Kooperativer Bibliotheksverbund

UID:

Format: VII, 322 S. : , Ill.

ISBN: 978-0-7734-5226-8 , 0-7734-5226-5

Note: Includes bibliographical references and index

Language: English

Subjects: Mathematics

Keywords: 1718-1799 Agnesi, Maria Gaetana ; Biografie ; Biografie

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016433261&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: Inhaltsverzeichnis

URL: Inhaltstext

UID:

Format: Online-Ressource (XIII, 258 p. 97 illus., 93 illus. in color, online resource)

Edition: 1st ed. 2015

ISBN: 9781493931613

Series Statement: Science Networks. Historical Studies 53

Content: Preface -- A Brief Biography of Jost Bürgi (1522-1632) -- Details of Aritmetische und Geometrische Progreß Tabulen: Printed Tables, Manuscripts, and Mathematical Details -- Aritmetische und Geometrische Progreß Tabulen: Edition, Translation, and Commentary -- Final Perspectives -- Appendix 1: Bürgi Biography at a Glance -- Appendix 2: Napier's Argument and Construction of Logarithms -- Appendix 3: The Tables of the Aritmetische und Geometrische Progreß Tabulen/Sambt gründlichem unterricht/wie solche nützlich in allerley Rechnungen zu gebrauchen/und verstanden werden sol (Bürgi, 1620) -- References

Content: This monograph presents a groundbreaking scholarly treatment of the German mathematician Jost Bürgi’s original work on logarithms, Arithmetische und Geometrische Progreß Tabulen. It provides the first-ever English translation of Bürgi’s text and illuminates his role in the development of the conception of logarithms, for which John Napier is traditionally given priority. High-resolution scans of each page of the his handwritten text are reproduced for the reader and as a means of preserving an important work for which there are very few surviving copies. The book begins with a brief biography of Bürgi to familiarize readers with his life and work, as well as to offer an historical context in which to explore his contributions. The second chapter then describes the extant copies of the Arithmetische und Geometrische Progreß Tabulen, with a detailed description of the copy that is the focus of this book, the 1620 “Graz manuscript”. A complete facsimile of the text is included in the next chapter, along with a corresponding transcription and an English translation; a transcription of a second version of the manuscript (the “Gdansk manuscript”) is included alongside that of the Graz edition so that readers can easily and closely examine the differences between the two. The final chapter considers two important questions about Bürgi’s work, such as who was the copyist of the Graz manuscript and what the relationship is between the Graz and Gdansk versions. Appendices are also included that contain a timeline of Bürgi’s life, the underlying concept of Napier’s construction of logarithms, and scans of all 58 sheets of the tables from Bürgi’s text. Anyone with an appreciation for the history of mathematics will find this book to be an insightful and interesting look at an important and often overlooked work. It will also be a valuable resource for undergraduates taking courses in the history of mathematics, researchers of the history of mathematics, and professors of mathematics education who wish to incorporate historical context into their teaching

Note: Description based upon print version of record , PrefaceA Brief Biography of Jost Bürgi (1522-1632) -- Details of Aritmetische und Geometrische Progreß Tabulen: Printed Tables, Manuscripts, and Mathematical Details -- Aritmetische und Geometrische Progreß Tabulen: Edition, Translation, and Commentary -- Final Perspectives -- Appendix 1: Bürgi  Biography at a Glance -- Appendix 2: Napier's Argument and Construction of Logarithms -- Appendix 3: The Tables of the Aritmetische und Geometrische Progreß Tabulen/Sambt gründlichem unterricht/wie solche nützlich in allerley Rechnungen zu gebrauchen/und verstanden werden sol (Bürgi, 1620) -- References.

Additional Edition: ISBN 9781493931606

Additional Edition: Erscheint auch als Druck-Ausgabe Clark, Kathleen Jost Bürgi's Aritmetische und Geometrische Progreß Tabulen (1620) New York : Birkhäuser, 2015 ISBN 9781493931606

Language: English

Subjects: Mathematics

Keywords: Bürgi, Jost 1552-1632 Arithmetische und geometrische Progreß-Tabulen

DOI: 10.1007/978-1-4939-3161-3

URL: lizenzpflichtig

URL: Volltext  (lizenzpflichtig)

URL: Cover

URL: Inhaltstext

UID:

Format: 1 online resource (458 p.)

ISBN: 981-4360-92-9

Series Statement: Interdisciplinary mathematical sciences ; v. 12

Content: The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random pheno

Note: Description based upon print version of record. , Editorial Foreword; Contents; A Biographical Note and Tribute to David Elworthy on His 70th Birthday; Edited Volumes; 1. Stochastic Geometric Partial Differential EquationsZdzisław Brze ́zniak, Beniamin Goldys and Martin Ondrej ́at; 1.1. Introduction; 1.2. Stochastic Geometric heat flow on S1 R+; 1.3. Proof of Theorem 1.1; 1.3.1. Differential Geometry preliminaries; 1.3.2. Existence of solutions to approximating equations; 1.3.3. Construction of a maximal local solution; 1.3.4. No explosion for approximate solutions; 1.4. Stochastic geometric wave equations; 1.4.1. Deterministic theory , 1.4.2. Historical remarks1.4.3. Objectives; 1.5. Spatially homogeneous Wiener process; 1.6. Intrinsic and extrinsic solutions; 1.6.1. Posing the problem; 1.6.2. Extrinsic form; 1.6.3. Intrinsic form; 1.6.4. Extrinsic vs. Intrinsic; 1.7. Strong solutions in H2 loc H1 loc on R1+1; 1.8. Weak solutions in H1 loc L2 loc on R1+1; 1.9. Weak solutions in compact homogeneous spaces on R1+m; 1.10. Energy estimates; 1.11. Stochastic Landau-Lifschitz-Gilbert Equation; Acknowledgements; References; 2. Rough Paths on Manifolds Thomas Cass, Christian Litterer and Terry Lyons; 2.1. Introduction , 2.2. Background: Rough paths on Banach spaces2.3. Lip- manifolds; 2.4. Rough paths on manifolds; 2.4.1. Introduction and motivation; 2.4.2. Definition and basic properties of rough paths on manifolds.; 2.4.3. Restriction and concatenations of rough paths on manifolds; 2.4.4. The support of a rough path on a manifold; 2.4.5. Rough paths on manifolds are concatenations of localisable rough paths.; 2.4.6. Proof of Theorem 2.7; 2.4.7. Proof of Theorem 2.8 and Corollary 2.2; 2.5. Rough differential equations on a manifold; 2.5.1. Geometric interpretation of the lift as an Ehresmann connection , 2.5.2. Formal definition of the RDE solution via the connection2.6. Perspectives; References; 3. Averaging, Homogenization and Slow Manifolds for Stochastic Partial Differential Equations Jinqiao Duan, Anthony Roberts and Wei Wang; 3.1. Introduction; 3.2. Random invariant manifold reduction for SPDEs; 3.2.1. Lipschitz case; 3.2.2. Non-Lipschitz case; 3.3. Averaging reduction for SPDEs; 3.3.1. Averaging for slow-fast SPDEs; 3.3.2. Macroscopic reduction for stochastic reaction-diffusion equations: an application of averaging reduction , 3.3.3. Large deviations: a further confirmation for averaged equation3.4. Homogenization for SPDEs; References; 4. A Burgers-Zeldovich Model for the Formation of Planetesimals via Nelson's Stochastic Mechanics Richard Durran, Andrew Neate, Aubrey Truman and Oleg Smolyanov; Dedication and Tribute to David Elworthy; 4.1. Introduction; 4.2. The First Epoch; 4.2.1. Stochastic mechanics for the atomic elliptic state; 4.2.2. A semiclassical celestial mechanics; 4.2.3. Internal states of the cloud and Markov chains; 4.3. The Second Epoch; 4.3.1. Burgers Equation with vorticity , 4.3.2. Fluid density for small eccentricities , English

Additional Edition: ISBN 981-4360-91-0

Language: English

Subjects: Mathematics

UID:

Format: 1 Online-Ressource (XXIV, 654 p.)

Edition: Springer eBook Collection. Mathematics and Statistics

ISBN: 9783540793847

Series Statement: Schriften der Mathematisch-naturwissenschaftlichen Klasse der Heidelberger Akademie der Wissenschaften 21

Content: 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.

Additional Edition: ISBN 9783540872252

Additional Edition: ISBN 9783642262098

Additional Edition: ISBN 9783540793830

Additional Edition: Erscheint auch als Druck-Ausgabe Zermelo, Ernst, 1871 - 1953 Collected works / Ernst Zermelo ; 1: Set theory, miscellanea Berlin : Springer, 2010 ISBN 9783540793830

Language: English

Subjects: Mathematics

DOI: 10.1007/978-3-540-79384-7

URL: lizenzpflichtig

URL: Volltext  (lizenzpflichtig)

URL: Inhaltsverzeichnis

URL: Inhaltstext

URL: Cover

Author information: Zermelo, Ernst 1871-1953

UID:

Format: 1 online resource (277 pages) : , illustrations.

