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Author : Elliott Mendelson
Publisher : Unknown
Page : 392 pages
File Size : 52,8 Mb
Release : 1985
Category : Mathematics
ISBN : CORNELL:31924001102726
Author : Solomon Feferman
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 55,5 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 : Joseph L. Taylor
Publisher : American Mathematical Soc.
Page : 411 pages
File Size : 51,9 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 : H. A. Thurston
Publisher : Courier Corporation
Page : 146 pages
File Size : 45,8 Mb
Release : 2012-10-23
Category : Mathematics
ISBN : 9780486154947
This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.
Author : Sergei Ovchinnikov
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 49,8 Mb
Release : 2015-02-26
Category : Mathematics
ISBN : 9781470420185
This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.
Author : Edmund Landau
Publisher : Unknown
Page : 142 pages
File Size : 42,6 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 : Steven G. Krantz
Publisher : CRC Press
Page : 312 pages
File Size : 40,6 Mb
Release : 2014-10-20
Category : Mathematics
ISBN : 9781482220759
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 : Terence Tao
Publisher : Springer
Page : 220 pages
File Size : 49,9 Mb
Release : 2016-08-22
Category : Mathematics
ISBN : 9789811018046
This is part two of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
Author : Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher : Courier Corporation
Page : 450 pages
File Size : 43,5 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 : Steven G. Krantz
Publisher : CRC Press
Page : 304 pages
File Size : 50,6 Mb
Release : 2016-12-12
Category : Mathematics
ISBN : 9781498777704
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.
Author : Howard Eves
Publisher : Courier Corporation
Page : 370 pages
File Size : 42,9 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 : David French Belding,Kevin J. Mitchell
Publisher : Courier Corporation
Page : 450 pages
File Size : 53,6 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486462967
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.
Author : C H C Little,K L Teo,B van Brunt
Publisher : World Scientific Publishing Company
Page : 240 pages
File Size : 48,8 Mb
Release : 2003-09-05
Category : Mathematics
ISBN : 9789813106185
Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth. An understanding of number systems at a fundamental level is necessary for a deeper grasp of analysis. Beginning with elementary concepts from logic and set theory, this book develops in turn the natural numbers, the integers and the rational, real and complex numbers. The development is motivated by the need to solve polynomial equations, and the book concludes by proving that such equations have solutions in the complex number system.
Author : Terence Tao
Publisher : Hindustan Book Agency and Indian National Science Academy
Page : 0 pages
File Size : 40,9 Mb
Release : 2009
Category : Mathematical analysis
ISBN : 8185931941
Suitable for undergraduates who have already been exposed to calculus, this title includes material that starts at the very beginning - the construction of number systems and set theory, then goes on to the basics of analysis, through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral.
Author : Ekkehard Kopp
Publisher : Open Book Publishers
Page : 280 pages
File Size : 43,5 Mb
Release : 2020-10-23
Category : Mathematics
ISBN : 9781800640979
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.