Ernst Zermelo

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Ernst Zermelo - Collected Works/Gesammelte Werke

Author : Ernst Zermelo
Publisher : Springer Science & Business Media
ISBN 13 : 3540793844
Total Pages : 673 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Ernst Zermelo - Collected Works/Gesammelte Werke by : Ernst Zermelo

Download or read book Ernst Zermelo - Collected Works/Gesammelte Werke written by Ernst Zermelo and published by Springer Science & Business Media. This book was released on 2010-01-20 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and best-known for the first formulation of the axiom of choice. However, his papers include also pioneering work in applied mathematics and mathematical physics. This edition of his collected papers will consist of two volumes. Besides providing a biography, the present Volume I covers set theory, the foundations of mathematics, and pure mathematics and is supplemented by selected items from his Nachlass and part of his translations of Homer's Odyssey. Volume II will contain his work in the calculus of variations, applied mathematics, and physics. The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field which comments on the historical background, motivations, accomplishments, and influence.

Ernst Zermelo

Author : Heinz Dieter Ebbinghaus
Publisher : Springer
ISBN 13 : 3662479974
Total Pages : 384 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Ernst Zermelo by : Heinz Dieter Ebbinghaus

Download or read book Ernst Zermelo written by Heinz Dieter Ebbinghaus and published by Springer. This book was released on 2015-08-27 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This biography sheds light on all facets of the life and the achievements of Ernst Zermelo (1871-1953). Zermelo is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of rating systems. The presentation of Zermelo's work explores motivations, aims, acceptance, and influence. Selected proofs and information gleaned from letters add to the analysis. The description of his personality owes much to conversations with his late wife Gertrud. This second edition provides additional information. The system of citations has been adapted to that of Zermelo's Collected Works in order to facilitate side-by-side reading and thus profit from the thorough commentaries written for the Collected Works by experts in the respective fields. All facts presented are documented by appropriate sources. The biography contains nearly 50 photos and facsimiles.

Ernst Zermelo - Collected Works/Gesammelte Werke II

Author : Ernst Zermelo
Publisher : Springer Science & Business Media
ISBN 13 : 3540708561
Total Pages : 781 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Ernst Zermelo - Collected Works/Gesammelte Werke II by : Ernst Zermelo

Download or read book Ernst Zermelo - Collected Works/Gesammelte Werke II written by Ernst Zermelo and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and is best-known for the first formulation of the axiom of choice. However, his papers also include pioneering work in applied mathematics and mathematical physics. This edition of his collected papers consists of two volumes. The present Volume II covers Ernst Zermelo’s work on the calculus of variations, applied mathematics, and physics. The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field who comments on the historical background, motivation, accomplishments, and influence.

Ernst Zermelo

Author : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
ISBN 13 : 3540495533
Total Pages : 368 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Ernst Zermelo by : Heinz-Dieter Ebbinghaus

Download or read book Ernst Zermelo written by Heinz-Dieter Ebbinghaus and published by Springer Science & Business Media. This book was released on 2007-06-02 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This biography attempts to shed light on all facets of Zermelo's life and achievements. Personal and scientific aspects are kept separate as far as coherence allows, in order to enable the reader to follow the one or the other of these threads. The presentation of his work explores motivations, aims, acceptance, and influence. Selected proofs and information gleaned from unpublished notes and letters add to the analysis.

Understanding the Infinite

Author : Shaughan Lavine
Publisher : Harvard University Press
ISBN 13 : 0674265335
Total Pages : 262 pages
Book Rating : 4.6/5 (742 download)

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Book Synopsis Understanding the Infinite by : Shaughan Lavine

Download or read book Understanding the Infinite written by Shaughan Lavine and published by Harvard University Press. This book was released on 2009-06-30 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical commentary on, the modern notion of infinity as formalized in axiomatic set theory . . . An amazingly readable [book] given the difficult subject matter. Most of all, it is an eminently sensible book. Anyone who wants to explore the deep issues surrounding the concept of infinity . . . will get a great deal of pleasure from it.” —Ian Stewart, New Scientist “How, in a finite world, does one obtain any knowledge about the infinite? Lavine argues that intuitions about the infinite derive from facts about the finite mathematics of indefinitely large size . . . The issues are delicate, but the writing is crisp and exciting, the arguments original. This book should interest readers whether philosophically, historically, or mathematically inclined, and large parts are within the grasp of the general reader. Highly recommended.” —D. V. Feldman, Choice

Foundations of Mathematics

Author : Andrés Eduardo Caicedo
Publisher : American Mathematical Soc.
ISBN 13 : 1470422565
Total Pages : 322 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Foundations of Mathematics by : Andrés Eduardo Caicedo

Download or read book Foundations of Mathematics written by Andrés Eduardo Caicedo and published by American Mathematical Soc.. This book was released on 2017-05-12 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas.

