Applied Nonstandard Analysis


Author: Martin Davis
Publisher: Courier Corporation
ISBN: 0486152340
Category: Mathematics
Page: 208
View: 4792

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This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.

Nonstandard Analysis


Author: Alain Robert
Publisher: Courier Corporation
ISBN: 9780486432793
Category: Mathematics
Page: 156
View: 7143

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This concise text is based on the axiomatic internal set theory approach. Theoretical topics include idealization, standardization, and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Applications cover invariant means, approximation of functions, differential equations, more. Exercises, hints, and solutions. "Mathematics teaching at its best." — European Journal of Physics. 1988 edition.

A Primer on Hilbert Space Theory

Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups
Author: Carlo Alabiso,Ittay Weiss
Publisher: Springer
ISBN: 3319037137
Category: Science
Page: 255
View: 1723

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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.

Nonstandard Methods in Stochastic Analysis and Mathematical Physics


Author: Sergio Albeverio,Jens Erik Fenstad,Raphael Høegh-Krohn,Tom Lindstrøm
Publisher: Courier Dover Publications
ISBN: 0486468992
Category: Mathematics
Page: 526
View: 5204

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Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.

A First Course in Functional Analysis


Author: Martin Davis
Publisher: Courier Corporation
ISBN: 0486499839
Category: Mathematics
Page: 110
View: 4182

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Designed for undergraduate mathematics majors, this introductory treatment is based on the distinguished author's lecture notes. The self-contained exposition of Gelfand's proof of Wiener's theorem explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and analytic functions into a Banach space. 1966 edition.

Mathematical Logic


Author: Stephen Cole Kleene
Publisher: Courier Corporation
ISBN: 0486317072
Category: Mathematics
Page: 416
View: 4265

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Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

Counterexamples in Analysis


Author: Bernard R. Gelbaum,John M. H. Olmsted
Publisher: Courier Corporation
ISBN: 9780486428758
Category: Mathematics
Page: 195
View: 7599

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These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.

The Diagonal Infinity

Problems of Multiple Scales
Author: H. M. Hubey
Publisher: World Scientific
ISBN: 9789810230814
Category: Mathematics
Page: 522
View: 7154

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CD-ROM consists of four directories: parametric plots, fractals, etc; nonlinear differential equations; fuzzy logics; and graphics files.

Mathe-Magie

Verblüffende Tricks für blitzschnelles Kopfrechnen und ein phänomenales Zahlengedächtnis
Author: Arthur Benjamin,Michael Shermer
Publisher: Heyne Verlag
ISBN: 3641148472
Category: Self-Help
Page: 304
View: 8409

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Zaubern mit Zahlen – wer dieses Buch gelesen hat, muss PISA nicht mehr fürchten Wer glaubt, Mathematik sei eine trockene Angelegenheit und Kopfrechnen eine unnötige Quälerei, der irrt sich gewaltig. Denn nach der Lektüre dieses Buches ist es für jeden ein Leichtes, Rechenoperationen mit vier- und fünfstelligen Zahlen in Sekundenschnelle im Kopf auszuführen. Und was wie Zauberei wirkt, ist letztendlich nichts anderes als mathematische Logik, die jedermann beherrschen kann und die dazu noch richtig Spaß macht. • So wird Kopfrechnen kinderleicht! • Mit zahlreichen Übungen und Lösungen

Geschichte der Analysis


Author: Hans Niels Jahnke
Publisher: Spektrum Akademischer Verlag
ISBN: 9783827403926
Category: Mathematics
Page: 564
View: 1521

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"Geschichte der Analysis" ist von einem internationalen Expertenteam geschrieben und stellt die gegenwärtig umfassendste Darstellung der Herausbildung und Entwicklung dieser mathematischen Kerndisziplin dar. Der tiefgreifende begriffliche Wandel, den die Analysis im Laufe der Zeit durchgemacht hat, wird ebenso dargestellt, wie auch der Einfluß, den vor allem physikalische Probleme gehabt haben. Biographische und philosophische Hintergründe werden ausgeleuchtet und ihre Relevanz für die Theorieentwicklung gezeigt. Neben der eigentlichen Geschichte der Analysis bis ungefähr 1900 enthält das Buch Spezialkapitel über die Entwicklung der analytischen Mechanik im 18. Jahrhundert, Randwertprobleme der mathematischen Physik im 19. Jahrhundert, die Theorie der komplexen Funktionen, die Grundlagenkrise sowie historische Überblicke über die Variationsrechnung, Differentialgleichungen und Funktionalanalysis.

Georg Cantor 1845-1918

Schöpfer der Mengenlehre
Author: Andor Kertész,Manfred Stern
Publisher: N.A
ISBN: N.A
Category: Mathematicians
Page: 118
View: 433

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Grundzüge der Mengenlehre


Author: Felix Hausdorff
Publisher: American Mathematical Soc.
ISBN: 9780828400619
Category: Mathematics
Page: 476
View: 8813

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This reprint of the original 1914 edition of this famous work contains many topics that had to be omitted from later editions, notably, Symmetric Sets, Principle of Duality, most of the ``Algebra'' of Sets, Partially Ordered Sets, Arbitrary Sets of Complexes, Normal Types, Initial and Final Ordering, Complexes of Real Numbers, General Topological Spaces, Euclidean Spaces, the Special Methods Applicable in the Euclidean Plane, Jordan's Separation Theorem, the Theory of Content and Measure, the Theory of the Lebesgue Integral. The text is in German.