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Book Synopsis The Strength of Nonstandard Analysis by : Imme van den Berg
Download or read book The Strength of Nonstandard Analysis written by Imme van den Berg and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects the progress made in the forty years since the appearance of Abraham 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.
Book Synopsis Encyclopedic Dictionary of Mathematics by : Nihon Sūgakkai
Download or read book Encyclopedic Dictionary of Mathematics written by Nihon Sūgakkai and published by MIT Press. This book was released on 1993 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A.N. v.2. O.Z. Apendices and indexes.
Book Synopsis Lectures on the Hyperreals by : Robert Goldblatt
Download or read book Lectures on the Hyperreals written by Robert Goldblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.
Book Synopsis Graphs and Networks by : Armen H. Zemanian
Download or read book Graphs and Networks written by Armen H. Zemanian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book examines results on transfinite graphs and networks achieved through continued research effort over the past several years. These new results, covering the mathematical theory of electrical circuits, are different from those presented in two previously published books by the author, Transfiniteness for Graphs, Electrical Networks, and Random Walks and Pristine Transfinite Graphs and Permissive Electrical Networks. Specific topics covered include connectedness ideas, distance ideas, and nontransitivity of connectedness. The book will appeal to a diverse readership, including graduate students, electrical engineers, mathematicians, and physicists working on infinite electrical networks. Moreover, the growing and presently substantial number of mathematicians working in nonstandard analysis may well be attracted by the novel application of the analysis employed in the work.
Book Synopsis Handbook of Virtual Environments by : Kelly S. Hale
Download or read book Handbook of Virtual Environments written by Kelly S. Hale and published by CRC Press. This book was released on 2014-09-10 with total page 1450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Homotopy Theories written by Alex Heller and published by American Mathematical Soc.. This book was released on 1988 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theories of Generalised Functions by : R F Hoskins
Download or read book Theories of Generalised Functions written by R F Hoskins and published by Elsevier. This book was released on 2005-01-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Nonstandard Analysis for the Working Mathematician by : Peter A. Loeb
Download or read book Nonstandard Analysis for the Working Mathematician written by Peter A. Loeb and published by Springer. This book was released on 2015-08-26 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a ‘secret weapon’ by those who know the technique. This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler’s internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems. All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.
Book Synopsis A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia by : Jacques Fleuriot
Download or read book A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia written by Jacques Fleuriot and published by Springer Science & Business Media. This book was released on 2012-09-30 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis What Kind of God? by : Terence E. Fretheim
Download or read book What Kind of God? written by Terence E. Fretheim and published by Penn State Press. This book was released on 2015-04-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Terence E. Fretheim has long been a leading voice in Old Testament theology. In this volume, thirty of his classic studies have been gathered together for the first time under the rubrics “God and the World”, “God and Suffering”, “God, Wrath, and Divine Violence”, “God and the Pentateuch”, “God and the Prophets”, and “God and the Church’s Book”. Here readers can find a compelling answer to the question that has motivated Fretheim’s work for more than forty years—namely, what kind of God is the God of Scripture? The studies are introduced by a critical overview of Fretheim’s career and theology by the editors and a retrospective by Fretheim himself.
Book Synopsis Hypernaturals Vol. 1 by : Dan Abnett
Download or read book Hypernaturals Vol. 1 written by Dan Abnett and published by Boom! Studios. This book was released on 2013-11-20 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Aesthetics of Necropolitics by : Natasha Lushetich
Download or read book The Aesthetics of Necropolitics written by Natasha Lushetich and published by Rowman & Littlefield. This book was released on 2018-12-11 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection comprises contributions from leading artist-theorists in the fields of necropolitics and tactical media, and from increasingly influential scholars of biomediality and urban performativity
Book Synopsis Old-Earth or Evolutionary Creation? by : Kenneth Keathley
Download or read book Old-Earth or Evolutionary Creation? written by Kenneth Keathley and published by InterVarsity Press. This book was released on 2017-07-18 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jesus Creed Book of the Year 2017, Science and Faith Christians confess that God created the heavens and the earth. But they are divided over how God created and whether the Bible gives us a scientifically accurate account of the process of creation. Representatives of two prominent positions—old-earth creation (Reasons to Believe) and evolutionary creation (BioLogos)—have been in dialogue over the past decade to understand where they agree and disagree on key issues in science and theology. This book is the result of those meetings. Moderated by Southern Baptist seminary professors, the discussion between Reasons to Believe and BioLogos touches on many of the pressing debates in science and faith, including biblical authority, the historicity of Adam and Eve, human genetics and common descent, the problem of natural evil, and methodological naturalism. While both organizations agree that God created the universe billions of years ago, their differences reveal that far more is at stake here than just the age of the earth. Old-Earth or Evolutionary Creation? invites readers to listen in as Christian scholars weigh the evidence, explore the options, and challenge each other on the questions of creation and evolution. In a culture of increasing polarization, this is a model for charitable Christian dialogue. BioLogos Books on Science and Christianity invite us to see the harmony between the sciences and biblical faith on issues including cosmology, biology, paleontology, evolution, human origins, the environment, and more.
Book Synopsis Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by : Mauro Di Nasso
Download or read book Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory written by Mauro Di Nasso and published by Springer. This book was released on 2019-05-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.
Download or read book Delta Functions written by R F Hoskins and published by Elsevier. This book was released on 2009-03-31 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delta Functions has now been updated, restructured and modernised into a second edition, to answer specific difficulties typically found by students encountering delta functions for the first time. In particular, the treatment of the Laplace transform has been revised with this in mind. The chapter on Schwartz distributions has been considerably extended and the book is supplemented by a fuller review of Nonstandard Analysis and a survey of alternative infinitesimal treatments of generalised functions. Dealing with a difficult subject in a simple and straightforward way, the text is readily accessible to a broad audience of scientists, mathematicians and engineers. It can be used as a working manual in its own right, and serves as a preparation for the study of more advanced treatises. Little more than a standard background in calculus is assumed, and attention is focused on techniques, with a liberal selection of worked examples and exercises. Second edition has been updated, restructured and modernised to answer specific difficulties typically found by students encountering delta functions for the first time Attention is focused on techniques, with a liberal selection of worked examples and exercises Readily accessible to a broad audience of scientists, mathematicians and engineers and can be used as a working manual in its own right
Book Synopsis Infinitesimal Methods of Mathematical Analysis by : J S Pinto
Download or read book Infinitesimal Methods of Mathematical Analysis written by J S Pinto and published by Elsevier. This book was released on 2004-05-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro. Surveys modern reformulations of the infinitesimal concept with a comprehensive exposition of important and influential hyperreal numbers Includes material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis
Book Synopsis How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers by : Vieri Benci
Download or read book How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers written by Vieri Benci and published by World Scientific. This book was released on 2019-02-19 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.
