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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."
This scarce antiquarian book is a selection from Kessinger
Publishing's Legacy Reprint Series. Due to its age, it may contain
imperfections such as marks, notations, marginalia and flawed
pages. Because we believe this work is culturally important, we
have made it available as part of our commitment to protecting,
preserving, and promoting the world's literature. Kessinger
Publishing is the place to find hundreds of thousands of rare and
hard-to-find books with something of interest for everyone
This is an EXACT reproduction of a book published before 1923. This
IS NOT an OCR'd book with strange characters, introduced
typographical errors, and jumbled words. This book may have
occasional imperfections such as missing or blurred pages, poor
pictures, errant marks, etc. that were either part of the original
artifact, or were introduced by the scanning process. We believe
this work is culturally important, and despite the imperfections,
have elected to bring it back into print as part of our continuing
commitment to the preservation of printed works worldwide. We
appreciate your understanding of the imperfections in the
preservation process, and hope you enjoy this valuable book.
This scarce antiquarian book is a selection from Kessinger
Publishing's Legacy Reprint Series. Due to its age, it may contain
imperfections such as marks, notations, marginalia and flawed
pages. Because we believe this work is culturally important, we
have made it available as part of our commitment to protecting,
preserving, and promoting the world's literature. Kessinger
Publishing is the place to find hundreds of thousands of rare and
hard-to-find books with something of interest for everyone!
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.
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