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Author: A. A. Kirillov Publisher: Springer Science & Business Media ISBN: 1461381533 Category : Mathematics Languages : en Pages : 351
Book Description
Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.
Author: A. A. Kirillov Publisher: Springer Science & Business Media ISBN: 1461381533 Category : Mathematics Languages : en Pages : 351
Book Description
Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.
Author: Duke Okes Publisher: Quality Press ISBN: 0873899822 Category : Business & Economics Languages : en Pages : 250
Book Description
This best-seller can help anyone whose role is to try to find specific causes for failures. It provides detailed steps for solving problems, focusing more heavily on the analytical process involved in finding the actual causes of problems. It does this using figures, diagrams, and tools useful for helping to make our thinking visible. This increases our ability to see what is truly significant and to better identify errors in our thinking. In the sections on finding root causes, this second edition now includes: more examples on the use of multi-vari charts; how thought experiments can help guide data interpretation; how to enhance the value of the data collection process; cautions for analyzing data; and what to do if one cant find the causes. In its guidance on solution identification, biomimicry and TRIZ have been added as potential solution identification techniques. In addition, the appendices have been revised to include: an expanded breakdown of the 7 Ms, which includes more than 50 specific possible causes; forms for tracking causes and solutions, which can help maintain alignment of actions; techniques for how to enhance the interview process; and example responses to problem situations that the reader can analyze for appropriateness.
Author: Asuman G. Aksoy Publisher: Springer Science & Business Media ISBN: 1441912967 Category : Mathematics Languages : en Pages : 257
Book Description
Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.
Author: John Reynolds Publisher: Routledge ISBN: 1317920899 Category : Education Languages : en Pages : 162
Book Description
This book explores the relationship between problem analysis, leadership, decision making, and change. It contains many problem scenarios, case studies, and vignettes.
Author: Daniel Alpay Publisher: Birkhäuser ISBN: 3319421816 Category : Mathematics Languages : en Pages : 592
Book Description
This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.
Author: Rachel Meltzer Publisher: Routledge ISBN: 1351807358 Category : Social Science Languages : en Pages : 227
Book Description
Drawing extensively from real-life cases, Policy Analysis as Problem Solving helps students develop the analytic skills necessary to advise government officials and nonprofit executives on a wide range of policy issues. Unlike other texts, Policy Analysis as Problem Solving employs a pragmatic, heterodox approach to the field. Whereas most texts on policy analysis are anchored in microeconomics, emphasizing economic efficiency, this book takes a broader view, using realistic examples to illustrate the full scope of policy analysis. The book provides succinct but thorough discussions of the key elements of the policy-analytic process, including problem definition, objectives and criteria, development of alternative policy options, and analysis of these alternatives. The text’s practical approach and extensive downloadable resources—which include interviews, case studies, and further readings—will be of enormous benefit to both students and instructors of policy analysis.
Author: Fredrik Milani Publisher: Springer ISBN: 3030057194 Category : Computers Languages : en Pages : 429
Book Description
This book frames business analysis in the context of digital technologies. It introduces modern business analysis techniques, including a selection of those in the Business Analysis Body of Knowledge (BABOK) by the International Institute of Business Analysis (IIBA), and exemplifies them by means of digital technologies applied to solve problems or exploit new business opportunities. It also includes in-depth case studies in which business problems and opportunities, drawn from real-world scenarios, are mapped to digital solutions. The work is summarized in seven guiding principles that should be followed by every business analyst. This book is intended mainly for students in business informatics and related areas, and for professionals who want to acquire a solid background for their daily work. It is suitable both for courses and for self-study. Additional teaching materials such as lecture videos, slides, question bank, exams, and seminar materials are accessible on the companion web-page.
Author: A. A. Kirillov
Author: A. A. Kirillov
Author: Duke Okes
Author: Asuman G. Aksoy
Author: John Reynolds
Author: Daniel Alpay
Author: Arthur Shirle Elstein
Author: Rachel Meltzer
Author: Fredrik Milani
Author: John C. Burkill
Author: John E. Eck