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Author: Felix Hausdorff
Publisher: Springer Science & Business Media
ISBN: 3540306242
Category : Mathematics
Languages : de
Pages : 939
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Book Description
Band 5 umfaßt die Themenbereiche Astronomie, Optik und Wahrscheinlichkeitstheorie. Er enthält Hausdorffs Dissertation über die Refraktion des Lichtes in der Atmosphäre, zwei Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift über die Extinktion des Lichtes in der Atmosphäre. Es folgt eine Arbeit über geometrische Optik, die unmittelbar an die berühmte Publikation von H. Bruns über das Eikonal anschließt und in der Hausdorff die damals ganz neuen Lieschen Theorien für die Optik nutzbar zu machen suchte. Auf dem Gebiet der Stochastik veröffentlichte Hausdorff zwei längere Arbeiten, die in verschiedenen Bereichen der Versicherungsmathematik und der Wahrscheinlichkeitsrechnung ihre Spuren hinterlassen haben. Von besonderem historischen Interesse sind die im Band publizierten Stücke aus Hausdorffs Nachlaß, etwa seine Vorlesung "Wahrscheinlichkeitsrechnung" vom Sommersemester 1923 oder seine Briefe an Richard von Mises aus dem Jahre 1919.
Author: Felix Hausdorff
Publisher: Springer Science & Business Media
ISBN: 3540306242
Category : Mathematics
Languages : de
Pages : 939
Get Book Here
Book Description
Band 5 umfaßt die Themenbereiche Astronomie, Optik und Wahrscheinlichkeitstheorie. Er enthält Hausdorffs Dissertation über die Refraktion des Lichtes in der Atmosphäre, zwei Folgearbeiten zum gleichen Thema sowie die Habilitationsschrift über die Extinktion des Lichtes in der Atmosphäre. Es folgt eine Arbeit über geometrische Optik, die unmittelbar an die berühmte Publikation von H. Bruns über das Eikonal anschließt und in der Hausdorff die damals ganz neuen Lieschen Theorien für die Optik nutzbar zu machen suchte. Auf dem Gebiet der Stochastik veröffentlichte Hausdorff zwei längere Arbeiten, die in verschiedenen Bereichen der Versicherungsmathematik und der Wahrscheinlichkeitsrechnung ihre Spuren hinterlassen haben. Von besonderem historischen Interesse sind die im Band publizierten Stücke aus Hausdorffs Nachlaß, etwa seine Vorlesung "Wahrscheinlichkeitsrechnung" vom Sommersemester 1923 oder seine Briefe an Richard von Mises aus dem Jahre 1919.
Author: Lorenz J. Halbeisen
Publisher: Springer Science & Business Media
ISBN: 1447121732
Category : Mathematics
Languages : en
Pages : 449
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Book Description
This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.
Author: Felix Hausdorff
Publisher: Springer Science & Business Media
ISBN: 3540768068
Category : Mathematics
Languages : de
Pages : 1010
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Book Description
Der Mathematiker Hausdorff hat in seinem 1914 erschienen Buch „Mengenlehre" erstmals den damals aktuellen Stand auf dem Gebiet der deskriptiven Mengenlehre dargestellt. Neben diesem Werk, das von Experten sorgfältig kommentiert wurde, präsentiert der 3. Band der Hausdorff-Edition seine veröffentlichten Arbeiten zur deskriptiven Mengenlehre und Topologie sowie zahlreiche Studien aus dem Nachlass. Darunter u. a. seine originelle Vorlesung im Sommersemester 1933 über algebraische Topologie.
Author: David E. Rowe
Publisher: Birkhäuser
ISBN: 3319120301
Category : Mathematics
Languages : en
Pages : 427
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Book Description
Joseph W. Dauben, a leading authority on the history of mathematics in Europe, China, and North America, has played a pivotal role in promoting international scholarship over the last forty years. This Festschrift volume, showcasing recent historical research by leading experts on three continents, offers a global perspective on important themes in this field.
Author: Felix Hausdorff
Publisher: American Mathematical Soc.
ISBN: 9780821890516
Category : Mathematics
Languages : en
Pages : 346
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Book Description
Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem of his famous lecture at the international congress in Paris. Thus, as the nineteenth century came to a close and the twentieth century began, Cantor's work was finally receiving its due and Hilbert had made one of Cantor's most important conjectures his number one problem. It was time for the second generation of Cantorians to emerge. Foremost among this group were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and developed set theory as a branch of mathematics worthy of study in its own right, capable of supporting both general topology and measure theory. He is recognized as the era's leading Cantorian. Hausdorff published seven articles in set theory during the period 1901-1909, mostly about ordered sets. This volume contains translations of these papers with accompanying introductory essays. They are highly accessible, historically significant works, important not only for set theory, but also for model theory, analysis and algebra. This book is suitable for graduate students and researchers interested in set theory and the history of mathematics. Also available from the AMS by Felix Hausdorff are the classic work, Grundzuge der Mengenlehre, and its English translation, Set Theory, as Volume 69 and Volume 119 in the AMS Chelsea Publishing series. Information for our distributors: Copublished with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
Author: René L. Schilling
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311074127X
Category : Mathematics
Languages : en
Pages : 533
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Book Description
Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.
Author: Hans Fischer
Publisher: Springer Science & Business Media
ISBN: 0387878572
Category : Mathematics
Languages : en
Pages : 415
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Book Description
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1164
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Book Description
Author:
Publisher:
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Category : Mathematics
Languages : en
Pages : 408
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Book Description
Author: Timothy Gowers
Publisher: Princeton University Press
ISBN: 0691118809
Category : Mathematics
Languages : en
Pages : 1056
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Book Description
A comprehensive guide to mathematics with over 200 entries divided thematically.