Edition: Core Textbook

ISBN: 0-691-16848-2 , 1-283-37987-2 , 9786613379870 , 1-4008-3234-9

Series Statement: Princeton Science Library ; 41

Content: The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

Note: Bibliographic Level Mode of Issuance: Monograph , Frontmatter -- , Contents -- , Preface -- , 1. John Napier, 1614 -- , 2 Recognition -- , Computing with Logarithms -- , 3 Financial Matters -- , 4. To the Limit, If It Exists -- , Some Curious Numbers Related to e -- , 5. Forefathers of the Calculus -- , 6. Prelude to Breakthrough -- , Indivisibles at Work -- , 7. Squaring the Hyperbola -- , 8. The Birth of a New Science -- , 9. The Great Controversy -- , The Evolution of a Notation -- , 10 ex: The Function That Equals Its Own Derivative -- , The Parachutist -- , Can Perceptions Be Quantified? -- , 11 eθ Spira Mirabilis -- , A Historic Meeting between J. S. Bach and Johann Bernoulli -- , The Logarithmic Spiral in Art and Nature -- , 12 (ex + e-x)/2: The Hanging Chain -- , Remarkable Analogies -- , Some Interesting Formulas Involving e -- , 13 eix. "The Most Famous of All Formulas" -- , A Curious Episode in the History of e -- , 14 ex+iy: The Imaginary Becomes Real -- , A Most Remarkable Discovery -- , 15. But What Kind of Number Is It? -- , Appendixes -- , Appendix 1. Some Additional Remarks on Napier's Logarithms -- , Appendix 2. The Existence of lim (1+1/n)n as n∞ -- , Appendix 3. A Heuristic Derivation of the Fundamental Theorem of Calculus -- , Appendix 4. The Inverse Relation between lim (bh-1)/h = 1 and lim (1+h)1/h as h0 -- , Appendix 5. An Alternative Definition of the Logarithmic Function -- , Appendix 6. Two Properties of the Logarithmic Spiral -- , Appendix 7. Interpretation of the Parameter Hyperbolic Functions -- , Appendix 8. e to One Hundred Decimal Places -- , Bibliography -- , Index , Issued also in print. , English

Additional Edition: ISBN 0-691-03390-0

Additional Edition: ISBN 0-691-14134-7

Language: English

Subjects: Mathematics

DOI: 10.1515/9781400832347

UID:

Format: 1 Online-Ressource(xx, 677 Seiten) , Illustrationen

ISBN: 9783030757854

Series Statement: Vita mathematica volume 20

Content: Preface -- 1 Introduction -- 2 Influencing groups -- 3 Professorship at the University of Erlangen -- 4 Professorship at the Polytechnikum Munich -- 5 Professorship of Geometry in Leipzig -- 6 Start as Professor in Göttingen, 1886-1892 -- Setting the course -- 8 Fruits of the efforts, 1895-1913 -- 9 World War I and post-war period -- 10 Concluding remarks -- Appendix: Selection of documents.

Content: About Felix Klein, the famous Greek mathematician Constantin Carathéodory once said: “It is only by illuminating him from all angles that one can come to understand his significance.” The author of this biography has done just this. A detailed study of original sources has made it possible to uncover new connections; to create a more precise representation of this important mathematician, scientific organizer, and educational reformer; and to identify misconceptions. Because of his edition of Julius Plücker’s work on line geometry and due to his own contributions to non-Euclidean geometry, Klein was already well known abroad before he received his first full professorship at the age of 23. By exchanging ideas with his most important cooperation partner, the Norwegian Sophus Lie, Klein formulated his Erlangen Program. Various other visionary programs followed, in which Klein involved mathematicians from Germany and abroad. Klein was the most active promoter of Riemann’s geometric-physical approach to function theory, but he also integrated the analytical approaches of the Weierstrass school into his arsenal of methods. Klein was a citizen of the world who repeatedly travelled to France, Great Britain, Italy, the United States, and elsewhere. Despite what has often been claimed, it must be emphasized that Klein expressly opposed national chauvinism. He promoted mathematically gifted individuals regardless of their nationality, religion, or gender. Many of his works have been translated into English, French, Italian, Russian, and other languages; more than 300 supporters from around the world made it possible for his portrait to be painted by the prominent impressionist Max Liebermann. Inspired by international developments, Klein paved the way for women to work in the field of mathematics. He was instrumental in reforming mathematical education, and he endorsed an understanding of mathematics that affirmed its cultural importance as well as its fundamental significance to scientific and technological progress.

Additional Edition: ISBN 9783030757847

Additional Edition: ISBN 9783030757861

Additional Edition: ISBN 9783030757878

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9783030757861

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9783030757878

Additional Edition: Erscheint auch als Druck-Ausgabe Tobies, Renate, 1947 - Felix Klein Cham, Switzerland : Birkhäuser, 2021 ISBN 9783030757847

Language: English

Subjects: Mathematics

Keywords: Mathematik ; Klein, Felix 1849-1925 ; Biografie

DOI: 10.1007/978-3-030-75785-4

URL: lizenzpflichtig

URL: Cover

Author information: Tobies, Renate 1947-

Author information: Pakis, Valentine 1978-