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Author: Ralph P. Boas (Jr.)
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Book Description
Author: Ralph P. Boas (Jr.)
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Book Description
Author: Lawrence M Graves
Publisher: Courier Corporation
ISBN: 0486158136
Category : Mathematics
Languages : en
Pages : 400
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Book Description
This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.
Author: F.A. Medvedev
Publisher: Birkhäuser
ISBN: 3034886608
Category : Science
Languages : en
Pages : 265
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Book Description
To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt.
Author: K. Ko
Publisher: Springer Science & Business Media
ISBN: 1468468022
Category : Computers
Languages : en
Pages : 318
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Book Description
Starting with Cook's pioneering work on NP-completeness in 1970, polynomial complexity theory, the study of polynomial-time com putability, has quickly emerged as the new foundation of algorithms. On the one hand, it bridges the gap between the abstract approach of recursive function theory and the concrete approach of analysis of algorithms. It extends the notions and tools of the theory of computability to provide a solid theoretical foundation for the study of computational complexity of practical problems. In addition, the theoretical studies of the notion of polynomial-time tractability some times also yield interesting new practical algorithms. A typical exam ple is the application of the ellipsoid algorithm to combinatorial op timization problems (see, for example, Lovasz [1986]). On the other hand, it has a strong influence on many different branches of mathe matics, including combinatorial optimization, graph theory, number theory and cryptography. As a consequence, many researchers have begun to re-examine various branches of classical mathematics from the complexity point of view. For a given nonconstructive existence theorem in classical mathematics, one would like to find a construc tive proof which admits a polynomial-time algorithm for the solution. One of the examples is the recent work on algorithmic theory of per mutation groups. In the area of numerical computation, there are also two tradi tionally independent approaches: recursive analysis and numerical analysis.
Author: KRANTZ
Publisher: Birkhäuser
ISBN: 3034876440
Category : Science
Languages : en
Pages : 190
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Book Description
The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.
Author: A. M. Bruckner
Publisher: Springer
ISBN: 3540357769
Category : Mathematics
Languages : en
Pages : 256
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Author: Alexander Kharazishvili
Publisher: CRC Press
ISBN: 1420034847
Category : Mathematics
Languages : en
Pages : 428
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Book Description
Weierstrass and Blancmange nowhere differentiable functions, Lebesgue integrable functions with everywhere divergent Fourier series, and various nonintegrable Lebesgue measurable functions. While dubbed strange or "pathological," these functions are ubiquitous throughout mathematics and play an important role in analysis, not only as counterexamples of seemingly true and natural statements, but also to stimulate and inspire the further development of real analysis. Strange Functions in Real Analysis explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line, and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, he considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms and demonstrates that their existence follows from certain set-theoretical hypotheses, such as the Continuum Hypothesis.
Author: Brian S. Thomson
Publisher: Springer
ISBN: 3540397426
Category : Mathematics
Languages : en
Pages : 237
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Book Description
Author: N. Bourbaki
Publisher: Springer Science & Business Media
ISBN: 3642593151
Category : Mathematics
Languages : en
Pages : 338
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Book Description
This is an English translation of Bourbaki’s Fonctions d'une Variable Réelle. Coverage includes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.
Author: P. P. Petrushev
Publisher: Cambridge University Press
ISBN: 9780521177405
Category : Mathematics
Languages : en
Pages : 388
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Book Description
This 1987 book examines the approximation of real functions by real rational functions. These are a more convenient tool than polynomials, and interest in them was growing, especially after D. Newman's work in the mid-sixties. The authors present the basic achievements of the subject and also discuss some topics from complex rational approximation.
