Scharlau, Winfried
Overview
Works:  45 works in 215 publications in 3 languages and 2,753 library holdings 

Genres:  History Conference papers and proceedings Records and correspondence Sources Biography 
Roles:  Author, Editor, Other, Contributor 
Classifications:  QA241, 512.944 
Publication Timeline
.
Most widely held works by
Winfried Scharlau
From Fermat to Minkowski : lectures on the theory of numbers and its historical development by
Winfried Scharlau(
Book
)
34 editions published between 1980 and 2010 in 3 languages and held by 765 WorldCat member libraries worldwide
This book arose from a course of lectures given by the first author during the winter term 1977/1978 at the University of Münster (West Germany). The course was primarily addressed to future high school teachers of mathematics; it was not meant as a systematic introduction to number theory but rather as a historically motivated invitation to the subject, designed to interest the audience in numbertheoretical questions and developments. This is also the objective of this book, which is certainly not meant to replace any of the existing excellent texts in number theory. Our selection of topics and examples tries to show how, in the historical development, the investigation of obvious or natural questions has led to more and more comprehensive and profound theories, how again and again, surprising connections between seemingly unrelated problems were discovered, and how the introduction of new methods and concepts led to the solution of hitherto unassailable questions. All this means that we do not present the student with polished proofs (which in turn are the fruit of a long historical development); rather, we try to show how these theorems are the necessary consequences of natural questions. Two examples might illustrate our objectives
34 editions published between 1980 and 2010 in 3 languages and held by 765 WorldCat member libraries worldwide
This book arose from a course of lectures given by the first author during the winter term 1977/1978 at the University of Münster (West Germany). The course was primarily addressed to future high school teachers of mathematics; it was not meant as a systematic introduction to number theory but rather as a historically motivated invitation to the subject, designed to interest the audience in numbertheoretical questions and developments. This is also the objective of this book, which is certainly not meant to replace any of the existing excellent texts in number theory. Our selection of topics and examples tries to show how, in the historical development, the investigation of obvious or natural questions has led to more and more comprehensive and profound theories, how again and again, surprising connections between seemingly unrelated problems were discovered, and how the introduction of new methods and concepts led to the solution of hitherto unassailable questions. All this means that we do not present the student with polished proofs (which in turn are the fruit of a long historical development); rather, we try to show how these theorems are the necessary consequences of natural questions. Two examples might illustrate our objectives
Quadratic and Hermitian forms by
Winfried Scharlau(
Book
)
15 editions published between 1984 and 2012 in English and Undetermined and held by 477 WorldCat member libraries worldwide
For a long time  at least from Fermat to Minkowski  the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic forms. On the basis of their work, Minkowski, Siegel, Hasse, Eichler and many others crea ted the impressive "arithmetic" theory of quadratic forms, which has been the object of the wellknown books by Bachmann (1898/1923), Eichler (1952), and O'Meara (1963). Parallel to this development the ideas of abstract algebra and abstract linear algebra introduced by Dedekind, Frobenius, E. Noether and Artin led to today's structural mathematics with its emphasis on classification problems and general structure theorems. On the basis of both  the number theory of quadratic forms and the ideas of modern algebra  Witt opened, in 1937, a new chapter in the theory of quadratic forms. His most fruitful idea was to consider not single "individual" quadratic forms but rather the entity of all forms over a fixed ground field and to construct from this an algebra ic object. This object  the Witt ring  then became the principal object of the entire theory. Thirty years later Pfister demonstrated the significance of this approach by his celebrated structure theorems
15 editions published between 1984 and 2012 in English and Undetermined and held by 477 WorldCat member libraries worldwide
