An Introduction To The Theory Of Real Functions
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Author | : Stanislaw Lojasiewicz |
Publisher | : |
Total Pages | : 248 |
Release | : 1988-08-18 |
Genre | : Mathematics |
ISBN | : |
A concise, classical approach to the theory of real functions, set in the topological context of metric spaces. Newly translated by G. H. Lawden of the Univ. of Sussex and expanded from the earlier Polish editions to include remarks on the extension of finitely many additive functions to a measure, construction of a continuous, non-differential function of a general type, the Banach-Vitali theorem, and Stepanov's theorem. Prerequisites are set theory, topology, and calculus.
Author | : Jewgeni H. Dshalalow |
Publisher | : CRC Press |
Total Pages | : 583 |
Release | : 2000-09-28 |
Genre | : Mathematics |
ISBN | : 1420036890 |
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 | : John Meigs Hubbell Olmsted |
Publisher | : |
Total Pages | : 332 |
Release | : 1956 |
Genre | : Mathematics |
ISBN | : |
Author | : Claude Chevalley |
Publisher | : American Mathematical Soc. |
Total Pages | : 204 |
Release | : 1951-12-31 |
Genre | : Mathematics |
ISBN | : 0821815067 |
Presents an approach to algebraic geometry of curves that is treated as the theory of algebraic functions on the curve. This book discusses such topics as the theory of divisors on a curve, the Riemann-Roch theorem, $p$-adic completion, and extensions of the fields of functions (covering theory) and of the fields of constants.
Author | : K. Ko |
Publisher | : Springer Science & Business Media |
Total Pages | : 318 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1468468022 |
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 | : N. Bourbaki |
Publisher | : Springer Science & Business Media |
Total Pages | : 343 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 3642593151 |
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 | : A. C. M. van Rooij |
Publisher | : Cambridge University Press |
Total Pages | : 222 |
Release | : 1982-03-25 |
Genre | : Mathematics |
ISBN | : 9780521239448 |
When considering a mathematical theorem one ought not only to know how to prove it but also why and whether any given conditions are necessary. All too often little attention is paid to to this side of the theory and in writing this account of the theory of real functions the authors hope to rectify matters. They have put the classical theory of real functions in a modern setting and in so doing have made the mathematical reasoning rigorous and explored the theory in much greater depth than is customary. The subject matter is essentially the same as that of ordinary calculus course and the techniques used are elementary (no topology, measure theory or functional analysis). Thus anyone who is acquainted with elementary calculus and wishes to deepen their knowledge should read this.
Author | : John Meigs Hubbell Olmsted |
Publisher | : |
Total Pages | : 646 |
Release | : 1959 |
Genre | : Functions of real variables |
ISBN | : |
Author | : Ralph P. Boas (Jr.) |
Publisher | : |
Total Pages | : 196 |
Release | : 1972 |
Genre | : |
ISBN | : |
Author | : I P (Isidor Pavlovich) Natanson |
Publisher | : Hassell Street Press |
Total Pages | : 288 |
Release | : 2021-09-09 |
Genre | : |
ISBN | : 9781013315244 |
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