Introduction To Abstract Analysis
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Introduction To Abstract Analysis
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Author : Marvin E. Goldstein
language : en
Publisher: Courier Corporation
Release Date : 2015-02-18
Introduction To Abstract Analysis written by Marvin E. Goldstein and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-18 with Mathematics categories.
Concise text prepares readers to pursue abstract analysis in the literature of pure mathematics. Detailed, easy-to-follow proofs and examples illustrate topics including real numbers, vector and metric spaces, infinite series, and other concepts. 1969 edition.
An Introduction To Abstract Analysis
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Author : William Allan Light
language : en
Publisher:
Release Date : 1990
An Introduction To Abstract Analysis written by William Allan Light and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematical analysis categories.
Introduction To Abstract Analysis
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Author : W. Light
language : en
Publisher: CRC Press
Release Date : 1990-07-01
Introduction To Abstract Analysis written by W. Light and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-07-01 with Mathematics categories.
Abstract analysis, and particularly the language of normed linear spaces, now lies at the heart of a major portion of modern mathematics. Unfortunately, it is also a subject which students seem to find quite challenging and difficult. This book presumes that the student has had a first course in mathematical analysis or advanced calculus, but it does not presume the student has achieved mastery of such a course. Accordingly, a gentle introduction to the basic notions of convergence of sequences, continuity of functions, open and closed set, compactness, completeness and separability is given. The pace in the early chapters does not presume in any way that the readers have at their fingertips the techniques provided by an introductory course. Instead, considerable care is taken to introduce and use the basic methods of proof in a slow and explicit fashion. As the chapters progress, the pace does quicken and later chapters on differentiation, linear mappings, integration and the implicit function theorem delve quite deeply into interesting mathematical areas. There are many exercises and many examples of applications of the theory to diverse areas of mathematics. Some of these applications take considerable space and time to develop, and make interesting reading in their own right. The treatment of the subject is deliberately not a comprehensive one. The aim is to convince the undergraduate reader that analysis is a stimulating, useful, powerful and comprehensible tool in modern mathematics. This book will whet the readers' appetite, not overwhelm them with material.
An Introduction To Abstract Analysis
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Author : Will A. Light
language : en
Publisher:
Release Date : 1990
An Introduction To Abstract Analysis written by Will A. Light and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Foundations Of Real And Abstract Analysis
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Author : Douglas S. Bridges
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
Foundations Of Real And Abstract Analysis written by Douglas S. Bridges 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 1998 with Business & Economics categories.
A complete course on metric, normed, and Hilbert spaces, including many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format, including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. The book begins with a fast-paced course on real analysis, followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as a preparation for students with only the typical sequence of undergraduate calculus courses as prerequisites. Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications. Of special interest are the 750 exercises, many with guidelines for their solutions, applications and extensions of the main propositions and theorems, pointers to new branches of the subject, and difficult challenges for the very best students.
A Course In Abstract Analysis
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Author : John B. Conway
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-10-03
A Course In Abstract Analysis written by John B. Conway 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 2012-10-03 with Mathematics categories.
This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.
Introduction To Abstract Harmonic Analysis
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Author : Lynn H. Loomis
language : en
Publisher: Courier Corporation
Release Date : 2013-05-09
Introduction To Abstract Harmonic Analysis written by Lynn H. Loomis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-09 with Mathematics categories.
Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.
Introduction To Static Analysis
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Author : Xavier Rival
language : en
Publisher: MIT Press
Release Date : 2020-02-11
Introduction To Static Analysis written by Xavier Rival and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-11 with Computers categories.
A self-contained introduction to abstract interpretation–based static analysis, an essential resource for students, developers, and users. Static program analysis, or static analysis, aims to discover semantic properties of programs without running them. It plays an important role in all phases of development, including verification of specifications and programs, the synthesis of optimized code, and the refactoring and maintenance of software applications. This book offers a self-contained introduction to static analysis, covering the basics of both theoretical foundations and practical considerations in the use of static analysis tools. By offering a quick and comprehensive introduction for nonspecialists, the book fills a notable gap in the literature, which until now has consisted largely of scientific articles on advanced topics. The text covers the mathematical foundations of static analysis, including semantics, semantic abstraction, and computation of program invariants; more advanced notions and techniques, including techniques for enhancing the cost-accuracy balance of analysis and abstractions for advanced programming features and answering a wide range of semantic questions; and techniques for implementing and using static analysis tools. It begins with background information and an intuitive and informal introduction to the main static analysis principles and techniques. It then formalizes the scientific foundations of program analysis techniques, considers practical aspects of implementation, and presents more advanced applications. The book can be used as a textbook in advanced undergraduate and graduate courses in static analysis and program verification, and as a reference for users, developers, and experts.
Elements Of Abstract Analysis
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Author : Mícheál O'Searcoid
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
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 2012-12-06 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.
Principles Of Abstract Interpretation
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Author : Patrick Cousot
language : en
Publisher: MIT Press
Release Date : 2021-09-21
Principles Of Abstract Interpretation written by Patrick Cousot and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-21 with Computers categories.
Introduction to abstract interpretation, with examples of applications to the semantics, specification, verification, and static analysis of computer programs. Formal methods are mathematically rigorous techniques for the specification, development, manipulation, and verification of safe, robust, and secure software and hardware systems. Abstract interpretation is a unifying theory of formal methods that proposes a general methodology for proving the correctness of computing systems, based on their semantics. The concepts of abstract interpretation underlie such software tools as compilers, type systems, and security protocol analyzers. This book provides an introduction to the theory and practice of abstract interpretation, offering examples of applications to semantics, specification, verification, and static analysis of programming languages with emphasis on calculational design. The book covers all necessary computer science and mathematical concepts--including most of the logic, order, linear, fixpoint, and discrete mathematics frequently used in computer science--in separate chapters before they are used in the text. Each chapter offers exercises and selected solutions. Chapter topics include syntax, parsing, trace semantics, properties and their abstraction, fixpoints and their abstractions, reachability semantics, abstract domain and abstract interpreter, specification and verification, effective fixpoint approximation, relational static analysis, and symbolic static analysis. The main applications covered include program semantics, program specification and verification, program dynamic and static analysis of numerical properties and of such symbolic properties as dataflow analysis, software model checking, pointer analysis, dependency, and typing (both for forward and backward analysis), and their combinations. Principles of Abstract Interpretation is suitable for classroom use at the graduate level and as a reference for researchers and practitioners.