Hypernatural
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The Strength Of Nonstandard Analysis
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Author : Imme van den Berg
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-03
The Strength Of Nonstandard Analysis written by Imme van den Berg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-03 with Mathematics categories.
Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations. This book reflects the progress made in the forty years since the appearance of Robinson’s revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.
Lectures On The Hyperreals
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Author : Robert Goldblatt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On The Hyperreals written by Robert Goldblatt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
There are good reasons to believe that nonstandard analysis, in some ver sion or other, will be the analysis of the future. KURT GODEL This book is a compilation and development of lecture notes written for a course on nonstandard analysis that I have now taught several times. Students taking the course have typically received previous introductions to standard real analysis and abstract algebra, but few have studied formal logic. Most of the notes have been used several times in class and revised in the light of that experience. The earlier chapters could be used as the basis of a course at the upper undergraduate level, but the work as a whole, including the later applications, may be more suited to a beginning graduate course. This prefacedescribes my motivationsand objectives in writingthe book. For the most part, these remarks are addressed to the potential instructor. Mathematical understanding develops by a mysterious interplay between intuitive insight and symbolic manipulation. Nonstandard analysis requires an enhanced sensitivity to the particular symbolic form that is used to ex press our intuitions, and so the subject poses some unique and challenging pedagogical issues. The most fundamental ofthese is how to turn the trans fer principle into a working tool of mathematical practice. I have found it vi Preface unproductive to try to give a proof of this principle by introducing the formal Tarskian semantics for first-order languages and working through the proofofLos's theorem.
Graphs And Networks
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Author : Armen H. Zemanian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Graphs And Networks written by Armen H. Zemanian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Scientia Gratiii Scientiae It is now thirteen years since the first book that discusses transfinite graphs and elec trical networks appeared [50]. This was followed by two more books [51] and [54] which compiled results from an ongoing research effort on that subject. Why then is a fourth book, this one, being offered? Simply because still more has been achieved beyond that appearing in those prior books. An exposition of these more recent re sults is the purpose of this book. The idea of transfiniteness for graphs and networks appeared as virgin research territory about seventeen years ago. Notwithstanding the progress that has since been achieved, much more remains to be done-or so it appears. Many conclusions con cerning conventionally infinite graphs and networks can be reformulated as open problems for transfinite graphs and networks. Furthermore, questions peculiar to transfinite concepts for graphs and networks can be suggested. Indeed, these two considerations have inspired the new results displayed herein.
Encyclopedic Dictionary Of Mathematics
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Author : Nihon Sūgakkai
language : en
Publisher: MIT Press
Release Date : 1993
Encyclopedic Dictionary Of Mathematics written by Nihon Sūgakkai and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
V.1. A.N. v.2. O.Z. Apendices and indexes.
Faith And Science
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Author : Kenneth D. Keathley
language : en
Publisher: B&H Publishing Group
Release Date : 2024-09-15
Faith And Science written by Kenneth D. Keathley and has been published by B&H Publishing Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-15 with Religion categories.
In Faith and Science: A Primer for a Hypernatural World, Kenneth Keathley argues that, rather than acting as opposing forces, scientific inquiry and the Christian faith go hand-in-hand. In his mission to offer a fully integrated theology of science, Keathley begins with the Lordship of Christ and the sufficiency of Scripture. He characterizes the study of science as a providential gift and a worthy vocation with Christian origins. Keathley then examines the twin challenges of scientism and fideism, observing their deficiencies as comprehensive worldviews. After defending Galileo as a scientist-theologian, Keathley offers readers a model for how to integrate their Christian faith with their scientific pursuits. Faith and Science provides a ready primer for students and everyday Christians to challenge their preconceptions about faith and science and to develop a more robust worldview to guide their examinations of our hypernatural world. The Christ in Everything series exists to demonstrate how Christ is connected to all of life. The primers in this series serve as introductions to important cultural topics, including science, freedom, politics, beauty, and the nature of truth. Each book offers a biblical and theological framework from which to view and approach the topic at hand, followed by examples for how to walk in the way of Jesus in that cultural domain.
