-486-34481-1}} {{mr|id=0363746}}

Alternatively, using the left residual ∈\C, the condition for a contact relation may be expressed $C\; (\backslash in\; \backslash backslash\; C)\; \backslash subseteq\; C$ through use of Schröder rules. Aumann contacts have been further developed by Gunther Schmidt and Michael Winter.Gunther Schmidt and Michael Winter (2018) Relational Topology, "Closures and their Aumann Contacts", pages 113 to 124, Lecture Notes in Mathematics #2208, Springer books

Aumann showed in 1977 how a neighborhood system r in the power set on A can be identified from a corresponding binary relation $\backslash sim\_r$ on maps from A to B, where B has at least two elements. The relation $f\; \backslash \; \backslash sim\_r\; \backslash \; g$ between two maps holds when there is a subset of A in r where f and g agree.G. Aumann (1978) "Die aufbildungstheoretische Zugang zur Topologie", (The construction-theoretic approach to Topology), Bayer Akad. Sitzungberichte 1977 Seiten 63 zu 71 {{mr|id=512567}}, Zweite Artikel 1978 Seiten 85 zu 93 {{mr|id=547697}}

{{Portal|Biography|Mathematics}}

• 1968: "Approximation of functions" (German:Approximation von Funktionen), in Robert Sauer, Istvan Szabo, editors, The mathematical tools of the engineer (German:Die mathematischen Hilfsmittel des Ingenieurs), Volume 3, Springer Verlag
• 1969: Real Functions (German:Reelle Funktionen), Fundamentals of Mathematical Sciences, Springer Verlag, 2nd Edition
• 1970,1: Higher Mathematics (German: Höhere Mathematik), Volumes 1–3, BI Universitätsaschenbücher
• 1974: Ad artem ultimam: an introduction to the world of thought in mathematics (German: Ad artem ultimam: eine Einführung in die Gedankenwelt der Mathematik), Oldenbourg
• 1974 – 1983: (with Otto Haupt) Introduction to Real Analysis (German: Einführung in die reelle Analysis), 3 Volumes, De Gruyter, 3rd Edition

{{Reflist}}

{{German signal intelligence organisations before and during World War II}}

{{Authority control}}

{{DEFAULTSORT:Aumann, Georg}}

Category:1906 births

Category:1980 deaths

Category:20th-century German mathematicians

Category:Members of the Bavarian Academy of Sciences