Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Download Foundations Of Real Numbers full books in PDF, epub, and Kindle. Read online Foundations Of Real Numbers ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author : Claude W. Burrill
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.F/5 ( download)
Download or read book Foundations of Real Numbers written by Claude W. Burrill and published by . This book was released on 1967 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Elliott Mendelson
Publisher : Dover Books on Mathematics
ISBN 13 : 9780486457925
Total Pages : 0 pages
Book Rating : 4.4/5 (579 download)
Download or read book Number Systems and the Foundations of Analysis written by Elliott Mendelson and published by Dover Books on Mathematics. This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 331901577X
Total Pages : 253 pages
Book Rating : 4.3/5 (19 download)
Download or read book The Real Numbers written by John Stillwell and published by Springer Science & Business Media. This book was released on 2013-10-16 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.
Author : Edmund Landau
Publisher :
ISBN 13 : 9781950217083
Total Pages : 142 pages
Book Rating : 4.2/5 (17 download)
Download or read book Foundations of Analysis written by Edmund Landau and published by . This book was released on 2021-02 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Natural numbers, zero, negative integers, rational numbers, irrational numbers, real numbers, complex numbers, . . ., and, what are numbers? The most accurate mathematical answer to the question is given in this book.
Author : Sergei Ovchinnikov
Publisher : Springer Nature
ISBN 13 : 3030647013
Total Pages : 178 pages
Book Rating : 4.0/5 (36 download)
Download or read book Real Analysis: Foundations written by Sergei Ovchinnikov and published by Springer Nature. This book was released on 2021-03-20 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.
Author : Richard Johnsonbaugh
Publisher : Courier Corporation
ISBN 13 : 0486134776
Total Pages : 450 pages
Book Rating : 4.4/5 (861 download)
Download or read book Foundations of Mathematical Analysis written by Richard Johnsonbaugh and published by Courier Corporation. This book was released on 2012-09-11 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Garret Sobczyk
Publisher : Springer Science & Business Media
ISBN 13 : 0817683852
Total Pages : 373 pages
Book Rating : 4.8/5 (176 download)
Download or read book New Foundations in Mathematics written by Garret Sobczyk and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
Author : Joseph L. Taylor
Publisher : American Mathematical Soc.
ISBN 13 : 0821889842
Total Pages : 411 pages
Book Rating : 4.8/5 (218 download)
Download or read book Foundations of Analysis written by Joseph L. Taylor and published by American Mathematical Soc.. This book was released on 2012 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.
Author : Chidume O. C
Publisher : Ibadan University Press
ISBN 13 : 9789788456322
Total Pages : 404 pages
Book Rating : 4.4/5 (563 download)
Download or read book Foundations of Mathematical Real Analysis: Computer Science Mathematical Analysis written by Chidume O. C and published by Ibadan University Press. This book was released on 2019-08-29 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a serious introduction to the studyof mathematical analysis. In contrast to calculus, mathematical analysis does not involve formula manipulation, memorizing integrals or applications to other fields of science. No.It involves geometric intuition and proofs of theorems. It ispure mathematics! Given the mathematical preparation andinterest of our intended audience which, apart from mathematics majors, includes students of statistics, computer science, physics, students of mathematics education and students of engineering, we have not given the axiomatic development of the real number system. However, we assumethat the reader is familiar with sets and functions. This bookis divided into two parts. Part I covers elements of mathematical analysis which include: the real number system, bounded subsets of real numbers, sequences of real numbers, monotone sequences, Bolzano-Weierstrass theorem, Cauchysequences and completeness of R, continuity, intermediatevalue theorem, continuous maps on [a, b], uniform continuity, closed sets, compact sets, differentiability, series of nonnegative real numbers, alternating series, absolute and conditional convergence; and re-arrangement of series. The contents of Part I are adequate for a semester course in mathematical analysis at the 200 level. Part II covers Riemannintegrals. In particular, the Riemann integral, basic properties of Riemann integral, pointwise convergence of sequencesof functions, uniform convergence of sequences of functions, series of real-valued functions: term by term differentiationand integration; power series: uniform convergence of powerseries; uniform convergence at end points; and equi-continuity are covered. Part II covers the standard syllabus for asemester mathematical analysis course at the 300 level. Thetopics covered in this book provide a reasonable preparationfor any serious study of higher mathematics. But for one toreally benefit from the book, one must spend a great deal ofixtime on it, studying the contents very carefully and attempting all the exercises, especially the miscellaneous exercises atthe end of the book. These exercises constitute an importantintegral part of the book.Each chapter begins with clear statements of the most important theorems of the chapter. The proofs of these theoremsgenerally contain fundamental ideas of mathematical analysis. Students are therefore encouraged to study them verycarefully and to discover these id
Author : Tim Maudlin
Publisher :
ISBN 13 : 0198701306
Total Pages : 374 pages
Book Rating : 4.1/5 (987 download)
Download or read book New Foundations for Physical Geometry written by Tim Maudlin and published by . This book was released on 2014-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Author : Solomon Feferman
Publisher : American Mathematical Soc.
