The Number Systems Foundations Of Algebra And Analysis
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The Number Systems Foundations Of Algebra And Analysis
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Author : Solomon Feferman
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
The Number Systems Foundations Of Algebra And Analysis written by Solomon Feferman 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 2003 with Mathematics categories.
The subject of this book is the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers, and complex numbers. This second edition expands upon the list of suggestions for further reading in Appendix III. From the Preface: ``The present book basically takes for granted the non-constructive set-theoretical foundation of mathematics, which is tacitly if not explicitly accepted by most working mathematicians but which I have since come to reject. Still, whatever one's foundational views, students must be trained in this approach in order to understand modern mathematics. Moreover, most of the material of the present book can be modified so as to be acceptable under alternative constructive and semi-constructive viewpoints, as has been demonstrated in more advanced texts and research articles.''
Number Systems And The Foundations Of Analysis
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Author : Elliott Mendelson
language : en
Publisher: Dover Books on Mathematics
Release Date : 2008
Number Systems And The Foundations Of Analysis written by Elliott Mendelson and has been published by Dover Books on Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.
Number Systems
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Author : Sergeĭ Ovchinnikov
language : en
Publisher:
Release Date : 2015
Number Systems written by Sergeĭ Ovchinnikov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students
The Number Systems
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Author : Solomon Feferman
language : en
Publisher:
Release Date : 1964
The Number Systems written by Solomon Feferman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Number Theory categories.
The Number System
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Author : H. A. Thurston
language : en
Publisher: Courier Corporation
Release Date : 2012-10-23
The Number System written by H. A. Thurston and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-23 with Mathematics categories.
This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.
The Number Systems
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Author : James Bausch Hendry
language : en
Publisher:
Release Date : 1964
The Number Systems written by James Bausch Hendry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
New Foundations In Mathematics
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Author : Garret Sobczyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-28
New Foundations In Mathematics written by Garret Sobczyk 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 2012-10-28 with Mathematics categories.
The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
Foundations Of Abstract Analysis
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Author : Jewgeni H. Dshalalow
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-09
Foundations Of Abstract Analysis written by Jewgeni H. Dshalalow 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 2012-11-09 with Mathematics categories.
Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study. While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of the potential overload of new words, definitions, and concepts, the book (in its unique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded by informal discussions and blueprints followed by thorough details and supported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of the book, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. Prerequisites include advanced calculus, linear algebra, complex variables, and calculus based probability.
Multidimensional Analysis
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Author : George W. Hart
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-03-17
Multidimensional Analysis written by George W. Hart 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 1995-03-17 with Mathematics categories.
This book deals with the mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity. Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications.
Real Analysis Foundations
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Author : Sergei Ovchinnikov
language : en
Publisher: Springer Nature
Release Date : 2021-02-16
Real Analysis Foundations written by Sergei Ovchinnikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-16 with Mathematics categories.
This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.