Zermelo's Axiom of Choice

Author : Gregory H. Moore
Publisher : Courier Corporation
ISBN 13 : 0486488411
Total Pages : 450 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Zermelo's Axiom of Choice by : Gregory H. Moore

Download or read book Zermelo's Axiom of Choice written by Gregory H. Moore and published by Courier Corporation. This book was released on 2012-09-20 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book chronicles the work of mathematician Ernst Zermelo (1871-1953) and his development of set theory's crucial principle, the axiom of choice. It covers the axiom's formulation during the early 20th century, the controversy it engendered, and its current central place in set theory and mathematical logic. 1982 edition"--

Mathematicians Under the Nazis

Author : Sanford L. Segal
Publisher : Princeton University Press
ISBN 13 : 9780691004518
Total Pages : 574 pages
Book Rating : 4.0/5 (45 download)

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Book Synopsis Mathematicians Under the Nazis by : Sanford L. Segal

Download or read book Mathematicians Under the Nazis written by Sanford L. Segal and published by Princeton University Press. This book was released on 2003 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: The effects of the Nazi regime on the lives of mathematicians ranged from limitations on foreign contact to power struggles that rattled entire institutions, from changed work patterns to military draft, deportation, and death. Based on extensive archival research, Mathematicians under the Nazis shows how these mathematicians, variously motivated, reacted to the period's intense political pressures. It details the consequences of their actions on their colleagues and on the practice and organs of German mathematics, including its curricula, institutions, and journals. Throughout, Segal's focus is on the biographies of individuals, including mathematicians who resisted the injection of ideology into their profession, some who worked in concentration camps, and others (such as Ludwig Bieberbach) who used the "Aryanization" of their profession to further their own agendas. Some of the figures are no longer well known; others still tower over the field. All lived lives complicated by Nazi power.

Combinatorial Set Theory

Author : Lorenz J. Halbeisen
Publisher : Springer Science & Business Media
ISBN 13 : 9781447121732
Total Pages : 456 pages
Book Rating : 4.1/5 (217 download)

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Book Synopsis Combinatorial Set Theory by : Lorenz J. Halbeisen

Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer Science & Business Media. This book was released on 2011-11-24 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ernst Zermelo - Collected Works/Gesammelte Werke

Author : Ernst Zermelo
Publisher : Springer
ISBN 13 : 9783540872252
Total Pages : 654 pages
Book Rating : 4.8/5 (722 download)

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Book Synopsis Ernst Zermelo - Collected Works/Gesammelte Werke by : Ernst Zermelo

Download or read book Ernst Zermelo - Collected Works/Gesammelte Werke written by Ernst Zermelo and published by Springer. This book was released on 2010-11-16 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and best-known for the first formulation of the axiom of choice. However, his papers include also pioneering work in applied mathematics and mathematical physics. This edition of his collected papers will consist of two volumes. Besides providing a biography, the present Volume I covers set theory, the foundations of mathematics, and pure mathematics and is supplemented by selected items from his Nachlass and part of his translations of Homer's Odyssey. Volume II will contain his work in the calculus of variations, applied mathematics, and physics. The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field which comments on the historical background, motivations, accomplishments, and influence.

Logic and Philosophy of Science in Uppsala

Author : D. Prawitz
Publisher : Springer Science & Business Media
ISBN 13 : 9401583110
Total Pages : 611 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Logic and Philosophy of Science in Uppsala by : D. Prawitz

Download or read book Logic and Philosophy of Science in Uppsala written by D. Prawitz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Congresses of Logic, Methodology and Philosophy of Science, which are held every fourth year, give a cross-section of ongoing research in logic and philosophy of science. Both the invited lectures and the many contributed papers are conductive to this end. At the 9th Congress held in Uppsala in 1991 there were 54 invited lectures and around 650 contributed papers divided into 15 different sections. Some of the speakers who presented contributed papers that attracted special interest were invited to submit their papers for publication, and the result is the present volume. A few papers appear here more or less as they were presented at the Congress whereas others are expansions or elaborations of the talks given at the Congress. A selection of this kind, containing 38 papers drawn from the 650 contributed papers presented at the Uppsala Congress, cannot do justice to all facets of the field as it appeared at the Congress. But it should allow the reader to get a representative survey of contemporary research in large areas of philosophical logic and philosophy of science. About half of the papers of the volume appear in sections listed at the Congress under the heading Philosophical and Foundational Problems about the Sciences. The section Foundations of Logic, Mathematics and Computer Science is represented by three papers, Foundations of Physical Sciences by six papers, Foundations of Biological Sciences by three papers, Foundations of Cognitive Science and AI by one paper, and Foundations of Linguistics by three papers.

