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The Swiss mathematician Jakob Steiner (1796-1863) came from a poor
background with an incomplete education, yet such was his
mathematical talent that eventually the Prussian university system
adapted itself to him rather than he to it. A geometer in an age
dominated by analysts, he pursued his own interests in his own way.
The elegant results which bear his name - including Steiner
circles, systems and symmetrisation - are known to most
mathematicians today. Considered by many to be the greatest
geometer since Apollonius of Perga, Steiner did important work on
systemising geometry, laying the foundation for much later work on
projective geometry. Edited by the eminent mathematician Karl
Weierstrass (1815-97), this two-volume edition of Steiner's
collected works offers scholars access to his influential writings
in the original German. Volume 1 was published in 1881.
The German mathematician Karl Weierstrass (1815-97) is generally
considered to be the father of modern analysis. His clear eye for
what was important is demonstrated by the publication, late in
life, of his polynomial approximation theorem; suitably generalised
as the Stone-Weierstrass theorem, it became a central tool for
twentieth-century analysis. Furthermore, the Weierstrass
nowhere-differentiable function is the seed from which springs the
entire modern theory of mathematical finance. The best students in
Europe came to Berlin to attend his lectures, and his rigorous
style still dominates the first analysis course at any university.
His seven-volume collected works in the original German contain not
only published treatises but also records of many of his famous
lecture courses. Edited by Johannes Knoblauch (1855-1915), Volume 5
was published in 1915.
The German mathematician Karl Weierstrass (1815-97) is generally
considered to be the father of modern analysis. His clear eye for
what was important is demonstrated by the publication, late in
life, of his polynomial approximation theorem; suitably generalised
as the Stone-Weierstrass theorem, it became a central tool for
twentieth-century analysis. Furthermore, the Weierstrass
nowhere-differentiable function is the seed from which springs the
entire modern theory of mathematical finance. The best students in
Europe came to Berlin to attend his lectures, and his rigorous
style still dominates the first analysis course at any university.
His seven-volume collected works in the original German contain not
only published treatises but also records of many of his famous
lecture courses. Edited by Rudolf Rothe (1873-1942), Volume 6 was
published in 1915.
The German mathematician Karl Weierstrass (1815-97) is generally
considered to be the father of modern analysis. His clear eye for
what was important is demonstrated by the publication, late in
life, of his polynomial approximation theorem; suitably generalised
as the Stone-Weierstrass theorem, it became a central tool for
twentieth-century analysis. Furthermore, the Weierstrass
nowhere-differentiable function is the seed from which springs the
entire modern theory of mathematical finance. The best students in
Europe came to Berlin to attend his lectures, and his rigorous
style still dominates the first analysis course at any university.
His seven-volume collected works in the original German contain not
only published treatises but also records of many of his famous
lecture courses. Edited by Rudolf Rothe (1873-1942), Volume 7 was
published in 1927.
The Swiss mathematician Jakob Steiner (1796-1863) came from a poor
background with an incomplete education, yet such was his
mathematical talent that eventually the Prussian university system
adapted itself to him rather than he to it. A geometer in an age
dominated by analysts, he pursued his own interests in his own way.
The elegant results which bear his name - including Steiner
circles, systems and symmetrisation - are known to most
mathematicians today. Considered by many to be the greatest
geometer since Apollonius of Perga, Steiner did important work on
systemising geometry, laying the foundation for much later work on
projective geometry. Edited by the eminent mathematician Karl
Weierstrass (1815-97), this two-volume edition of Steiner's
collected works offers scholars access to his influential writings
in the original German. Volume 2 was published in 1882.
The German mathematician Karl Weierstrass (1815-97) is generally
considered to be the father of modern analysis. His clear eye for
what was important is demonstrated by the publication, late in
life, of his polynomial approximation theorem; suitably generalised
as the Stone-Weierstrass theorem, it became a central tool for
twentieth-century analysis. Furthermore, the Weierstrass
nowhere-differentiable function is the seed from which springs the
entire modern theory of mathematical finance. The best students in
Europe came to Berlin to attend his lectures, and his rigorous
style still dominates the first analysis course at any university.
His seven-volume collected works in the original German contain not
only published treatises but also records of many of his famous
lecture courses. Volume 1 was published in 1894.
The German mathematician Karl Weierstrass (1815-97) is generally
considered to be the father of modern analysis. His clear eye for
what was important is demonstrated by the publication, late in
life, of his polynomial approximation theorem; suitably generalised
as the Stone-Weierstrass theorem, it became a central tool for
twentieth-century analysis. Furthermore, the Weierstrass
nowhere-differentiable function is the seed from which springs the
entire modern theory of mathematical finance. The best students in
Europe came to Berlin to attend his lectures, and his rigorous
style still dominates the first analysis course at any university.
His seven-volume collected works in the original German contain not
only published treatises but also records of many of his famous
lecture courses. Volume 2 was published in 1895.
