Download Full eBooks in PDF
Foundations Of Real Numbers Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Foundations Of Real Numbers book. This book definitely worth reading, it is an incredibly well-written.
Author : Claude W. Burrill
Publisher : Unknown
Page : 182 pages
File Size : 54,5 Mb
Release : 1967
Category : Arithmetic
ISBN : STANFORD:36105033263794
Author : Elliott Mendelson
Publisher : Dover Books on Mathematics
Page : 0 pages
File Size : 41,7 Mb
Release : 2008
Category : Mathematics
ISBN : 0486457923
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 : Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 55,5 Mb
Release : 2012-10-26
Category : Mathematics
ISBN : 9780817683856
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.
Page : 411 pages
File Size : 51,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821889848
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 : Edmund Landau
Publisher : Unknown
Page : 142 pages
File Size : 40,8 Mb
Release : 2021-02
Category : Electronic
ISBN : 1950217086
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
Page : 178 pages
File Size : 42,5 Mb
Release : 2021-03-20
Category : Mathematics
ISBN : 9783030647018
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 : Edmund Landau
Publisher : Unknown
Page : 142 pages
File Size : 51,7 Mb
Release : 2021-02
Category : Electronic
ISBN : 1950217094
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 : Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher : Courier Corporation
Page : 450 pages
File Size : 43,8 Mb
Release : 2012-09-11
Category : Mathematics
ISBN : 9780486134772
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 : Ian Stewart,David Orme Tall
Publisher : Oxford University Press, USA
Page : 409 pages
File Size : 48,6 Mb
Release : 2015
Category : Mathematics
ISBN : 9780198706434
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 48,5 Mb
Release : 2013-10-16
Category : Mathematics
ISBN : 9783319015774
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 : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 52,6 Mb
Release : 1991
Category : Mathematics
ISBN : 0387974970
This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the mystery surrounding imaginary numbers in the 17th century and views some major developments of the 20th century.
Author : Howard Eves
Publisher : Courier Corporation
Page : 370 pages
File Size : 51,7 Mb
Release : 2012-04-10
Category : Mathematics
ISBN : 9780486132204
Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.
Author : K. Vela Velupillai
Publisher : Routledge
Page : 514 pages
File Size : 48,7 Mb
Release : 2012-07-26
Category : Business & Economics
ISBN : 9781134253364
Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.
Author : Solomon Feferman
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 54,7 Mb
Release : 2003
Category : Number theory
ISBN : 9780821829158
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 : John M. H. Olmsted
Publisher : Courier Dover Publications
Page : 241 pages
File Size : 43,5 Mb
Release : 2018-09-12
Category : Mathematics
ISBN : 9780486827643
Concise but thorough and systematic, this categorical discussion presents a series of step-by-step axioms. The highly accessible text includes numerous examples and more than 300 exercises, all with answers. 1962 edition.