ISBN 13 : 0821829157
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Number Systems: Foundations of Algebra and Analysis written by Solomon Feferman and published by American Mathematical Soc.. This book was released on 2003 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers, and complex numbers. This second edition expands upon the list of suggestions for further reading in Appendix III. From the Preface: ``The present book basically takes for granted the non-constructive set-theoretical foundation of mathematics, which is tacitly if not explicitly accepted by most working mathematicians but which I have since come to reject. Still, whatever one's foundational views, students must be trained in this approach in order to understand modern mathematics. Moreover, most of the material of the present book can be modified so as to be acceptable under alternative constructive and semi-constructive viewpoints, as has been demonstrated in more advanced texts and research articles.''
Author : Raymond L. Wilder
Publisher : Courier Corporation
ISBN 13 : 0486276201
Total Pages : 354 pages
Book Rating : 4.4/5 (862 download)
Download or read book Introduction to the Foundations of Mathematics written by Raymond L. Wilder and published by Courier Corporation. This book was released on 2013-09-26 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.
Author : Miklós Laczkovich
Publisher : Springer
ISBN 13 : 1493927663
Total Pages : 486 pages
Book Rating : 4.4/5 (939 download)
Download or read book Real Analysis written by Miklós Laczkovich and published by Springer. This book was released on 2015-10-08 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.
Author : Steven G. Krantz
Publisher : CRC Press
ISBN 13 : 148222075X
Total Pages : 312 pages
Book Rating : 4.4/5 (822 download)
Download or read book Foundations of Analysis written by Steven G. Krantz and published by CRC Press. This book was released on 2014-10-20 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Analysis covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way, it helps students understand the key ideas and apply the theorems. The book's accessible approach will appeal to a wide range of students and instructors.Each section begins with a boxed introduction that familiarizes
Author : Edmund Landau
Publisher :
ISBN 13 : 9781950217090
Total Pages : 142 pages
Book Rating : 4.2/5 (17 download)
Download or read book Foundations of Analysis written by Edmund Landau and published by . This book was released on 2021-02 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Natural numbers, zero, negative integers, rational numbers, irrational numbers, real numbers, complex numbers, . . ., and, what are numbers? The most accurate mathematical answer to the question is given in this book.
Author : Kenneth Kunen
Publisher :
ISBN 13 : 9781904987147
Total Pages : 251 pages
Book Rating : 4.9/5 (871 download)
Download or read book The Foundations of Mathematics written by Kenneth Kunen and published by . This book was released on 2009 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.
Author : Steven G. Krantz
Publisher : CRC Press
ISBN 13 : 1498777708
Total Pages : 306 pages
Book Rating : 4.4/5 (987 download)
Download or read book Real Analysis and Foundations, Fourth Edition written by Steven G. Krantz and published by CRC Press. This book was released on 2016-12-12 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Readable yet Rigorous Approach to an Essential Part of Mathematical Thinking Back by popular demand, Real Analysis and Foundations, Third Edition bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier analysis, metric spaces and applications, and differential equations. New to the Third Edition Offering a more streamlined presentation, this edition moves elementary number systems and set theory and logic to appendices and removes the material on wavelet theory, measure theory, differential forms, and the method of characteristics. It also adds a chapter on normed linear spaces and includes more examples and varying levels of exercises. Extensive Examples and Thorough Explanations Cultivate an In-Depth Understanding This best-selling book continues to give students a solid foundation in mathematical analysis and its applications. It prepares them for further exploration of measure theory, functional analysis, harmonic analysis, and beyond.
