WorldCat Identities

Laugwitz, Detlef

Overview
Works: 198 works in 546 publications in 3 languages and 3,572 library holdings
Genres: History  Biography  Conference papers and proceedings 
Roles: Author, Editor, Honoree, Contributor, Other, Creator
Classifications: QA641, 516.7
Publication Timeline
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Most widely held works by Detlef Laugwitz
Differential and Riemannian geometry by Detlef Laugwitz( Book )

49 editions published between 1960 and 1977 in 4 languages and held by 876 WorldCat member libraries worldwide

Bernhard Riemann, 1826-1866 : turning points in the conception of mathematics by Detlef Laugwitz( Book )

22 editions published between 1998 and 2008 in English and held by 401 WorldCat member libraries worldwide

This book, originally written in German and presented here in an English-language translation, is the first attempt to examine Riemann's scientific work from a single unifying perspective. Laugwitz describes Riemann's development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle - for mathematics and physics alike - to be a matter of "understanding the world through its behavior in the infinitely small." This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann's work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics
Ingenieurmathematik by Detlef Laugwitz( Book )

28 editions published between 1964 and 1984 in German and Undetermined and held by 288 WorldCat member libraries worldwide

Ingenieurmathematik by Detlef Laugwitz( Book )

26 editions published between 1964 and 1974 in 3 languages and held by 152 WorldCat member libraries worldwide

Differentialgeometrie in Vektorräumen, unter besonderer Berücksichtigung der unendlichdimensionalen Räume by Detlef Laugwitz( Book )

18 editions published in 1965 in German and Undetermined and held by 148 WorldCat member libraries worldwide

Bernhard Riemann, 1826-1866 : Wendepunkte in der Auffassung der Mathematik by Detlef Laugwitz( Book )

12 editions published between 1995 and 1996 in German and English and held by 120 WorldCat member libraries worldwide

Das Riemannsche Integral lernen schon die Schüler kennen, die Theorien der reellen und der komplexen Funktionen bauen auf wichtigen Begriffsbildungen und Sätzen Riemanns auf, die Riemannsche Geometrie ist für Einsteins Gravitationstheorie und ihre Erweiterungen unentbehrlich, und in der Zahlentheorie ist die berühmte Riemannsche Vermutung noch immer offen. Riemann und sein um fünf Jahre jüngerer Freund Richard Dedekind sahen sich als Schüler von Gauss und Dirichlet. Um die Mitte des 19. Jahrhunderts leiteten sie den Übergang zur "modernen Mathematik" ein, der eine in Analysis und Geometrie, der andere in der Algebra mit der Hinwendung zu Mengen und Strukturen. Dieses Buch ist der erste Versuch, Riemanns wissenschaftliches Werk unter einem einheitlichen Gesichtspunkt zusammenzufassend darzustellen. Riemann gilt als einer der Philosophen unter den Mathematikern. Er stellte das Denken in Begriffen neben die zuvor vorherrschende algorithmische Auffassung von der Mathematik, welche die Gegenstände der Untersuchung, in Formeln und Figuren, in Termumformungen und regelhaften Konstruktionen als die allein legitimen Methoden sah. David Hilbert hat als Riemanns Grundsatz herausgestellt, die Beweise nicht durch Rechnung, sondern lediglich durch Gedanken zu zwingen. Hermann Weyl sah als das Prinzip Riemanns in Mathematik und Physik, "die Welt als das erkenntnistheoretische Motiv ..., die Welt aus ihrem Verhalten im un- endlich kleinen zu verstehen."
Zahlen und Kontinuum : eine Einführung in die Infinitesimalmathematik by Detlef Laugwitz( Book )

12 editions published between 1986 and 1994 in German and held by 103 WorldCat member libraries worldwide

Konzepte des mathematischen Unendlichen im 19. Jahrhundert( Book )

5 editions published in 1990 in German and Undetermined and held by 99 WorldCat member libraries worldwide

Ingenieurmathematik by Detlef Laugwitz( Book )

12 editions published between 1964 and 1984 in German and Undetermined and held by 96 WorldCat member libraries worldwide

Ingenieurmathematik by Detlef Laugwitz( Book )

7 editions published between 1964 and 1976 in German and held by 83 WorldCat member libraries worldwide

Infinitesimalkalkül : Kontinuum und Zahlen : eine elementare Einführung in die Nichtstandard-Analysis by Detlef Laugwitz( Book )

9 editions published in 1978 in German and held by 80 WorldCat member libraries worldwide

Funktionalanalysis by Benno Fuchssteiner( Book )

6 editions published in 1974 in German and held by 78 WorldCat member libraries worldwide

Beiträge zur affinen Flächentheorie mit Anwendungen auf die allgemein-metrische Differentialgeometrie by Detlef Laugwitz( Book )

8 editions published between 1958 and 1959 in German and held by 77 WorldCat member libraries worldwide

Analysis and geometry : trends in research and teaching( Book )

9 editions published in 1992 in English and German and held by 58 WorldCat member libraries worldwide

Aufgaben zur Ingenieurmathematik by Detlef Laugwitz( Book )

7 editions published between 1966 and 1976 in German and held by 50 WorldCat member libraries worldwide

Schulmathematik vom höheren Standpunkt by Detlef Laugwitz( Book )

10 editions published in 1969 in German and Undetermined and held by 43 WorldCat member libraries worldwide

Schulmathematik vom höheren Standpunkt by Detlef Laugwitz( Book )

4 editions published in 1969 in German and Undetermined and held by 37 WorldCat member libraries worldwide

Die allgemeine Functionentheorie. 1 Theil. Metaphysik und Theorie der mathematischen Grundbegriffe: Grösse, Grenze, Argument und Function by Paul Du Bois-Reymond( Book )

6 editions published in 1968 in German and held by 37 WorldCat member libraries worldwide

Über die Invarianz quadratischer Formen bei linearen Transformationen und das Raumproblem by Detlef Laugwitz( Book )

3 editions published in 1956 in German and held by 33 WorldCat member libraries worldwide

The theory of infinitesimals : an introduction to nonstandard analysis : ciclo di lezioni tenute nel marzo 1977 by Detlef Laugwitz( Book )

10 editions published between 1977 and 1980 in 3 languages and held by 31 WorldCat member libraries worldwide

 
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Bernhard Riemann, 1826-1866 : turning points in the conception of mathematics
Languages
German (183)

English (63)

Italian (2)

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