Number Systems and the Foundations of Analysis PDF Download

Author: Elliott Mendelson
Publisher: Dover Books on Mathematics
ISBN: 9780486457925
Category : Mathematics
Languages : en
Pages : 0

View

Book Description
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: H. A. Thurston
Publisher: Courier Corporation
ISBN: 0486154947
Category : Mathematics
Languages : en
Pages : 146

View

Book Description
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: Edmund Landau
Publisher:
ISBN: 9781950217083
Category :
Languages : en
Pages : 142

View

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: Joseph L. Taylor
Publisher: American Mathematical Soc.
ISBN: 0821889842
Category : Mathematics
Languages : en
Pages : 411

View

Book Description
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: Terence Tao
Publisher: Springer
ISBN: 9811017891
Category : Mathematics
Languages : en
Pages : 366

View

Book Description
This is part one 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: Solomon Feferman
Publisher: American Mathematical Soc.
ISBN: 0821829157
Category : Number theory
Languages : en
Pages : 434

View

Book Description
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: Steven G. Krantz
Publisher: CRC Press
ISBN: 148222075X
Category : Mathematics
Languages : en
Pages : 312

View

Book Description
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: David French Belding
Publisher: Courier Corporation
ISBN: 048646296X
Category : Mathematics
Languages : en
Pages : 450

View

Book Description
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: Steven G. Krantz
Publisher: CRC Press
ISBN: 1498777708
Category : Mathematics
Languages : en
Pages : 306

View

Book Description
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: Terence Tao
Publisher: Springer
ISBN: 9811018049
Category : Mathematics
Languages : en
Pages : 235

View

Book Description
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.