metric spaces springer undergraduate mathematics series

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Metric Spaces

Author : Mícheál O'Searcoid
ISBN : 1846286271
Genre : Mathematics
File Size : 49. 10 MB
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The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.

A Primer On Hilbert Space Theory

Author : Carlo Alabiso
ISBN : 9783319037134
Genre : Science
File Size : 89. 12 MB
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This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

Special Relativity

Author : Nicholas M.J. Woodhouse
ISBN : 9783540466765
Genre : Science
File Size : 59. 19 MB
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Perspectives Of Systems Informatics

Author : Amir Pnueli
ISBN : 9783642114861
Genre : Computers
File Size : 49. 80 MB
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This volume contains the ?nal proceedings of the 7th International Andrei Ershov Memorial Conference on Perspectives of System Informatics Akad- gorodok (Novosibirsk, Russia), June 15–19, 2009. PSI is a forum for academic and industrial researchers, developers and users working on topics relating to computer, software and information sciences. The conference serves to bridge the gaps between di?erent communities whose - searchareasarecoveredbybutnotlimitedtofoundationsofprogramandsystem development and analysis, programming methodology and softwareengineering, and information technologies. PSI 2009 was dedicated to the memory of a prominent scientist, academician Andrei Ershov (1931–1988),and to a signi?cant date in the history of computer science in the country, namely, the 50th anniversary of the Programming - partment founded by Andrei Ershov. Initially, the department was a part of the Institute of Mathematics and later, in 1964, it joined the newly established Computing Center of the Siberian Branch of the USSR Academy of Sciences. Andrei Ershov, who was responsible for forming the department, gathered a team of young graduates from leading Soviet universities. The ?rst signi?cant project of the department was aimed at the development of ALPHA system, an optimizing compiler for an extension of Algol 60 implemented on a Soviet c- puterM-20. Later,theresearchersofthedepartmentcreatedtheAlgibr,Epsilon, Sigma, and Alpha-6 programming systems for the BESM-6 computers. The list of their achievements also includes the ?rst Soviet time-sharing system AIST-0, the multi-language system BETA, research projects in arti?cial intelligence and parallel programming, integrated tools for text processing and publishing, and many others.

Advances In Spatial And Temporal Databases

Author : Nikos Mamoulis
ISBN : 9783642029813
Genre : Business & Economics
File Size : 57. 46 MB
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This volume constitutes the refereed proceedings of the 11th International Symposium on Spatial and Temporal Databases, SSTD 2009, held in Aalborg, Denmark, in July 2009. The 20 revised full papers presented together with 3 keynotes, 7 short papers, and 10 demonstration papers, were thoroughly reviewed and selected from a total of 62 research submissions and 11 demonstration submissions. The papers are organized in topical sections on spatial and flow networks, integrity and security, uncertain data and new technologies, indexing and monitoring moving objects, advanced queries, as well as on models and languages.

Lineare Funktionalanalysis

Author : Hans Wilhelm Alt
ISBN : 9783642222610
Genre : Mathematics
File Size : 36. 17 MB
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Die lineare Funktionalanalysis ist ein Teilgebiet der Mathematik, das Algebra mit Topologie und Analysis verbindet. Das Buch führt in das Fachgebiet ein, dabei bezieht es sich auf Anwendungen in Mathematik und Physik. Neben den vollständigen Beweisen aller mathematischen Sätze enthält der Band zahlreiche Aufgaben, meist mit Lösungen. Für die Neuauflage wurden die Inhalte komplett überarbeitet. Das Standardwerk auf dem Gebiet der Funktionalanalysis richtet sich insbesondere an Leser mit Interesse an Anwendungen auf Differentialgleichungen.

Lineare Algebra

Author : Gilbert Strang
ISBN : 9783642556319
Genre : Mathematics
File Size : 82. 65 MB
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Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

From Real To Complex Analysis

Author : R. H. Dyer
ISBN : 9783319062099
Genre : Mathematics
File Size : 46. 79 MB
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The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology. Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectedness and various forms of homotopy. The final chapter develops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using the approach due to Dixon. Special features are the inclusion of proofs of Montel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included in each of the chapters, detailed solutions of the majority of which are given at the end. From Real to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding in analysis; in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be made.

Distributionen Und Hilbertraumoperatoren

Author : Philippe Blanchard
ISBN : 321182507X
Genre : Science
File Size : 68. 20 MB
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Das Buch bietet eine Einführung in die zum Studium der Theoretischen Physik notwendigen mathematischen Grundlagen. Der erste Teil des Buches beschäftigt sich mit der Theorie der Distributionen und vermittelt daneben einige Grundbegriffe der linearen Funktionalanalysis. Der zweite Teil baut darauf auf und gibt eine auf das Wesentliche beschränkte Einführung in die Theorie der linearen Operatoren in Hilbert-Räumen. Beide Teile werden von je einer Übersicht begleitet, die die zentralen Ideen und Begriffe knapp erläutert und den Inhalt kurz beschreibt. In den Anhängen werden einige grundlegende Konstruktionen und Konzepte der Funktionalanalysis dargestellt und wichtige Konsequenzen entwickelt.

Essential Real Analysis

Author : Michael Field
ISBN : 9783319675466
Genre : Mathematics
File Size : 21. 87 MB
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This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.

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