Hypernaturals Vol 1
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Author : Dan Abnett
language : en
Publisher: Boom! Studios
Release Date : 2013-11-20
Hypernaturals Vol 1 written by Dan Abnett and has been published by Boom! Studios this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-20 with Comics & Graphic Novels categories.
It is the far future; the human race has finally colonized the galaxy, preserving an era of prosperity that's only possible because of The Hypernaturals. They're a celebrated, galaxy-wide superhero task force that keeps the peace. That is, until they all mysteriously vanish. Now, as the galaxy teeters on the brink of chaos, it's up to a group of retired and long forgotten Hypernaturals -- and their novice recruits -- to save the galaxy from complete destruction. Dan Abnett and Andy Lanning, the superstar writing duo behind ANNIHILATION and THE LEGION, launch an all-new original graphic novel series that takes cosmic super-heroes to a new frontier.
Homotopy Theories
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Author : Alex Heller
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Homotopy Theories written by Alex Heller and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
This memoir deals with much of the familiar structure of homotopy theory, including standard theorems on homotopy limits and localization, and gives a description of algebras-up-to-homotopy designed to illuminate the theory of loop-spaces.
Handbook Of Virtual Environments
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Author : Kelly S. Hale
language : en
Publisher: CRC Press
Release Date : 2014-09-10
Handbook Of Virtual Environments written by Kelly S. Hale and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-10 with Technology & Engineering categories.
A Complete Toolbox of Theories and Techniques The second edition of a bestseller, Handbook of Virtual Environments: Design, Implementation, and Applications presents systematic and extensive coverage of the primary areas of research and development within VE technology. It brings together a comprehensive set of contributed articles that address the principles required to define system requirements and design, build, evaluate, implement, and manage the effective use of VE applications. The contributors provide critical insights and principles associated with their given areas of expertise to provide extensive scope and detail on VE technology and its applications. What’s New in the Second Edition: Updated glossary of terms to promote common language throughout the community New chapters on olfactory perception, avatar control, motion sickness, and display design, as well as a whole host of new application areas Updated information to reflect the tremendous progress made over the last decade in applying VE technology to a growing number of domains This second edition includes nine new, as well as forty-one updated chapters that reflect the progress made in basic and applied research related to the creation, application, and evaluation of virtual environments. Contributions from leading researchers and practitioners from multidisciplinary domains provide a wealth of theoretical and practical information, resulting in a complete toolbox of theories and techniques that you can rely on to develop more captivating and effective virtual worlds. The handbook supplies a valuable resource for advancing VE applications as you take them from the laboratory to the real-world lives of people everywhere.
A Combination Of Geometry Theorem Proving And Nonstandard Analysis With Application To Newton S Principia
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Author : Jacques Fleuriot
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-30
A Combination Of Geometry Theorem Proving And Nonstandard Analysis With Application To Newton S Principia written by Jacques Fleuriot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-30 with Mathematics categories.
Sir Isaac Newton's philosophi Naturalis Principia Mathematica'(the Principia) contains a prose-style mixture of geometric and limit reasoning that has often been viewed as logically vague. In A Combination of Geometry Theorem Proving and Nonstandard Analysis, Jacques Fleuriot presents a formalization of Lemmas and Propositions from the Principia using a combination of methods from geometry and nonstandard analysis. The mechanization of the procedures, which respects much of Newton's original reasoning, is developed within the theorem prover Isabelle. The application of this framework to the mechanization of elementary real analysis using nonstandard techniques is also discussed.
Theories Of Generalised Functions
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Author : R F Hoskins
language : en
Publisher: Elsevier
Release Date : 2005-01-01
Theories Of Generalised Functions written by R F Hoskins and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions. The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins. - Explains and compares the various standard types of generalised functions that have been developed during the 20th Century - Contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions