Unit Aa1
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Unit Aa1
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Author : Open University
language : en
Publisher:
Release Date : 2006-03-04
Unit Aa1 written by Open University and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-04 with categories.
This unit is devoted to the real numbers and their properties. In particular, inequalities are discussed, which play a crucial role in analysis. The five sections of the unit cover revision of rational numbers and their decimal representations, real numbers as infinite decimals, their properties and the difficulties involved in doing arithmetic with such decimals, rules for manipulating inequalities, techniques for proving inequalities, and the concept of least upper bound.One subsection, of this unit, is intended to be studied in conjunction with an audio, available in the Analysis A Block Pack (order code M208/MMPAA). The general video programme, Coping with irrationality, is available on DVD00126 (order code M208/DVD02).
Real Numbers Generalizations Of The Reals And Theories Of Continua
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Author : P. Ehrlich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Real Numbers Generalizations Of The Reals And Theories Of Continua written by P. Ehrlich 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 2013-06-29 with Mathematics categories.
Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics
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Author : John L. Bell
language : en
Publisher: Springer Nature
Release Date : 2019-09-09
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics written by John L. Bell and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
Noneuclidean Geometry
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Author : Herbert Meschkowski
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Noneuclidean Geometry written by Herbert Meschkowski and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Noneuclidean Geometry focuses on the principles, methodologies, approaches, and importance of noneuclidean geometry in the study of mathematics. The book first offers information on proofs and definitions and Hilbert's system of axioms, including axioms of connection, order, congruence, and continuity and the axiom of parallels. The publication also ponders on lemmas, as well as pencil of circles, inversion, and cross ratio. The text examines the elementary theorems of hyperbolic geometry, particularly noting the value of hyperbolic geometry in noneuclidian geometry, use of the Poincaré model, and numerical principles in proving hyperparallels. The publication also tackles the issue of construction in the Poincaré model, verifying the relations of sides and angles of a plane through trigonometry, and the principles involved in elliptic geometry. The publication is a valuable source of data for mathematicians interested in the principles and applications of noneuclidean geometry.
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Author :
language : en
Publisher: Delene Kvasnicka
Release Date :
written by and has been published by Delene Kvasnicka this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Isv Ibm Zpdt Guide And Reference
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Author : Bill Ogden
language : en
Publisher: IBM Redbooks
Release Date : 2022-12-13
Isv Ibm Zpdt Guide And Reference written by Bill Ogden and has been published by IBM Redbooks this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-13 with Computers categories.
This IBM® Redbooks® publication provides both introductory information and technical details for ISV IBM Z® Program Development Tool (IBM zPDT®), which produces a small IBM zSystems environment that is suitable for application development. ISV zPDT is a personal computer (PC) Linux application. When ISV zPDT is installed on Linux, normal IBM zSystems operating systems (such as IBM z/OS®) may be run on it. ISV zPDT provides the basic IBM zSystems architecture and provides emulated IBM 3390 disk drives, 3270 interfaces, Open Systems Adapter (OSA) interfaces, and other items. The systems that are described in this publication are complex, with elements of Linux (for the underlying PC machine), IBM z/Architecture® (for the core zPDT elements), IBM zSystems I/O functions (for emulated I/O devices), z/OS (the most common IBM zSystems operating system), and various applications and subsystems under z/OS. We assume that the reader is familiar with general concepts and terminology of IBM zSystems hardware and software elements, and with basic PC Linux characteristics. This publication provides the primary documentation for ISV zPDT and corresponds to zPDT V1 R11, commonly known as GA11.
A Grammar And Dictionary Of Zaiwa 2 Vols
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Author : Anton Lustig
language : en
Publisher: BRILL
Release Date : 2010-09-24
A Grammar And Dictionary Of Zaiwa 2 Vols written by Anton Lustig and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-24 with Language Arts & Disciplines categories.
This work is a thorough and unique documentation of the conceptual universe expressed through the typologically highly interesting Zaiwa language of the Jingpo minority in China.
Cahuachi In The Ancient Nasca World
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Author : Helaine Silverman
language : en
Publisher: University of Iowa Press
Release Date :
Cahuachi In The Ancient Nasca World written by Helaine Silverman and has been published by University of Iowa Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with History categories.
Ever since its scientific discovery, the great Nasca site of Cahuachi on the south coast of the Central Andes has captured the attention of archaeologists, art historians, and the general public. Until Helaine Silverman's fieldwork, however, ancient Nasca culture was seen as an archaeological construct devoid of societal context. Silverman's long-term, multistage research as published in this volume reconstructs Nasca society and contextualizes the traces of this brilliant civilization (ca. 200 B.C.-A.D. 600). Silverman shows that Cahuachi was much larger and more complex than portrayed in the current literature but that, surprisingly, it was not a densely populated city. Rather, Cahuachi was a grand ceremonial center whose population, size, density, and composition changed to accommodate a ritual and political calendar. Silverman meticulously presents and interprets an abundance of current data on the physical complexities, burials, and artifacts of this prominent site; in addition, she synthesizes the history of previous fieldwork at Cahuachi and introduces a corrected map and a new chronological chart for the Rio Grande de Nazca drainage system. On the basis of empirical field data, ethnographic analogy, and settlement pattern analysis, Silverman constructs an Andean model of Nasca culture that is crucial to understanding the development of complex society in the Central Andes. Written in a clear and concise style and generously illustrated, this first synthesis of the published data about the ancient Nasca world will appeal to all archaeologists, art historians, urban anthropologists, and historians of ancient civilizations.
Instrument Practice
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Author :
language : en
Publisher:
Release Date : 1960
Instrument Practice written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Engineering instruments categories.
Banach Space Theory And Its Applications
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Author : A. Pietsch
language : en
Publisher: Springer
Release Date : 2006-11-15
Banach Space Theory And Its Applications written by A. Pietsch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
