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This book provides a thrilling history of the famous priority dispute between Gottfried Wilhelm Leibniz and Isaac Newton, presenting the episode for the first time in the context of cultural history. It introduces readers to the background of the dispute, details its escalation, and discusses the aftermath of the big divide, which extended well into recent times. One of the unique features of the book is that the mathematics behind the story is very intelligibly explained – an approach that offers general readers interested in the history of sciences and mathematics a window into the world of these two giants in their field. From the epilogue to the German edition by Eberhard Knobloch: Thomas Sonar has traced the emergence and the escalation of this conflict, which was heightened by Leibniz’s rejection of Newton’s gravitation theory, in a grandiose, excitingly written monograph. With absolute competence, he also explains the mathematical context so that non-mathematicians will also profit from the book. Quod erat demonstrandum! From the reviews for the German language edition ….. This book provides a vivid and easy-reading picture of many political and scientific aspects of the end of the 17th and the beginning of the 18th century, and constitutes an excellent guide to the existing secondary literature for laymen as well as for specialists…. Stefan Neuwirth in: Zentralblatt MATH 1343 — 1 (1343.01005) An extremely readable book on one of the most memorable episodes in the history of sciences. Manfred Jacobi in: Physik in unserer Zeit, Jg. 47, Heft 5, September 2016.
Calculus --- History --- Newton, Isaac, --- Leibniz, Gottfried Wilhelm, --- Mathematics. --- History. --- History of Mathematical Sciences. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Leibnitz, Gottfried Wilhelm --- Leibniz, Gottfried Wilhelm --- Newton, Izaak, --- Niu-tun, --- Nʹi︠u︡ton, Isaak, --- Niutun, Yisake, --- Niyu̇ton, Isak, --- Nyuṭon, Ayzaḳ, --- Nyuṭon, Ayziḳ, --- ניוטאן, אייזאק, --- ניוטון, אייזק --- ניוטון, אייזיק --- 牛頓, --- 牛頓, 伊萨克, --- Annals --- Auxiliary sciences of history --- Math --- Science
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What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis. From the reviews of the German edition: Three wishes granted at once: the book “3000 Jahre Analysis” is anything but a dry mixture of mathematical facts and formulae. Instead, it is a skillful blend of textbook, nonfiction, and history book rolled into one, which has been very vibrantly written. The author Thomas Sonar has managed to present the history of Analysis vividly, thrillingly, and full of intriguing details. Florian Modler, Spektrum der Wissenschaft The book [...] is simply wonderful. Everybody [...] picks up this book with a certain expectation, of course, and they won’t be disappointed! ... It is truly fun browsing the book. Peter Littelmann, Mitteilungen der DMV.
Mathematics. --- History. --- History of Mathematical Sciences. --- Annals --- Auxiliary sciences of history --- Math --- Science --- Mathematical analysis --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis - History
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The goal of this book is to provide readers with an update on recent developments in surgical treatment of some shoulder disorders. The perspective of this book involves highlighting management of complex shoulder conditions in better ways. This book is divided into four main sections: 'Repair' involves chapters related to primary repair; 'Replacement' section provides detailed perspective on shoulder replacement procedures for different conditions; 'Reconstruction' includes a chapter on reconstructive procedures where primary repair is not possible; and lastly 'Rehab and Miscellaneous' section includes chapters on surgical management of rheumatoid arthritis and rehab. Individual chapters provide a base for a wide range of readers including students, professors, physiotherapists and orthopaedic surgeons, who will find in this book simply explained basics as well as advanced techniques of shoulder surgeries. The book consists of ten chapeters, compiled by experts from institutes across the globe.
MEDICAL / Surgery / Oral & Maxillofacial. --- Medicine --- Surgery --- Orthopedics --- Health Sciences --- Medicine. --- Surgery. --- Orthopedics. --- Health sciences. --- Basic medical sciences --- Basic sciences, Medical --- Biomedical sciences --- Health sciences --- Preclinical sciences --- Sciences, Medical --- Life sciences --- Orthopaedics --- Orthopedia --- Surgery, Primitive --- Health Workforce --- Medical sciences.
