Ernst Zermelo Collected Works Gesammelte Werke Ii

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Ernst Zermelo - Collected Works/Gesammelte Werke II

Author : Ernst Zermelo
Publisher : Springer Science & Business Media
ISBN 13 : 3540708561
Total Pages : 803 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 803 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 - 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 : 397 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 397 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.

The Real Numbers

Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 331901577X
Total Pages : 253 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis The Real Numbers by : John Stillwell

Download or read book The Real Numbers written by John Stillwell and published by Springer Science & Business Media. This book was released on 2013-10-16 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

Atoms, Mechanics, and Probability

Author : Olivier Darrigol
Publisher : Oxford University Press
ISBN 13 : 0198816170
Total Pages : 639 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Atoms, Mechanics, and Probability by : Olivier Darrigol

Download or read book Atoms, Mechanics, and Probability written by Olivier Darrigol and published by Oxford University Press. This book was released on 2018 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the pillars of modern science, statistical mechanics, owes much to one man, the Austrian physicist Ludwig Boltzmann (1844-1906). As a result of his unusual working and writing styles, his enormous contribution remains little read and poorly understood. The purpose of this book is to make the Boltzmann corpus more accessible to physicists, philosophers, and historians, and so give it new life. The means are introductory biographical and historical materials, detailed and lucid summaries of every relevant publication, and a final chapter of critical synthesis. Special attention is given to Boltzmann's theoretical tool-box and to his patient construction of lofty formal systems even before their full conceptual import could be known. This constructive tendency largely accounts for his lengthy style, for the abundance of new constructions, for the relative vagueness of their object--and for the puzzlement of commentators. This book will help the reader cross the stylistic barrier and see how ingeniously Boltzmann combined atoms, mechanics, and probability to invent new bridges between the micro- and macro-worlds.

Max Dehn

Author : Jemma Lorenat
Publisher : American Mathematical Society
ISBN 13 : 1470461064
Total Pages : 292 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Max Dehn by : Jemma Lorenat

Download or read book Max Dehn written by Jemma Lorenat and published by American Mathematical Society. This book was released on 2024-10-04 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Max Dehn (1878?1952) is known to mathematicians today for his seminal contributions to geometry and topology?Dehn surgery, Dehn twists, the Dehn invariant, etc. He is also remembered as the first mathematician to solve one of Hilbert?s famous problems. However, Dehn's influence as a scholar and teacher extended far beyond his mathematics. Dehn also lived a remarkable life, described in this book in three phases. The first phase focuses on his early career as one of David Hilbert?s most gifted students. The second, after World War I, treats his time in Frankfurt where he led an intimate community of mathematicians in explorations of historical texts. The final phase, after 1938, concerns his flight from Nazi Germany to Scandinavia and eventually to the United States where, after various teaching experiences, the Dehns settled at iconic Black Mountain College. This book is a collection of essays written by mathematicians and historians of art and science. It treats Dehn?s mathematics and its influence, his journeys, and his remarkable engagement in history and the arts. A great deal of the information found in this book has never before been published.

The Oxford Handbook of The History of Analytic Philosophy

Author : Michael Beaney
Publisher : OUP Oxford
ISBN 13 : 0191662666
Total Pages : 1182 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis The Oxford Handbook of The History of Analytic Philosophy by : Michael Beaney

Download or read book The Oxford Handbook of The History of Analytic Philosophy written by Michael Beaney and published by OUP Oxford. This book was released on 2013-06-20 with total page 1182 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the course of the twentieth century, analytic philosophy developed into the dominant philosophical tradition in the English-speaking world. In the last two decades, it has become increasingly influential in the rest of the world, from continental Europe to Latin America and Asia. At the same time there has been deepening interest in the origins and history of analytic philosophy, as analytic philosophers examine the foundations of their tradition and question many of the assumptions of their predecessors. This has led to greater historical self-consciousness among analytic philosophers and more scholarly work on the historical contexts in which analytic philosophy developed. This historical turn in analytic philosophy has been gathering pace since the 1990s, and the present volume is the most comprehensive collection of essays to date on the history of analytic philosophy. It contains state-of-the-art contributions from many of the leading scholars in the field, all of the contributions specially commissioned. The introductory essays discuss the nature and historiography of analytic philosophy, accompanied by a detailed chronology and bibliography. Part One elucidates the origins of analytic philosophy, with special emphasis on the work of Frege, Russell, Moore, and Wittgenstein. Part Two explains the development of analytic philosophy, from Oxford realism and logical positivism to the most recent work in analytic philosophy, and includes essays on ethics, aesthetics, and political philosophy as well as on the areas usually seen as central to analytic philosophy, such as philosophy of language and mind. Part Three explores certain key themes in the history of analytic philosophy.

Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics

Author : Juliet Floyd
Publisher : Springer Nature
ISBN 13 : 3030484815
Total Pages : 330 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics by : Juliet Floyd

Download or read book Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics written by Juliet Floyd and published by Springer Nature. This book was released on 2020-08-31 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein’s remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized. The authors first establish the context behind the annotations and discuss the historical role of Hardy’s textbook. They then go on to outline Wittgenstein’s non-extensionalist point of view on real numbers, assessing his manuscripts and published remarks and discussing attitudes in play in the philosophy of mathematics since Dedekind. Next, coverage focuses on the annotations themselves. The discussion encompasses irrational numbers, the law of excluded middle in mathematics and the notion of an “improper picture," the continuum of real numbers, and Wittgenstein’s attitude toward functions and limits.

Combinatorial Set Theory

Author : Lorenz J. Halbeisen
Publisher : Springer Science & Business Media
ISBN 13 : 1447121732
Total Pages : 449 pages
Book Rating : 4.4/5 (471 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 449 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.

Foundations of Mathematics

Author : Andrés Eduardo Caicedo
Publisher : American Mathematical Soc.
ISBN 13 : 1470422565
Total Pages : 346 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 346 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.

Research in History and Philosophy of Mathematics

Author : Maria Zack
Publisher : Springer
ISBN 13 : 3319909835
Total Pages : 209 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Research in History and Philosophy of Mathematics by : Maria Zack

Download or read book Research in History and Philosophy of Mathematics written by Maria Zack and published by Springer. This book was released on 2018-09-14 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh’s techniques for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.

Models of Science Dynamics

Author : Andrea Scharnhorst
Publisher : Springer Science & Business Media
ISBN 13 : 3642230679
Total Pages : 292 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Models of Science Dynamics by : Andrea Scharnhorst

Download or read book Models of Science Dynamics written by Andrea Scharnhorst and published by Springer Science & Business Media. This book was released on 2012-01-23 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models of Science Dynamics aims to capture the structure and evolution of science, the emerging arena in which scholars, science and the communication of science become themselves the basic objects of research. In order to capture the essence of phenomena as diverse as the structure of co-authorship networks or the evolution of citation diffusion patterns, such models can be represented by conceptual models based on historical and ethnographic observations, mathematical descriptions of measurable phenomena, or computational algorithms. Despite its evident importance, the mathematical modeling of science still lacks a unifying framework and a comprehensive study of the topic. This volume fills this gap, reviewing and describing major threads in the mathematical modeling of science dynamics for a wider academic and professional audience. The model classes presented cover stochastic and statistical models, system-dynamics approaches, agent-based simulations, population-dynamics models, and complex-network models. The book comprises an introduction and a foundational chapter that defines and operationalizes terminology used in the study of science, as well as a review chapter that discusses the history of mathematical approaches to modeling science from an algorithmic-historiography perspective. It concludes with a survey of remaining challenges for future science models and their relevance for science and science policy.

Ernst Zermelo

Author : Heinz-Dieter Ebbinghaus
Publisher : Springer
ISBN 13 : 9783642080500
Total Pages : 0 pages
Book Rating : 4.0/5 (85 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 2010-10-14 with total page 0 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.

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.

Ernst Zermelo - Collected Works/Gesammelte Werke

Author : Ernst Zermelo
Publisher : Springer
ISBN 13 : 9783540793830
Total Pages : 654 pages
Book Rating : 4.7/5 (938 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 2010-01-13 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.

Empiricism, Logic and Mathematics

Author : Hans Hahn
Publisher : Springer Science & Business Media
ISBN 13 : 9400989822
Total Pages : 159 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Empiricism, Logic and Mathematics by : Hans Hahn

Download or read book Empiricism, Logic and Mathematics written by Hans Hahn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: The role Hans Hahn played in the Vienna Circle has not always been sufficiently appreciated. It was important in several ways. In the ftrst place, Hahn belonged to the trio of the original planners of the Circle. As students at the University of Vienna and throughout the fIrst decade of this century, he and his friends, Philipp Frank and Otto Neurath, met more or less regularly to discuss philosophical questions. When Hahn accepted his fIrSt professorial position, at the University of Czernowitz in the north east of the Austrian empire, and the paths of the three friends parted, they decided to continue such informal discussions at some future time - perhaps in a somewhat larger group and with the cooperation of a philosopher from the university. Various events delayed the execution of the project. Drafted into the Austrian army during the first world war" Hahn was wounded on the Italian front. Toward the end of the war he accepted an offer from the University of Bonn extended in recognition of his remarkable 1 mathematical achievements. He remained in Bonn until the spring of 1921 when he returm:d to Vienna and a chair of mathe matics at his alma mater. There, in 1922, the Mach-Boltzmann professorship for the philosophy of the inductive sciences became vacant by the death of Adolf Stohr; and Hahn saw a chance to realize his and his friends' old plan.

Philosophy of Mathematics

Author : Charles S. Peirce
Publisher : Indiana University Press
ISBN 13 : 0253004691
Total Pages : 336 pages
Book Rating : 4.2/5 (53 download)

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Book Synopsis Philosophy of Mathematics by : Charles S. Peirce

Download or read book Philosophy of Mathematics written by Charles S. Peirce and published by Indiana University Press. This book was released on 2010-08-19 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce's most important writings on the subject, many appearing in print for the first time. Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.