The Arch Papers On The Mathematics Of Abstraction
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The Arch Papers On The Mathematics Of Abstraction
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Author : Roy T. Cook
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-27
The Arch Papers On The Mathematics Of Abstraction written by Roy T. Cook 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 2007-11-27 with Mathematics categories.
This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut- or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies.
Abstract Analytic Function Theory And Hardy Algebras
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Author : K. Barbey
language : en
Publisher: Springer
Release Date : 2006-11-15
Abstract Analytic Function Theory And Hardy Algebras written by K. Barbey 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.
Improved Bonferroni Inequalities Via Abstract Tubes
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Author : Klaus Dohmen
language : en
Publisher: Springer
Release Date : 2003-12-10
Improved Bonferroni Inequalities Via Abstract Tubes written by Klaus Dohmen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-10 with Mathematics categories.
This introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Möbius functions.
Technical Abstract Bulletin
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Author :
language : en
Publisher:
Release Date :
Technical Abstract Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
A History Of Abstract Algebra
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Author : Jeremy Gray
language : en
Publisher: Springer
Release Date : 2018-08-07
A History Of Abstract Algebra written by Jeremy Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-07 with Mathematics categories.
This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
Abstract Analytic Number Theory
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Author : Knopfmacher
language : en
Publisher: Newnes
Release Date : 2009-02-04
Abstract Analytic Number Theory written by Knopfmacher and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-04 with Computers categories.
North-Holland Mathematical Library, Volume 12: Abstract Analytic Number Theory focuses on the approaches, methodologies, and principles of the abstract analytic number theory. The publication first deals with arithmetical semigroups, arithmetical functions, and enumeration problems. Discussions focus on special functions and additive arithmetical semigroups, enumeration and zeta functions in special cases, infinite sums and products, double series and products, integral domains and arithmetical semigroups, and categories satisfying theorems of the Krull-Schmidt type. The text then ponders on semigroups satisfying Axiom A, asymptotic enumeration and "statistical" properties of arithmetical functions, and abstract prime number theorem. Topics include asymptotic properties of prime-divisor functions, maximum and minimum orders of magnitude of certain functions, asymptotic enumeration in certain categories, distribution functions of prime-independent functions, and approximate average values of special arithmetical functions. The manuscript takes a look at arithmetical formations, additive arithmetical semigroups, and Fourier analysis of arithmetical functions, including Fourier theory of almost even functions, additive abstract prime number theorem, asymptotic average values and densities, and average values of arithmetical functions over a class. The book is a vital reference for researchers interested in the abstract analytic number theory.
Elements Of Abstract Analysis
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Author : Mícheál O'Searcoid
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-09
Elements Of Abstract Analysis written by Mícheál O'Searcoid 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 2001-11-09 with Mathematics categories.
While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. The book has been clearly written and contains numerous exercises and examples, making it an a rigorous and self-contained introductory text on functional analysis.
Dummett On Abstract Objects
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Author : G. Duke
language : en
Publisher: Springer
Release Date : 2012-03-20
Dummett On Abstract Objects written by G. Duke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-20 with Philosophy categories.
This historically-informed critical assessment of Dummett's account of abstract objects, examines in detail some of the Fregean presuppositions of Dummett's account whilst also engaging with phenomenological approaches and recent work on the problem of abstract entities.
A History Of Abstract Algebra
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Author : Israel Kleiner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-02
A History Of Abstract Algebra written by Israel Kleiner 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 2007-10-02 with Mathematics categories.
This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.
A Primer Of Abstract Mathematics
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Author : Robert B. Ash
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-03-02
A Primer Of Abstract Mathematics written by Robert B. Ash 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 2020-03-02 with Mathematics categories.
The purpose of this book is to prepare the reader for coping with abstract mathematics. The intended audience is both students taking a first course in abstract algebra who feel the need to strengthen their background and those from a more applied background who need some experience in dealing with abstract ideas. Learning any area of abstract mathematics requires not only ability to write formally but also to think intuitively about what is going on and to describe that process clearly and cogently in ordinary English. Ash tries to aid intuition by keeping proofs short and as informal as possible and using concrete examples as illustration. Thus, it is an ideal textbook for an audience with limited experience in formalism and abstraction. A number of expository innovations are included, for example, an informal development of set theory which teaches students all the basic results for algebra in one chapter.