Book Description
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 : Edmund Landau
Publisher :
Page : 142 pages
File Size : 36,12 MB
Release : 2021-02
Category :
ISBN : 9781950217083
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 : Joseph L. Taylor
Publisher : American Mathematical Soc.
Page : 411 pages
File Size : 39,3 MB
Release : 2012
Category : Mathematics
ISBN : 0821889842
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 : Richard Johnsonbaugh
Publisher : Courier Corporation
Page : 450 pages
File Size : 23,85 MB
Release : 2012-09-11
Category : Mathematics
ISBN : 0486134776
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 : Elliott Mendelson
Publisher : Dover Books on Mathematics
Page : 0 pages
File Size : 26,45 MB
Release : 2008
Category : Mathematics
ISBN : 9780486457925
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 : Eric Schechter
Publisher : Academic Press
Page : 907 pages
File Size : 30,1 MB
Release : 1996-10-24
Category : Mathematics
ISBN : 0080532993
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
Author : Avner Friedman
Publisher : Courier Corporation
Page : 276 pages
File Size : 35,29 MB
Release : 1982-01-01
Category : Mathematics
ISBN : 9780486640624
Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.
Author : Steven G. Krantz
Publisher : CRC Press
Page : 312 pages
File Size : 25,5 MB
Release : 2014-10-20
Category : Mathematics
ISBN : 148222075X
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 : K. G. Binmore
Publisher :
Page : 0 pages
File Size : 13,65 MB
Release : 1980
Category :
ISBN :
Author : Herbert S. Gaskill
Publisher : HarperCollins Publishers
Page : 664 pages
File Size : 45,80 MB
Release : 1989
Category : Mathematics
ISBN :
Author : Sergei Ovchinnikov
Publisher : Springer Nature
Page : 178 pages
File Size : 24,20 MB
Release : 2021-03-20
Category : Mathematics
ISBN : 3030647013
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.