The German mathematician Karl Weierstrass (1815-97) is generally
considered to be the father of modern analysis. His clear eye for
what was important is demonstrated by the publication, late in
life, of his polynomial approximation theorem; suitably generalised
as the Stone-Weierstrass theorem, it became a central tool for
twentieth-century analysis. Furthermore, the Weierstrass
nowhere-differentiable function is the seed from which springs the
entire modern theory of mathematical finance. The best students in
Europe came to Berlin to attend his lectures, and his rigorous
style still dominates the first analysis course at any university.
His seven-volume collected works in the original German contain not
only published treatises but also records of many of his famous
lecture courses. Edited by Johannes Knoblauch (1855-1915), Volume 3
was published in 1903.
The German mathematician Karl Weierstrass (1815-97) is generally
considered to be the father of modern analysis. His clear eye for
what was important is demonstrated by the publication, late in
life, of his polynomial approximation theorem; suitably generalised
as the Stone-Weierstrass theorem, it became a central tool for
twentieth-century analysis. Furthermore, the Weierstrass
nowhere-differentiable function is the seed from which springs the
entire modern theory of mathematical finance. The best students in
Europe came to Berlin to attend his lectures, and his rigorous
style still dominates the first analysis course at any university.
His seven-volume collected works in the original German contain not
only published treatises but also records of many of his famous
lecture courses. Edited by Johannes Knoblauch (1885-1915) and Georg
Hettner (1854-1914), Volume 4 was published in 1902.
One of the greatest mathematicians of the nineteenth century, Carl
Gustav Jacob Jacobi (1804-51) burst into the limelight with his
redevelopment, together with Niels Henrik Abel (1802-29), of the
theory of elliptic functions. His pioneering work was characterised
by the variety of problems tackled and the power of the tools used
to tackle them. His lasting influence on rational mechanics, number
theory, partial differential equations, complex variable theory and
computation is marked by the number of fundamental concepts that
bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol,
among others). His collected works, comprising treatises, letters
and papers written in German, Latin and French, were published in
eight volumes between 1881 and 1891. Edited by fellow German
mathematician Karl Weierstrass (1815-97), Volume 2 appeared in
1882.
One of the greatest mathematicians of the nineteenth century, Carl
Gustav Jacob Jacobi (1804-51) burst into the limelight with his
redevelopment, together with Niels Henrik Abel (1802-29), of the
theory of elliptic functions. His pioneering work was characterised
by the variety of problems tackled and the power of the tools used
to tackle them. His lasting influence on rational mechanics, number
theory, partial differential equations, complex variable theory and
computation is marked by the number of fundamental concepts that
bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol,
among others). His collected works, comprising treatises, letters
and papers written in German, Latin and French, were published in
eight volumes between 1881 and 1891. Edited by fellow German
mathematician Karl Weierstrass (1815-97), Volume 3 appeared in
1884.
One of the greatest mathematicians of the nineteenth century, Carl
Gustav Jacob Jacobi (1804-51) burst into the limelight with his
redevelopment, together with Niels Henrik Abel (1802-29), of the
theory of elliptic functions. His pioneering work was characterised
by the variety of problems tackled and the power of the tools used
to tackle them. His lasting influence on rational mechanics, number
theory, partial differential equations, complex variable theory and
computation is marked by the number of fundamental concepts that
bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol,
among others). His collected works, comprising treatises, letters
and papers written in German, Latin and French, were published in
eight volumes between 1881 and 1891. Edited by fellow German
mathematician Karl Weierstrass (1815-97), Volume 4 appeared in
1886.
One of the greatest mathematicians of the nineteenth century, Carl
Gustav Jacob Jacobi (1804-51) burst into the limelight with his
redevelopment, together with Niels Henrik Abel (1802-29), of the
theory of elliptic functions. His pioneering work was characterised
by the variety of problems tackled and the power of the tools used
to tackle them. His lasting influence on rational mechanics, number
theory, partial differential equations, complex variable theory and
computation is marked by the number of fundamental concepts that
bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol,
among others). His collected works, comprising treatises, letters
and papers written in German, Latin and French, were published in
eight volumes between 1881 and 1891. Edited by fellow German
mathematician Karl Weierstrass (1815-97), Volume 5 appeared in
1890.
One of the greatest mathematicians of the nineteenth century, Carl
Gustav Jacob Jacobi (1804-51) burst into the limelight with his
redevelopment, together with Niels Henrik Abel (1802-29), of the
theory of elliptic functions. His pioneering work was characterised
by the variety of problems tackled and the power of the tools used
to tackle them. His lasting influence on rational mechanics, number
theory, partial differential equations, complex variable theory and
computation is marked by the number of fundamental concepts that
bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol,
among others). His collected works, comprising treatises, letters
and papers written in German, Latin and French, were published in
eight volumes between 1881 and 1891. Edited by fellow German
mathematician Karl Weierstrass (1815-97), Volume 6 appeared in
1891.
