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Author: John Wallis Publisher: Springer Science & Business Media ISBN: 1475743122 Category : Mathematics Languages : en Pages : 226
Book Description
John Wallis (1616-1703) was the most influential English mathematician prior to Newton. He published his most famous work, Arithmetica Infinitorum, in Latin in 1656. This book studied the quadrature of curves and systematised the analysis of Descartes and Cavelieri. Upon publication, this text immediately became the standard book on the subject and was frequently referred to by subsequent writers. This will be the first English translation of this text ever to be published.
Author: John Wallis Publisher: Springer Science & Business Media ISBN: 1475743122 Category : Mathematics Languages : en Pages : 226
Book Description
John Wallis (1616-1703) was the most influential English mathematician prior to Newton. He published his most famous work, Arithmetica Infinitorum, in Latin in 1656. This book studied the quadrature of curves and systematised the analysis of Descartes and Cavelieri. Upon publication, this text immediately became the standard book on the subject and was frequently referred to by subsequent writers. This will be the first English translation of this text ever to be published.
Author: Yaroslav D. Sergeyev Publisher: Yaroslav D. Sergeyev ISBN: 8889064013 Category : Science Languages : en Pages : 112
Book Description
The first chapter of the book gives a brief description of the modern viewpoint on real numbers and presents the famous results of Georg Cantor regarding infinity. The second chapter has a preparative character and links the first and the third parts of the book. On the one hand, it shows that the commonly accepted point of view on numbers and infinity is not so clear as it seems at first sight (for example, it leads to numerous paradoxes). On the other hand, the chapter contains preliminary observations that will be used in the constructive introduction of a new arithmetic of infinity, given in the third chapter. This last part of the book contains the main results. It introduces notions of infinite and infinitesimal numbers, extended natural and real numbers, and operations with them. Surprisingly, the introduced arithmetical operations result in being very simple and are obtained as immediate extensions of the usual addition, multiplication, and division of finite numbers to infinite ones. This simplicity is a consequence of a newly developed positional numeral system used to express infinite numbers. Finally, the chapter contains solutions to a number of paradoxes regarding infinity (we can say that the new approach allows us to avoid paradoxes) and some examples of applications. In order to broaden the audience, the book was written as a popular one. The interested reader can find a number of technical articles of several researches that use the approach introduced here for solving a variety of research problems at the web page of the author. The author Yaroslav D. Sergeyev is Distinguished Professor and Head of Numerical Calculus Laboratory at the University of Calabria, Italy. He is also Professor (part-time contract) at Lobachevsky Nizhni Novgorod State University, Russia. His research interests include numerical analysis, global optimization, infinity computing, set theory, number theory, fractals, and parallel computing. He has been awarded several national and international prizes (Pythagoras International Prize in Mathematics, Italy; Lagrange Lecture, Turin University, Italy; MAIK Prize for the best scientific monograph published in Russian, Moscow, etc.). His list of scientific publications contains more than 200 items. He is a member of editorial boards of 5 international journals and has given more than 50 plenary and keynote lectures at prestigious international congresses.
Author: Amir Alexander Publisher: Simon and Schuster ISBN: 1780745338 Category : Science Languages : en Pages : 368
Book Description
On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.
Author: Margaret E. Baron Publisher: Elsevier ISBN: 1483280926 Category : Mathematics Languages : en Pages : 312
Book Description
The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.
Author: Vieri Benci Publisher: World Scientific ISBN: 9813276606 Category : Mathematics Languages : en Pages : 346
Book Description
'This text shows that the study of the almost-forgotten, non-Archimedean mathematics deserves to be utilized more intently in a variety of fields within the larger domain of applied mathematics.'CHOICEThis book contains an original introduction to the use of infinitesimal and infinite numbers, namely, the Alpha-Theory, which can be considered as an alternative approach to nonstandard analysis.The basic principles are presented in an elementary way by using the ordinary language of mathematics; this is to be contrasted with other presentations of nonstandard analysis where technical notions from logic are required since the beginning. Some applications are included and aimed at showing the power of the theory.The book also provides a comprehensive exposition of the Theory of Numerosity, a new way of counting (countable) infinite sets that maintains the ancient Euclid's Principle: 'The whole is larger than its parts'. The book is organized into five parts: Alpha-Calculus, Alpha-Theory, Applications, Foundations, and Numerosity Theory.
Author: Abraham Robinson Publisher: Princeton University Press ISBN: 1400884225 Category : Mathematics Languages : en Pages : 308
Book Description
Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
Author: John Wallis
Author: John Wallis
Author: Yaroslav D. Sergeyev
Author: Amir Alexander
Author: H. Jerome Keisler
Author: Margaret E. Baron
Author: H. Jerome Keisler
Author: Dan Sloughter
Author: Vieri Benci
Author: Abraham Robinson
Author: Nader Vakil