For a long time  at least from Fermat to Minkowski  the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic forms. On the basis of their work, Minkowski, Siegel, Hasse, Eichler and many others crea ted the impressive "arithmetic" theory of quadratic forms, which has been the object of the wellknown books by Bachmann (1898/1923), Eichler (1952), and O'Meara (1963). Parallel to this development the ideas of abstract algebra and abstract linear algebra introduced by Dedekind, Frobenius, E. Noether and Artin led to today's structural mathematics with its emphasis on classification problems and general structure theorems. On the basis of both  the number theory of quadratic forms and the ideas of modern algebra  Witt opened, in 1937, a new chapter in the theory of quadratic forms. His most fruitful idea was to consider not single "individual" quadratic forms but rather the entity of all forms over a fixed ground field and to construct from this an algebra ic object. This object  the Witt ring  then became the principal object of the entire theory. Thirty years later Pfister demonstrated the significance of this approach by his celebrated structure theorems
Algebraic theory of quadratic forms : generic methods and Pfister forms by
Manfred Knebusch(
Book
)
13 editions published in 1980 in English and Undetermined and held by 266 WorldCat member libraries worldwide
13 editions published in 1980 in English and Undetermined and held by 266 WorldCat member libraries worldwide
Quadratic forms by
Winfried Scharlau(
Book
)
9 editions published between 1969 and 1970 in English and Undetermined and held by 228 WorldCat member libraries worldwide
9 editions published between 1969 and 1970 in English and Undetermined and held by 228 WorldCat member libraries worldwide
Einführung in die Funktionalanalysis by
Friedrich Hirzebruch(
Book
)
28 editions published between 1971 and 1996 in German and Undetermined and held by 212 WorldCat member libraries worldwide
28 editions published between 1971 and 1996 in German and Undetermined and held by 212 WorldCat member libraries worldwide
Schulwissen Mathematik : ein Überblick ; was ein Studienanfänger von der Mathematik wissen sollte by
Winfried Scharlau(
Book
)
11 editions published between 1994 and 2010 in German and held by 178 WorldCat member libraries worldwide
Dieses Buch fasst in knapper Form zusammen, was ein Student von der Schule her an Wissen mitbringen muss, um mit einem Studium, in dem man Mathematik braucht (Natur und Wirtschaftswissenschaften oder auch Ingenieurstudiengänge), beginnen zu können. Zahlen und Rechnen mit Zahlen  Rechnen mit Buchstaben  Die quadratische Gleichung  Grundbegriffe der Mengenlehre  Geometrische Grundbegriffe  Kongruenz, Ähnlichkeit, Strahlensatz  Geometrie des Dreiecks  Das rechtwinklige Dreieck  Geometrische Figuren im Raum  Analytische Geometrie der Ebene  Geraden in der Ebene  Kegelschnitte. Kurven zweiten Grades  Analytische Geometrie des Raumes  Lineare Gleichungen  Grundbegriffe der Kombinatorik  Funktionen  Grundbegriffe der Differential und Integralrechnung  Die elementaren Funktionen  Was ist ein mathematischer Satz und ein mathematischer Beweis?  Überblick: Geschichte der Mathematik  Studienanfänger Mathematik  Schüler(innen) der Oberstufe  Interessierte Laien Prof. Dr. Winfried Scharlau, Mathematisches Institut der Universität Münster
11 editions published between 1994 and 2010 in German and held by 178 WorldCat member libraries worldwide
Dieses Buch fasst in knapper Form zusammen, was ein Student von der Schule her an Wissen mitbringen muss, um mit einem Studium, in dem man Mathematik braucht (Natur und Wirtschaftswissenschaften oder auch Ingenieurstudiengänge), beginnen zu können. Zahlen und Rechnen mit Zahlen  Rechnen mit Buchstaben  Die quadratische Gleichung  Grundbegriffe der Mengenlehre  Geometrische Grundbegriffe  Kongruenz, Ähnlichkeit, Strahlensatz  Geometrie des Dreiecks  Das rechtwinklige Dreieck  Geometrische Figuren im Raum  Analytische Geometrie der Ebene  Geraden in der Ebene  Kegelschnitte. Kurven zweiten Grades  Analytische Geometrie des Raumes  Lineare Gleichungen  Grundbegriffe der Kombinatorik  Funktionen  Grundbegriffe der Differential und Integralrechnung  Die elementaren Funktionen  Was ist ein mathematischer Satz und ein mathematischer Beweis?  Überblick: Geschichte der Mathematik  Studienanfänger Mathematik  Schüler(innen) der Oberstufe  Interessierte Laien Prof. Dr. Winfried Scharlau, Mathematisches Institut der Universität Münster
Richard Dedekind, 18311981 : eine Würdigung zu seinem 150. Geburtstag by
Winfried Scharlau(
Book
)
7 editions published in 1981 in German and Undetermined and held by 138 WorldCat member libraries worldwide
7 editions published in 1981 in German and Undetermined and held by 138 WorldCat member libraries worldwide
Mathematische Institute in Deutschland 18001945 by
Winfried Scharlau(
Book
)
