Foundations of Mathematical Analysis


Author: Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher: Courier Corporation
ISBN: 0486134776
Category: Mathematics
Page: 448
View: 5792

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Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Number Systems and the Foundations of Analysis


Author: Elliott Mendelson
Publisher: Courier Corporation
ISBN: 0486457923
Category: Mathematics
Page: 358
View: 6899

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Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.

The Foundations of Computability Theory


Author: Borut Robič
Publisher: Springer
ISBN: 3662448084
Category: Computers
Page: 331
View: 1039

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This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.

Foundations of Analysis


Author: David French Belding,Kevin J. Mitchell
Publisher: Courier Corporation
ISBN: 048646296X
Category: Mathematics
Page: 427
View: 8914

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This treatment develops the real number system and the theory of calculus on the real line, extending the theory to real and complex planes. Designed for students with one year of calculus, it features extended discussions of key ideas and detailed proofs of difficult theorems. 1991 edition.

Mathematical Foundations of Elasticity


Author: Jerrold E. Marsden,Thomas J. R. Hughes
Publisher: Courier Corporation
ISBN: 0486142272
Category: Technology & Engineering
Page: 576
View: 4884

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Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.

Foundations and Fundamental Concepts of Mathematics


Author: Howard Whitley Eves
Publisher: Courier Corporation
ISBN: 9780486696096
Category: Mathematics
Page: 344
View: 1299

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This third edition of a popular, well-received text offers undergraduates an opportunity to obtain an overview of the historical roots and the evolution of several areas of mathematics. The selection of topics conveys not only their role in this historical development of mathematics but also their value as bases for understanding the changing nature of mathematics. Among the topics covered in this wide-ranging text are: mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, the real numbers system, sets, logic and philosophy and more. The emphasis on axiomatic procedures provides important background for studying and applying more advanced topics, while the inclusion of the historical roots of both algebra and geometry provides essential information for prospective teachers of school mathematics. The readable style and sets of challenging exercises from the popular earlier editions have been continued and extended in the present edition, making this a very welcome and useful version of a classic treatment of the foundations of mathematics. "A truly satisfying book." — Dr. Bruce E. Meserve, Professor Emeritus, University of Vermont.

Foundations of Probability


Author: Alfred Renyi
Publisher: Courier Corporation
ISBN: 0486462617
Category: Mathematics
Page: 366
View: 5936

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Introducing many innovations in content and methods, this book involves the foundations, basic concepts, and fundamental results of probability theory. Geared toward readers seeking a firm basis for study of mathematical statistics or information theory, it also covers the mathematical notions of experiments and independence. 1970 edition.

Introduction to Analysis


Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 0486134687
Category: Mathematics
Page: 272
View: 3380

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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

Foundations of the Theory of Probability

Second English Edition
Author: A.N. Kolmogorov
Publisher: Courier Dover Publications
ISBN: 0486829790
Category: Mathematics
Page: 96
View: 7669

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This famous little book remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of probability and to historians of modern mathematics. 1956 second edition.

The Continuum

A Critical Examination of the Foundation of Analysis
Author: Hermann Weyl
Publisher: Courier Corporation
ISBN: 0486679829
Category: Mathematics
Page: 130
View: 2092

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Concise classic by great mathematician and physicist deals with logic and mathematics of set and function, concept of number and the continuum. Bibliography. Originally published 1918.

Analysis II


Author: Vladimir A. Zorich
Publisher: Springer
ISBN: 9783540462316
Category: Mathematics
Page: 708
View: 3834

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Ausführlich, klar, exakt, solide: die Anfänge der Analysis in 2 Bänden. Von der Einführung der reellen Zahlen bis hin zu fortgeschrittenen Themen wie u.a. Differenzialformen auf Mannigfaltigkeiten, asymptotische Betrachtungen, Fourier-, Laplace- und Legendre-Transformationen, elliptische Funktionen und Distributionen. Deutlich auf naturwissenschaftliche Fragen ausgerichtet, erläutert dieses Werk detailliert Begriffe, Inhalte und Sätze der Integral- und Differenzialrechnung. Die Fülle hilfreicher Beispiele, Aufgaben und Anwendungen ist selten in Analysisbüchern zu finden. Band 2 beschreibt den heutigen Stand der klassischen Analysis.

The Analytical Foundations of Celestial Mechanics


Author: Aurel Wintner
Publisher: Courier Corporation
ISBN: 0486780600
Category: Science
Page: 464
View: 9070

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With this 1941 monograph, Aurel Wintner joined Poincaré, Birkhoff, and others in placing celestial mechanics on a sound mathematical basis. The product of many years of work by the author, it remains an extremely valuable contribution to the literature of this field. Starting with a review of dynamical operations, the treatment advances to local and non-local questions, dynamical systems, the problem of two bodies and the problem of several bodies, and an introduction to the restricted problem. Suitable for advanced undergraduates and graduate students of physics, the text is amply supplemented by a substantial section of notes and references in which a great deal of the historical literature from which it derives is discussed.

Mathematical Foundations of Image Processing and Analysis


Author: Jean-Charles Pinoli
Publisher: John Wiley & Sons
ISBN: 1118984552
Category: Technology & Engineering
Page: 496
View: 9760

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Mathematical Imaging is currently a rapidly growing field inapplied mathematics, with an increasing need for theoreticalmathematics. This book, the second of two volumes, emphasizes the role ofmathematics as a rigorous basis for imaging sciences. It provides acomprehensive and convenient overview of the key mathematicalconcepts, notions, tools and frameworks involved in the variousfields of gray-tone and binary image processing and analysis, byproposing a large, but coherent, set of symbols and notations, acomplete list of subjects and a detailed bibliography. Itestablishes a bridge between the pure and applied mathematicaldisciplines, and the processing and analysis of gray-tone andbinary images. It is accessible to readers who have neitherextensive mathematical training, nor peer knowledge in ImageProcessing and Analysis. It is a self-contained book focusing on the mathematicalnotions, concepts, operations, structures, and frameworks that arebeyond or involved in Image Processing and Analysis. The notationsare simplified as far as possible in order to be more explicativeand consistent throughout the book and the mathematical aspects aresystematically discussed in the image processing and analysiscontext, through practical examples or concrete illustrations.Conversely, the discussed applicative issues allow the role ofmathematics to be highlighted. Written for a broad audience – students, mathematicians,image processing and analysis specialists, as well as otherscientists and practitioners – the author hopes that readerswill find their own way of using the book, thus providing amathematical companion that can help mathematicians become morefamiliar with image processing and analysis, and likewise, imageprocessing and image analysis scientists, researchers and engineersgain a deeper understanding of mathematical notions andconcepts.

Partielle Differentialgleichungen

Eine Einführung
Author: Walter A. Strauss
Publisher: Springer-Verlag
ISBN: 366312486X
Category: Mathematics
Page: 458
View: 1366

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Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.

Proof Theory


Author: Gaisi Takeuti
Publisher: Courier Corporation
ISBN: 0486490734
Category: Mathematics
Page: 490
View: 5663

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Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics. The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.

Foundations of Mathematical Logic


Author: Haskell B. Curry
Publisher: Courier Corporation
ISBN: 0486153053
Category: Mathematics
Page: 416
View: 7368

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Comprehensive graduate-level account of constructive theory of first-order predicate calculus covers formal methods: algorithms and epitheory, brief treatment of Markov's approach to algorithms, elementary facts about lattices, logical connectives, and more. 1963 edition.