1# Library to Find Best eBook for Read
Author : Claude W. Burrill
Release : 1967
Genre : Arithmetic
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Foundations of Real Numbers by : Claude W. Burrill
Download or read book Foundations of Real Numbers written by Claude W. Burrill. This book was released on 1967. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Elliott Mendelson
Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 925/5 ( reviews)
Book Synopsis Number Systems and the Foundations of Analysis by : Elliott Mendelson
Download or read book Number Systems and the Foundations of Analysis written by Elliott Mendelson. This book was released on 2008. 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 : Sergei Ovchinnikov
Release : 2021-03-20
Genre : Mathematics
Kind : eBook
Book Rating : 013/5 ( reviews)
Book Synopsis Real Analysis: Foundations by : Sergei Ovchinnikov
Download or read book Real Analysis: Foundations written by Sergei Ovchinnikov. This book was released on 2021-03-20. 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 : John Stillwell
Release : 2013-10-16
Genre : Mathematics
Kind : eBook
Book Rating : 77X/5 ( reviews)
Book Synopsis The Real Numbers by : John Stillwell
Download or read book The Real Numbers written by John Stillwell. This book was released on 2013-10-16. 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
Release : 2021-02
Genre :
Kind : eBook
Book Rating : 083/5 ( reviews)
Book Synopsis Foundations of Analysis by : Edmund Landau
Download or read book Foundations of Analysis written by Edmund Landau. This book was released on 2021-02. 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.