8 editions published between 1989 and 1990 in 3 languages and held by 98 WorldCat member libraries worldwide
8 editions published between 1989 and 1990 in 3 languages and held by 98 WorldCat member libraries worldwide
Briefwechsel mit Cantor, Dedekind, Helmholtz, Kronecker, Weierstrass und anderen by
Rudolf Lipschitz(
Book
)
7 editions published in 1986 in German and held by 91 WorldCat member libraries worldwide
7 editions published in 1986 in German and held by 91 WorldCat member libraries worldwide
Mathematik in Biologie und Geowissenschaften by
Winfried Scharlau(
Book
)
2 editions published in 2000 in German and held by 27 WorldCat member libraries worldwide
2 editions published in 2000 in German and held by 27 WorldCat member libraries worldwide
Differentiable manifolds and quadratic forms by
Friedrich Hirzebruch(
Book
)
7 editions published between 1971 and 1992 in English and held by 21 WorldCat member libraries worldwide
7 editions published between 1971 and 1992 in English and held by 21 WorldCat member libraries worldwide
Wer ist Alexander Grothendieck? : Anarchie, Mathematik, Spiritualität ; eine Biographie by
Winfried Scharlau(
Book
)
13 editions published between 2007 and 2013 in German and held by 18 WorldCat member libraries worldwide
13 editions published between 2007 and 2013 in German and held by 18 WorldCat member libraries worldwide
Mathematik für Naturwissenschaftler : [Stochastik für Lehramtsstudenten] by
Winfried Scharlau(
Book
)
2 editions published in 2005 in German and Undetermined and held by 17 WorldCat member libraries worldwide
2 editions published in 2005 in German and Undetermined and held by 17 WorldCat member libraries worldwide
Wer ist Alexander Grothendieck? Oberwolfach lecture 2006 by
Winfried Scharlau(
)
2 editions published in 2007 in German and held by 16 WorldCat member libraries worldwide
2 editions published in 2007 in German and held by 16 WorldCat member libraries worldwide
Who is Alexander Grothendieck? : anarchy, mathematics, spirituality, solitude : a biography by
Winfried Scharlau(
Book
)
3 editions published in 2011 in English and held by 15 WorldCat member libraries worldwide
3 editions published in 2011 in English and held by 15 WorldCat member libraries worldwide
The cohomological theory of quadratic forms by
Winfried Scharlau(
Book
)
4 editions published between 1965 and 1970 in English and held by 14 WorldCat member libraries worldwide
4 editions published between 1965 and 1970 in English and held by 14 WorldCat member libraries worldwide
Conference on Quadratic Forms, 1976 by
T. Y Lam(
Book
)
1 edition published in 1977 in English and held by 14 WorldCat member libraries worldwide
1 edition published in 1977 in English and held by 14 WorldCat member libraries worldwide
Wer ist Alexander Grothendieck? : Anarchie, Mathematik, Spiritualität; eine Biographie by
Winfried Scharlau(
Book
)
8 editions published between 2010 and 2013 in German and held by 12 WorldCat member libraries worldwide
8 editions published between 2010 and 2013 in German and held by 12 WorldCat member libraries worldwide
Wer ist Alexander Grothendieck? : Anarchie, Mathematik, Spiritualität, Einsamkeit : eine Biographie by
Winfried Scharlau(
Book
)
in German and Undetermined and held by 8 WorldCat member libraries worldwide
in German and Undetermined and held by 8 WorldCat member libraries worldwide
FunktionalAnalysis by
Friedrich Hirzebruch(
Book
)
in German and held by 7 WorldCat member libraries worldwide
in German and held by 7 WorldCat member libraries worldwide
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Audience Level
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Kids  General  Special 
Related Identities
 Opolka, Hans Author
 Knebusch, Manfred Author Editor
 Hirzebruch, Friedrich Author Editor
 Dedekind, Richard 18311916 Honoree Author
 Lipschitz, Rudolf 18321903 Other Author
 Cantor, Georg 18451918
 Grothendieck, A. (Alexandre)
 Lee, Heisook Annotator
 Mathematisches Forschungsinstitut <Oberwolfach>
 Dedekind, Richard
Useful Links
Associated Subjects
Algebraic fields Algebraic number theory College teachers Dedekind, Richard, Differentiable manifolds Differential topology Forms, Pfister Forms, Quadratic France Functional analysis Geometry, Algebraic Germany Grothendieck, A.(Alexandre) Hermitian forms Lipschitz, Rudolf, Mathematicians Mathematics MathematicsStudy and teaching MathematicsStudy and teaching (Higher) Number theory Social sciences Universities and colleges
Alternative Names
ScharlauOpolka, ... 1940
Scharlau, W.
Scharlau, W. 1940
Scharlau, Windfried 1940
Scharlau, Winfried
Winfried Scharlau deutscher Mathematiker
Winfried Scharlau Duits wiskundige
Winfried Scharlau German mathematician and historian of mathematics
シャーラウ, W
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