Ernst Zermelo - Collected Works/Gesammelte Werke

Volume I/Band I - Set Theory, Miscellanea/Mengenlehre, Varia

Author: Ernst Zermelo

Publisher: Springer Science & Business Media

ISBN: 3540793844

Category: Mathematics

Page: 654

View: 7746

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 II

Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik

Author: Ernst Zermelo

Publisher: Springer Science & Business Media

ISBN: 3540708561

Category: Mathematics

Page: 781

View: 4020

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.

Combinatorial Set Theory

With a Gentle Introduction to Forcing

Author: Lorenz J. Halbeisen

Publisher: Springer Science & Business Media

ISBN: 9781447121732

Category: Mathematics

Page: 456

View: 753

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.

Models of Science Dynamics

Encounters Between Complexity Theory and Information Sciences

Author: Andrea Scharnhorst,Katy Börner,Peter van den Besselaar

Publisher: Springer Science & Business Media

ISBN: 3642230679

Category: Social Science

Page: 270

View: 7697

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.

Metaphern in der Mathematik

Die Bildlichkeit des abstrakten Denkens

Author: Martin Raschauer

Publisher: epubli

ISBN: 3737531404


Page: N.A

View: 6254


Ernst Zermelo

An Approach to His Life and Work

Author: Heinz-Dieter Ebbinghaus,Volker Peckhaus

Publisher: Springer

ISBN: 3662479974

Category: Mathematics

Page: 384

View: 3695

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.

Finite Model Theory

Author: Heinz-Dieter Ebbinghaus,Jörg Flum

Publisher: Springer Science & Business Media

ISBN: 3540287884

Category: Mathematics

Page: 360

View: 4822

This is a thoroughly revised and enlarged second edition that presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently.

The Development of Modern Logic

Author: Leila Haaparanta

Publisher: OUP USA

ISBN: 0195137310

Category: Mathematics

Page: 994

View: 3526

This volume contains newly-commissioned articles covering the development of modern logic from the late medieval period (fourteenth century) through the end of the twentieth-century. It is the first volume to discuss the field with this breadth of coverage and depth. It will appeal to scholars and students of philosophical logic and the philosophy of logic.

Logic Colloquium '87

Proceedings of the Colloquium Held in Granada, Spain July 20-25, 1987

Author: Heinz-Dieter Ebbinghaus

Publisher: Elsevier

ISBN: 0444880224

Category: Electronic books

Page: 375

View: 6046

Fourteen papers presented at the 1987 European Summer Meeting of the Association for Symbolic Logic are collected in this volume. The main areas covered by the conference were Logic, Set Theory, Recursion Theory, Model Theory, Logic for Computer Science and Semantics of Natural Languages.

Harmonic Analysis of Spherical Functions on Real Reductive Groups

Author: Ramesh Gangolli,Veeravalli S. Varadarajan

Publisher: Springer Science & Business Media

ISBN: 3642729568

Category: Mathematics

Page: 365

View: 8910

Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.

History and Philosophy of Modern Mathematics

Author: William Aspray,Philip Kitcher

Publisher: U of Minnesota Press

ISBN: 9780816615674

Category: Mathematics

Page: 386

View: 8633

History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

50 Years with Hardy Spaces

A Tribute to Victor Havin

Author: Anton Baranov,Sergei Kisliakov,Nikolai Nikolski

Publisher: Birkhäuser

ISBN: 3319590782

Category: Mathematics

Page: 484

View: 6626

Written in honor of Victor Havin (1933–2015), this volume presents a collection of surveys and original papers on harmonic and complex analysis, function spaces and related topics, authored by internationally recognized experts in the fields. It also features an illustrated scientific biography of Victor Havin, one of the leading analysts of the second half of the 20th century and founder of the Saint Petersburg Analysis Seminar. A complete list of his publications, as well as his public speech "Mathematics as a source of certainty and uncertainty", presented at the Doctor Honoris Causa ceremony at Linköping University, are also included.


Pituitary, Parathyroid and Pancreas

Author: Katalin Balogh,Attila Patocs

Publisher: Springer Science & Business Media

ISBN: 1441916644

Category: Medical

Page: 136

View: 2451

The vast expansion in research on tumorigenesis has greatly increased our understanding of tumor development in patients with inherited endocrine tumor syndromes. This book provides an up-to-date summaryfrom clinical basics and latest follow-up guidelines to the most recent molecular findings in multiple endocrine neoplasia Type I syndrome. Articles have been assembled by acknowledged experts in their respective fields to provide current perspectives on the clinical and genetic backgroundsofthis syndrome and to review carefully the latest discoveries concerning the possible functions and interactions ofmenin, the protein encoded by the MEN1gene,including itspossible role incell cycle regulation,hematopoiesis,and bone development. The goal ofthe book is also to present the most recent findings and the broadest aspects of the role of menin in tumorigenesis of the endocrine glands involved in MEN I syndrome (pituitary, parathyroid, endocrine pancreas and adrenal). The connection between the basic experimental and clinical points of view are highlighted through a discussion on animal models, which explores the field in both an inspiring and questioning manner with a focus on areas that remain to be clarified. Our goal was to bring together clinicians and basic researchers who represent a wide range of interests in this particular field of endocrine oncology. Presentingacomprehensive and current overviewofbasic experimental and clinical findings, this book can bring us closer to understanding endocrine tumorigenesis in multiple endocrine neoplasia Type I. Katalin Balogh, MD, PhD Attita Patocs, MD, MSc, PhD v ABOUT THEEDITORS. . .

Elementary Symplectic Topology and Mechanics

Author: Franco Cardin

Publisher: Springer

ISBN: 3319110268

Category: Science

Page: 222

View: 6911

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.

Geometrical Themes Inspired by the N-body Problem

Author: Luis Hernández-Lamoneda,Haydeé Herrera,Rafael Herrera

Publisher: Springer

ISBN: 3319714287

Category: Mathematics

Page: 128

View: 6615

Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order to motivate the McGehee transformation. A. Pedroza’s notes provide a brief introduction to Lagrangian Floer homology and its relation to the solution of the Arnol’d conjecture on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism.

Unpublished Manuscripts of Lars Hörmander

from 1951 to 2007

Author: Lars Hörmander

Publisher: Springer

ISBN: 3319698508

Category: Mathematics

Page: 329

View: 7751

This volume presents the unpublished articles of Lars Hörmander from 1951 to 2007.The organisation of these articles and the notes explaining their origins, are by Lars Hörmander himself, as he fully intended these to be published in this form. The material presented therein is of historical and mathematical value and will undoubtedly inspire mathematicians of different horizons.

Handbook of Set Theory

Author: Matthew Foreman,Akihiro Kanamori

Publisher: Springer Science & Business Media

ISBN: 1402057644

Category: Mathematics

Page: 2230

View: 5556

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

Was Sind und was Sollen Die Zahlen?

Author: Richard Dedekind

Publisher: Cambridge University Press

ISBN: 1108050387

Category: Mathematics

Page: 84

View: 2060

This influential 1888 publication explained the real numbers, and their construction and properties, from first principles.

M.C. Escher’s Legacy

A Centennial Celebration

Author: Michele Emmer,Doris Schattschneider

Publisher: Springer

ISBN: 354028849X

Category: Mathematics

Page: 458

View: 7038

Softcover printing of a popular title (h/c sold over 400 copies in North America) at a price that will make it accessible to a much wider audience Richly illustrated with original art works in addition to well-known and little-known works by Escher A CD-ROM complements the articles, containing color illustrations of work by contemporary artists, movies, animations, and other demonstrations