Foundations Of Abstract Analysis
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Author | : Jewgeni H. Dshalalow |
Publisher | : Springer Science & Business Media |
Total Pages | : 756 |
Release | : 2012-11-09 |
Genre | : Mathematics |
ISBN | : 1461459621 |
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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 | : Springer |
Publisher | : |
Total Pages | : 764 |
Release | : 2012-11-10 |
Genre | : |
ISBN | : 9781461459637 |
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Author | : Jewgeni H. Dshalalow |
Publisher | : Springer |
Total Pages | : 764 |
Release | : 2016-05-01 |
Genre | : |
ISBN | : 9781493943883 |
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The first of a two book series which comprises the expanded second edition of the previously published text Real Analysis, this volume covers topics in point-set topology and measure and integration. Includes examples and figures, and some 580 problems.
Author | : Douglas S. Bridges |
Publisher | : Springer Science & Business Media |
Total Pages | : 328 |
Release | : 1998 |
Genre | : Business & Economics |
ISBN | : 0387982396 |
Download Foundations of Real and Abstract Analysis Book in PDF, Epub and Kindle
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 | : Andrew Gleason |
Publisher | : A K Peters/CRC Press |
Total Pages | : 440 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 9780867202090 |
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This classic is an ideal introduction for students into the methodology and thinking of higher mathematics. It covers material not usually taught in the more technically-oriented introductory classes and will give students a well-rounded foundation for future studies.
Author | : Marvin E. Goldstein |
Publisher | : Courier Corporation |
Total Pages | : 257 |
Release | : 2014-10-27 |
Genre | : Mathematics |
ISBN | : 0486799913 |
Download Introduction to Abstract Analysis Book in PDF, Epub and Kindle
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 | : Douglas S. Bridges |
Publisher | : |
Total Pages | : 344 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9781475771602 |
Download Foundations of Real and Abstract Analysis Book in PDF, Epub and Kindle
Author | : Herbert Amann |
Publisher | : Springer Science & Business Media |
Total Pages | : 436 |
Release | : 2006-03-14 |
Genre | : Mathematics |
ISBN | : 3764373237 |
Download Analysis I Book in PDF, Epub and Kindle
"This textbook provides an outstanding introduction to analysis. It is distinguished by its high level of presentation and its focus on the essential.'' (Zeitschrift für Analysis und ihre Anwendung 18, No. 4 - G. Berger, review of the first German edition) "One advantage of this presentation is that the power of the abstract concepts are convincingly demonstrated using concrete applications.'' (W. Grölz, review of the first German edition)
Author | : Joseph L. Taylor |
Publisher | : American Mathematical Soc. |
Total Pages | : 411 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 0821889842 |
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Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.
Author | : Jewgeni H. Dshalalow |
Publisher | : CRC Press |
Total Pages | : 583 |
Release | : 2000-09-28 |
Genre | : Mathematics |
ISBN | : 1420036890 |
Download Real Analysis Book in PDF, Epub and Kindle
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