Introduction To Abstract Analysis

Author : W. Light
Publisher : CRC Press
Page : 212 pages
File Size : 53,9 Mb
Release : 1990-07-01
Category : Mathematics
ISBN : 0412310902

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Introduction to Abstract Analysis by W. Light Pdf

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.

Author : Marvin E. Goldstein,Burt M. Rosenbaum
Publisher : Courier Corporation
Page : 256 pages
File Size : 52,5 Mb
Release : 2014-10-27
Category : Mathematics
ISBN : 9780486799919

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Introduction to Abstract Analysis by Marvin E. Goldstein,Burt M. Rosenbaum Pdf

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.

Author : John B. Conway
Publisher : American Mathematical Soc.
Page : 385 pages
File Size : 46,8 Mb
Release : 2012-10-03
Category : Mathematics
ISBN : 9780821890837

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A Course in Abstract Analysis by John B. Conway Pdf

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.

Author : Douglas S. Bridges
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 50,6 Mb
Release : 1998
Category : Business & Economics
ISBN : 9780387982397

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Foundations of Real and Abstract Analysis by Douglas S. Bridges Pdf

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.

Author : Lynn H. Loomis
Publisher : Courier Corporation
Page : 208 pages
File Size : 46,6 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 9780486282312

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Introduction to Abstract Harmonic Analysis by Lynn H. Loomis Pdf

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.

Author : Xavier Rival,Kwangkeun Yi
Publisher : MIT Press
Page : 315 pages
File Size : 48,5 Mb
Release : 2020-02-11
Category : Computers
ISBN : 9780262043410

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Introduction to Static Analysis by Xavier Rival,Kwangkeun Yi Pdf

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.

Author : Marvin E. Goldstein,Burt M. Rosenbaum
Publisher : Courier Corporation
Page : 257 pages
File Size : 41,6 Mb
Release : 2015-02-18
Category : Mathematics
ISBN : 9780486789460

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Introduction to Abstract Analysis by Marvin E. Goldstein,Burt M. Rosenbaum Pdf

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.

Author : William Allan Light
Publisher : Unknown
Page : 194 pages
File Size : 49,5 Mb
Release : 1990
Category : Mathematical analysis
ISBN : 7506212064

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An Introduction to Abstract Analysis by William Allan Light Pdf

Author : Jewgeni H. Dshalalow
Publisher : Springer Science & Business Media
Page : 756 pages
File Size : 46,7 Mb
Release : 2012-11-09
Category : Mathematics
ISBN : 9781461459620

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Foundations of Abstract Analysis by Jewgeni H. Dshalalow Pdf

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.

Author : Patrick Cousot
Publisher : MIT Press
Page : 833 pages
File Size : 41,8 Mb
Release : 2021-09-21
Category : Computers
ISBN : 9780262044905

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Principles of Abstract Interpretation by Patrick Cousot Pdf

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.

Author : Corey M. Dunn
Publisher : CRC Press
Page : 419 pages
File Size : 54,6 Mb
Release : 2017-06-26
Category : Mathematics
ISBN : 9781498732024

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Introduction to Analysis by Corey M. Dunn Pdf

Introduction to Analysis is an ideal text for a one semester course on analysis. The book covers standard material on the real numbers, sequences, continuity, differentiation, and series, and includes an introduction to proof. The author has endeavored to write this book entirely from the student’s perspective: there is enough rigor to challenge even the best students in the class, but also enough explanation and detail to meet the needs of a struggling student. From the Author to the student: "I vividly recall sitting in an Analysis class and asking myself, ‘What is all of this for?’ or ‘I don’t have any idea what’s going on.’ This book is designed to help the student who finds themselves asking the same sorts of questions, but will also challenge the brightest students." Chapter 1 is a basic introduction to logic and proofs. Informal summaries of the idea of proof provided before each result, and before a solution to a practice problem. Every chapter begins with a short summary, followed by a brief abstract of each section. Each section ends with a concise and referenced summary of the material which is designed to give the student a "big picture" idea of each section. There is a brief and non-technical summary of the goals of a proof or solution for each of the results and practice problems in this book, which are clearly marked as "Idea of proof," or as "Methodology", followed by a clearly marked formal proof or solution. Many references to previous definitions and results. A "Troubleshooting Guide" appears at the end of each chapter that answers common questions.

Author : Jewgeni H. Dshalalow
Publisher : CRC Press
Page : 583 pages
File Size : 40,9 Mb
Release : 2000-09-28
Category : Mathematics
ISBN : 9781420036893

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Real Analysis by Jewgeni H. Dshalalow Pdf

Designed for use in a two-semester course on abstract analysis, REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration illuminates the principle topics that constitute real analysis. Self-contained, with coverage of topology, measure theory, and integration, it offers a thorough elaboration of major theorems, notions, and co

Author : Andrew Browder
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207153

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Mathematical Analysis by Andrew Browder Pdf

Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.

Author : Andrew Wohlgemuth
Publisher : Courier Corporation
Page : 385 pages
File Size : 51,9 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9780486141688

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Introduction to Proof in Abstract Mathematics by Andrew Wohlgemuth Pdf

The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.

Author : Will A. Light
Publisher : Unknown
Page : 194 pages
File Size : 45,7 Mb
Release : 1990
Category : Electronic
ISBN : OCLC:801866512

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An Introduction to Abstract Analysis by Will A. Light Pdf