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Introduction to Abstract Analysis

Introduction to Abstract Analysis PDF Author: Marvin E. Goldstein
Publisher: Courier Corporation
ISBN: 0486799913
Category : Mathematics
Languages : en
Pages : 257

Book Description
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.

Introduction to Abstract Analysis

Introduction to Abstract Analysis PDF Author: Marvin E. Goldstein
Publisher: Courier Corporation
ISBN: 0486799913
Category : Mathematics
Languages : en
Pages : 257

Book Description
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.

A Course in Abstract Analysis

A Course in Abstract Analysis PDF Author: John B. Conway
Publisher: American Mathematical Soc.
ISBN: 0821890832
Category : Mathematics
Languages : en
Pages : 385

Book Description
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

Introduction to Abstract Harmonic Analysis PDF Author: Lynn H. Loomis
Publisher: Courier Corporation
ISBN: 0486481239
Category : Mathematics
Languages : en
Pages : 210

Book Description
"Harmonic analysis is a branch of advanced mathematics with applications in such diverse areas as signal processing, medical imaging, and quantum mechanics. This classic monograph is the work of a prominent contributor to the field. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition"--

Introduction to Static Analysis

Introduction to Static Analysis PDF Author: Xavier Rival
Publisher: MIT Press
ISBN: 0262043416
Category : Computers
Languages : en
Pages : 315

Book Description
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.

Real and Abstract Analysis

Real and Abstract Analysis PDF Author: E. Hewitt
Publisher: Springer Science & Business Media
ISBN: 3642880444
Category : Mathematics
Languages : en
Pages : 485

Book Description
This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present cus tomarily offered as a first or second year graduate course in United States universities, although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts, and we have also gone down a number of interesting bypaths. We hope too that the book will be useful as a reference for mature mathematicians and other scientific workers. Hence we have presented very general and complete versions of a number of important theorems and constructions. Since these sophisticated versions may be difficult for the beginner, we have given elementary avatars of all important theorems, with appro priate suggestions for skipping. We have given complete definitions, ex planations, and proofs throughout, so that the book should be usable for individual study as well as for a course text. Prerequisites for reading the book are the following. The reader is assumed to know elementary analysis as the subject is set forth, for example, in TOM M. ApOSTOL'S Mathematical Analysis [Addison-Wesley Publ. Co., Reading, Mass., 1957], or WALTER RUDIN'S Principles of M athe nd matical Analysis [2 Ed., McGraw-Hill Book Co., New York, 1964].

Foundations of Real and Abstract Analysis

Foundations of Real and Abstract Analysis PDF Author: Douglas S. Bridges
Publisher:
ISBN: 9781475771602
Category :
Languages : en
Pages : 344

Book Description


Introduction to Analysis

Introduction to Analysis PDF Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 0486134687
Category : Mathematics
Languages : en
Pages : 270

Book Description
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

Mathematical Analysis

Mathematical Analysis PDF Author: Andrew Browder
Publisher: Springer Science & Business Media
ISBN: 1461207150
Category : Mathematics
Languages : en
Pages : 348

Book Description
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.

Introduction to the Theory of Abstract Algebras

Introduction to the Theory of Abstract Algebras PDF Author: Richard S Pierce
Publisher: Courier Corporation
ISBN: 0486789985
Category : Mathematics
Languages : en
Pages : 162

Book Description
"Suitable for introductory graduate-level courses and independent study, this text presents the basic definitions of the theory of abstract algebra. Following introductory material, each of four chapters focuses on a major theme of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebra. Problems and a bibliography supplement the text. "--

Real Analysis

Real Analysis PDF Author: Jewgeni H. Dshalalow
Publisher: CRC Press
ISBN: 1420036890
Category : Mathematics
Languages : en
Pages : 583

Book Description
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