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Der Einsatz von künstlicher Intelligenz im Gesundheitsbereich verspricht besonders großen Nutzen durch eine bessere Versorgung sowie effizientere Abläufe und bietet damit letztlich auch ökonomische Vorteile. Dem stehen unter anderem Befürchtungen entgegen, dass sich durch den Einsatz von künstlicher Intelligenz das Arzt-Patienten-Verhältnis verändern könnte, Arbeitsplätze gefährdet seien oder die Ökonomisierung des Gesundheitswesens einen weiteren Schub erfahren könnte. Zuweilen wird die Debatte um diese Technologie, zumal in der Öffentlichkeit, emotional und fern sachlicher Argumente geführt. Die Autorinnen und Autoren untersuchen die Geschichte des KI-Einsatzes in der Medizin, deren öffentliche Wahrnehmung, Governance der KI, die Möglichkeiten und Grenzen der Technik sowie Einsatzgebiete, die bisher noch nicht oder nur wenig im Fokus der Aufmerksamkeit waren. Dabei erweist sich die KI als leistungsfähiges Werkzeug, das zahlreiche ethische und soziale Fragen aufwirft, die bei der Einführung anderer Technologien bereits gestellt wurden; allerdings gibt es auch neue Herausforderungen, denen sich Professionen, Politik und Gesellschaft stellen müssen.
Computers --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Artificial intelligence --- Medical applications. --- Medicine --- Data processing
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During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
Mathematics. --- Earth sciences. --- Applied mathematics. --- Engineering mathematics. --- Applications of Mathematics. --- Earth Sciences, general. --- Geology --- Mathematics --- Geognosy --- Geoscience --- Earth sciences --- Natural history --- Geography. --- Cosmography --- World history --- Math --- Science --- Geosciences --- Environmental sciences --- Physical sciences --- Engineering --- Engineering analysis --- Mathematical analysis
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During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as space borne data of better and better quality explain the strong need of new mathematical structures, tools and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook of Geomathematics’ deals with the qualitative and quantitative properties for the current and possible structures of the system Earth. As a central reference work it comprises the following geoscientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Earth sciences. --- Mathematics, general. --- Earth Sciences, general. --- Geosciences --- Environmental sciences --- Physical sciences --- Math --- Science --- Geography. --- Cosmography --- Earth sciences --- World history --- Geology
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Der umfangreiche Briefwechsel zwischen den Mathematikern Richard Dedekind und Heinrich Weber liegt nun erstmals in transkribierter Form vor. Es handelt sich dabei um einen der wichtigsten - wenn nicht um den wichtigsten -- Briefwechsel von Mathematikern der zweiten Hälfte des 19. und des beginnenden 20. Jahrhunderts, da nahezu jedes Teilgebiet der Mathematik angesprochen wird und damals beginnende Entwicklungen intensiv diskutiert wurden. Personen- und Werkverzeichnisse erleichtern den Überblick über die in den Briefen diskutierten Personen und Themen. Mit diesem Band wird ein Desiderat der Mathematikgeschichte geliefert, denn im Briefwechsel Dedekind-Weber spiegeln sich die großen Veränderungen und die Fortschritte, die die Mathematik in der stürmischen Entwicklungsphase des 19. Jahrhunderts kennzeichnete.
Algebra --- Numbers, Real --- Mathematicians --- Scientists --- Real numbers --- Arithmetic --- Numbers, Complex --- History. --- Dedekind, Richard, --- Weber, Heinrich, --- Weber, Heinrich Martin, --- Weber, H. --- Dedekind, Julius Wilhelm Richard, --- Dedekind, J. W. Richard --- Famous mathematicians. --- history of science. --- mathematics. --- mathematics/history.
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During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
Applied mathematics. --- Engineering mathematics. --- Earth sciences. --- Applications of Mathematics. --- Earth Sciences, general.
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The conflict of priorities over the discovery of differential and integral calculus between Leibniz and Newton is one of the most violent and far-reaching conflicts in the history of science. It developed slowly - and interestingly- not as a result of a personal conflict between the two scientists, but rather as a result of a conflict that the employees of these men conjured up. The lectures documented in this volume deal with the development of the priority dispute up to its consequences for English analysis in the centuries after Newton. The volume follows the presentation of Thomas Sonar: The history of the priority dispute between Leibniz and Newton (Springer Spektrum 2016).
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