Correspondence H-Z

Author : Kurt Gödel
Publisher : Oxford University Press
ISBN 13 : 0198500750
Total Pages : 691 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Correspondence H-Z by : Kurt Gödel

Download or read book Correspondence H-Z written by Kurt Gödel and published by Oxford University Press. This book was released on 1986 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collected works of Kurt Godel is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy.

Mathematical Analyses of Decisions, Voting and Games

Author : Michael A. Jones
Publisher : American Mathematical Society
ISBN 13 : 1470469782
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematical Analyses of Decisions, Voting and Games by : Michael A. Jones

Download or read book Mathematical Analyses of Decisions, Voting and Games written by Michael A. Jones and published by American Mathematical Society. This book was released on 2024-03-25 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022. Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.

Ludwig Boltzmann His Later Life and Philosophy, 1900–1906

Author : J.T. Blackmore
Publisher : Springer Science & Business Media
ISBN 13 : 9401704899
Total Pages : 286 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Ludwig Boltzmann His Later Life and Philosophy, 1900–1906 by : J.T. Blackmore

Download or read book Ludwig Boltzmann His Later Life and Philosophy, 1900–1906 written by J.T. Blackmore and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2 But already he had done important work on thermal equilibrium which helped generalize Maxwell's distribution law. Indeed, there is part of a letter by James Clerk Maxwell to Loschmidt from this period which runs: "I am very pleased over the outstanding work of your student; in England experi mental physics is much neglected. Sir William Thomson has done the most in this connection, but you [in Austria] are ahead of us with your good example. "2 But while praise was fine, Boltzmann lusted after further travel. He wanted to know what other physicists were doing first hand. In 1870 he attended lectures by Bunsen and Konigsberger in Heid elberg, and in the same year went to Berlin only to scurry back to Vienna with the outbreak of the Franco-Prussian War, but Boltzmann was back in Berlin the next year attending lectures, visiting laboratories, and working on dielectricity more or less under the direction of Kirchhhoff and Helmholtz.

Recollections of a Jewish Mathematician in Germany

Author : Abraham A. Fraenkel
Publisher : Birkhäuser
ISBN 13 : 3319308475
Total Pages : 234 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Recollections of a Jewish Mathematician in Germany by : Abraham A. Fraenkel

Download or read book Recollections of a Jewish Mathematician in Germany written by Abraham A. Fraenkel and published by Birkhäuser. This book was released on 2016-10-21 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abraham A. Fraenkel was a world-renowned mathematician in pre–Second World War Germany, whose work on set theory was fundamental to the development of modern mathematics. A friend of Albert Einstein, he knew many of the era’s acclaimed mathematicians personally. He moved to Israel (then Palestine under the British Mandate) in the early 1930s. In his autobiography Fraenkel describes his early years growing up as an Orthodox Jew in Germany and his development as a mathematician at the beginning of the twentieth century. This memoir, originally written in German in the 1960s, has now been translated into English, with an additional chapter covering the period from 1933 until his death in 1965 written by the editor, Jiska Cohen-Mansfield. Fraenkel describes the world of mathematics in Germany in the first half of the twentieth century, its origins and development, the systems influencing it, and its demise. He also paints a unique picture of the complex struggles within the world of Orthodox Jewry in Germany. In his personal life, Fraenkel merged these two worlds during periods of turmoil including the two world wars and the establishment of the state of Israel. Including a new foreword by Menachem Magidor Foreword to the 1967 German edition by Yehoshua Bar-Hillel

Logik und Mathematik: Frege-Kolloquium, Jena, 1993 (Perspectives in Analytical Philosophy)

Author : Ingolf Max
Publisher : Walter de Gruyter
ISBN 13 : 9783110145458
Total Pages : 576 pages
Book Rating : 4.1/5 (454 download)

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Book Synopsis Logik und Mathematik: Frege-Kolloquium, Jena, 1993 (Perspectives in Analytical Philosophy) by : Ingolf Max

Download or read book Logik und Mathematik: Frege-Kolloquium, Jena, 1993 (Perspectives in Analytical Philosophy) written by Ingolf Max and published by Walter de Gruyter. This book was released on 1995 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hausdorff on Ordered Sets

Author : Felix Hausdorff
Publisher : American Mathematical Soc.
ISBN 13 : 0821837885
Total Pages : 343 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Hausdorff on Ordered Sets by : Felix Hausdorff

Download or read book Hausdorff on Ordered Sets written by Felix Hausdorff and published by American Mathematical Soc.. This book was released on 2005 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.