One of the greatest mathematicians of the nineteenth century, Carl
Gustav Jacob Jacobi (1804-51) burst into the limelight with his
redevelopment, together with Niels Henrik Abel (1802-29), of the
theory of elliptic functions. His pioneering work was characterised
by the variety of problems tackled and the power of the tools used
to tackle them. His lasting influence on rational mechanics, number
theory, partial differential equations, complex variable theory and
computation is marked by the number of fundamental concepts that
bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol,
among others). His collected works, comprising treatises, letters
and papers written in German, Latin and French, were published in
eight volumes between 1881 and 1891. Edited by fellow German
mathematician Karl Weierstrass (1815-97), Volume 7 appeared in
1891.
One of the greatest mathematicians of the nineteenth century, Carl
Gustav Jacob Jacobi (1804-51) burst into the limelight with his
redevelopment, together with Niels Henrik Abel (1802-29), of the
theory of elliptic functions. His pioneering work was characterised
by the variety of problems tackled and the power of the tools used
to tackle them. His lasting influence on rational mechanics, number
theory, partial differential equations, complex variable theory and
computation is marked by the number of fundamental concepts that
bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol,
among others). His collected works, comprising treatises, letters
and papers written in German, Latin and French, were published in
eight volumes between 1881 and 1891, edited chiefly by Karl
Weierstrass (1815-97). Published in 1884, this supplementary volume
contains Jacobi's 1842-3 lectures on dynamics as compiled by Alfred
Clebsch (1833-72) in the revised second edition by Eduard Lottner
(1826-87).
Dieser Band enthalt die Vorlesung Ausgewahlte Kapitel aus der
Funktionenlehre, die Karl Weierstrass im Sommersemester 1886 an der
Berliner Universitat gehalten hat. Sie war von ihm als Erganzung
seiner turnusmassigen Vorlesung "Einleitung in die Theorie der
analytischen Funktionen" konzipiert worden, und er hielt sie nur
dieses eine Mal. Inhaltliche Schwerpunkte sind der Weierstrasssche
Approximationssatz (mit Verallgemeinerungen auf unstetige
Funktionen mittels des Cantorschen Begriffs des ausseren Inhalts
einer beschrankten Punktmenge) und eine Einfuhrung in die Theorie
der Weierstrassschen "analytischen Gebilde." Der editierte Text,
dem eine Autobiographie zugrunde liegt, enthalt zahlreiche
historische und methodologische Reflexionen. Die Vorlesung, der
Kommentar des Herausgebers sowie die vier im Anhang enthaltenen
fotomechanischen Nachdrucke von Arbeiten der Jahre 1857 bis 1880
verdeutlichen in besonderem Masse Weierstrass' Beitrag zur strengen
Begrundung der Analysis."
Als Schuler von KARL WEIERSTRASS zu Beginn unseres Jahrhunderts an
der Ausgabe der Werke ihres Lehrers arbeiteten, ging es ihnen vor
allem darum, den nachfolgenden Generationen den Schatz der
unveroffentlichten Weierstrassschen Vorlesungen uber elliptische
und Abelsche Funktionen sowie uber Variationsrechnung zu
uberliefern. Dass die Vorlesungen uber allgemeine Funktionentheorie
nicht in den Editionsplan auf genommen wurden, durfte nicht zuletzt
auch damit im Zusammenhang gestanden haben, dass deren Wirkung
bereits allenthalben erkennbar und unwiderruflich war. Was den
Zeitgenossen von WEIERSTRASS nicht erforderlich schien, will uns
heute UD verzichtbar scheinen, wenn wir uns als Historiker und als
Mathematiker der grossen Gestalt von KARL WEIERSTRASS nahern
wollen. Was aber den Zeitgenossen noch recht leicht gefallen ware -
eine moglichst exakte historische Dokumentation des Weierstrass
schen Beitrages zur strengen Begrundung der Analysis -, erfordert
heute einen erhohten Aufwand an geistiger Arbeit, bedingt einen
kritischen Vergleich der nur bruchstuckhaft auf uns gekommenen und
zumeist nicht autorisierten Nachschriften, ein Einfuhlen in die
personlichen und wissenschaftlichen Umstande des Weierstrassschen
Wirkens. Die allgemein anerkannte pragende Bedeutung des
Weierstrassschen Grundlagen beitrages fur die moderne Mathematik
widerspiegelt sich bisher in der internationalen
mathematikhistorischen Literatur nur unzureichend. Es ist deshalb
sehr zu begrussen, dass es der Herausgeber mit der Edition der von
WEIERSTRASS nur einmal gehaltenen Vorlesung "Ausgewahlte Kapitel
aus der Funktionenlehre" (1886) unternommen hat, jene Lucke
schliessen zu helfen."
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