Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh,W.E. Pfaffenberger

Publisher: Courier Corporation

ISBN: 0486134776

Category: Mathematics

Page: 448

View: 7782

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.
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Number Systems and the Foundations of Analysis

Author: Elliott Mendelson

Publisher: Courier Corporation

ISBN: 0486457923

Category: Mathematics

Page: 358

View: 6431

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.
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Foundations of Analysis

Author: David French Belding,Kevin J. Mitchell

Publisher: Courier Corporation

ISBN: 048646296X

Category: Mathematics

Page: 427

View: 384

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.
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The Foundations of Computability Theory

Author: Borut Robič

Publisher: Springer

ISBN: 3662448084

Category: Computers

Page: 331

View: 1478

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.
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Mathematical Foundations of Elasticity

Author: Jerrold E. Marsden,Thomas J. R. Hughes

Publisher: Courier Corporation

ISBN: 0486142272

Category: Technology & Engineering

Page: 576

View: 6891

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.
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Foundations and Fundamental Concepts of Mathematics

Author: Howard Whitley Eves

Publisher: Courier Corporation

ISBN: 9780486696096

Category: Mathematics

Page: 344

View: 4477

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.
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Foundations of Probability

Author: Alfred Renyi

Publisher: Courier Corporation

ISBN: 0486462617

Category: Mathematics

Page: 366

View: 4729

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.
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Das Spiel der Logik

Author: Lewis Carroll

Publisher: Klett-Cotta

ISBN: 9783772819988

Category: Games

Page: 119

View: 8027

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Lineare Algebra

Author: Gilbert Strang

Publisher: Springer-Verlag

ISBN: 3642556310

Category: Mathematics

Page: 656

View: 2352

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.
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Introduction to Analysis

Author: Maxwell Rosenlicht

Publisher: Courier Corporation

ISBN: 0486134687

Category: Mathematics

Page: 272

View: 1707

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.
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The Continuum

A Critical Examination of the Foundation of Analysis

Author: Hermann Weyl

Publisher: Courier Corporation

ISBN: 0486679829

Category: Mathematics

Page: 130

View: 8950

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.
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Foundations of the Theory of Probability

Second English Edition

Author: A.N. Kolmogorov

Publisher: Courier Dover Publications

ISBN: 0486829790

Category: Mathematics

Page: 96

View: 399

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.
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Analysis II

Author: Vladimir A. Zorich

Publisher: Springer

ISBN: 9783540462316

Category: Mathematics

Page: 708

View: 5081

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.
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The History of the Calculus and Its Conceptual Development

Author: Carl B. Boyer

Publisher: Courier Corporation

ISBN: 0486175383

Category: Mathematics

Page: 368

View: 3466

Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz.
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Mathematical Foundations of Image Processing and Analysis

Author: Jean-Charles Pinoli

Publisher: John Wiley & Sons

ISBN: 1118984552

Category: Technology & Engineering

Page: 496

View: 9307

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.
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Foundations of Mathematical Logic

Author: Haskell B. Curry

Publisher: Courier Corporation

ISBN: 0486153053

Category: Mathematics

Page: 416

View: 782

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.
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