Ernst Zermelo

Author : Heinz Dieter Ebbinghaus,Volker Peckhaus
Publisher : Springer
Page : 384 pages
File Size : 46,9 Mb
Release : 2015-08-27
Category : Mathematics
ISBN : 9783662479971

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Ernst Zermelo by Heinz Dieter Ebbinghaus,Volker Peckhaus Pdf

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.

Author : Ernst Zermelo
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 53,5 Mb
Release : 2010-01-20
Category : Mathematics
ISBN : 9783540793847

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Ernst Zermelo - Collected Works/Gesammelte Werke by Ernst Zermelo Pdf

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.

Author : Ernst Zermelo
Publisher : Springer Science & Business Media
Page : 803 pages
File Size : 52,5 Mb
Release : 2013-08-15
Category : Mathematics
ISBN : 9783540708568

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Ernst Zermelo - Collected Works/Gesammelte Werke II by Ernst Zermelo Pdf

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.

Author : Heinz-Dieter Ebbinghaus
Publisher : Springer
Page : 0 pages
File Size : 51,6 Mb
Release : 2010-10-14
Category : Mathematics
ISBN : 3642080502

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Ernst Zermelo by Heinz-Dieter Ebbinghaus Pdf

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.

Author : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 45,7 Mb
Release : 2007-06-02
Category : Mathematics
ISBN : 9783540495536

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Ernst Zermelo by Heinz-Dieter Ebbinghaus Pdf

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.

Author : Shaughan Lavine
Publisher : Harvard University Press
Page : 262 pages
File Size : 55,5 Mb
Release : 2009-06-30
Category : Mathematics
ISBN : 9780674265332

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Understanding the Infinite by Shaughan Lavine Pdf

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

Author : Andrés Eduardo Caicedo,James Cummings,Peter Koellner,Paul B. Larson
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 40,5 Mb
Release : 2017-05-12
Category : Continuum hypothesis
ISBN : 9781470422561

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Foundations of Mathematics by Andrés Eduardo Caicedo,James Cummings,Peter Koellner,Paul B. Larson Pdf

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.

Author : Gregory H. Moore
Publisher : Courier Corporation
Page : 450 pages
File Size : 45,7 Mb
Release : 2012-09-20
Category : Mathematics
ISBN : 9780486488417

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Zermelo's Axiom of Choice by Gregory H. Moore Pdf

"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"--

Author : Sanford L. Segal
Publisher : Princeton University Press
Page : 574 pages
File Size : 41,8 Mb
Release : 2003
Category : History
ISBN : 069100451X

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Mathematicians Under the Nazis by Sanford L. Segal Pdf

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.

Author : Lorenz J. Halbeisen
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 44,8 Mb
Release : 2011-11-24
Category : Mathematics
ISBN : 9781447121732

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Combinatorial Set Theory by Lorenz J. Halbeisen Pdf

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 : D. Prawitz,Dag Westerståhl
Publisher : Springer Science & Business Media
Page : 611 pages
File Size : 52,7 Mb
Release : 2013-06-29
Category : Philosophy
ISBN : 9789401583114

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Logic and Philosophy of Science in Uppsala by D. Prawitz,Dag Westerståhl Pdf

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.

Author : Kurt Gödel
Publisher : Oxford University Press
Page : 691 pages
File Size : 40,7 Mb
Release : 1986
Category : Computers
ISBN : 9780198500759

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Correspondence H-Z by Kurt Gödel Pdf

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.

Author : Michael A. Jones,David McCune,Jennifer M. Wilson
Publisher : American Mathematical Society
Page : 210 pages
File Size : 40,6 Mb
Release : 2024-03-25
Category : Mathematics
ISBN : 9781470469788

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Mathematical Analyses of Decisions, Voting and Games by Michael A. Jones,David McCune,Jennifer M. Wilson Pdf

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.

Author : J.T. Blackmore
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 52,7 Mb
Release : 2013-03-09
Category : History
ISBN : 9789401704892

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

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.

Author : Ingolf Max,Werner Stelzner
Publisher : Walter de Gruyter
Page : 576 pages
File Size : 40,5 Mb
Release : 1995
Category : Mathematics
ISBN : 3110145456

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Logik und Mathematik: Frege-Kolloquium, Jena, 1993 (Perspectives in Analytical Philosophy) by Ingolf Max,Werner Stelzner Pdf