Basic Real Analysis
Autor Houshang H. Sohraben Limba Engleză Paperback – 14 noi 2014
The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus.
With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide.
Reviews of first edition:
The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis.
—Zentralblatt MATH
The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest.
—Mathematical Reviews
[This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear.
—CHOICE Reviews
| Toate formatele și edițiile | Preț | Express |
|---|---|---|
| Paperback (2) | 397.36 lei 6-8 săpt. | |
| Birkhäuser Boston – 28 sep 2012 | 397.36 lei 6-8 săpt. | |
| Springer – 14 noi 2014 | 469.43 lei 6-8 săpt. | |
| Hardback (1) | 544.35 lei 6-8 săpt. | |
| Springer – 14 noi 2014 | 544.35 lei 6-8 săpt. |
Preț: 469.43 lei
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Specificații
ISBN-13: 9781493937141
ISBN-10: 1493937146
Pagini: 683
Ilustrații: XI, 683 p. 3 illus.
Dimensiuni: 155 x 235 x 35 mm
Greutate: 0.96 kg
Ediția:2nd ed. 2014
Editura: Springer
Colecția Birkhäuser
Locul publicării:New York, NY, United States
ISBN-10: 1493937146
Pagini: 683
Ilustrații: XI, 683 p. 3 illus.
Dimensiuni: 155 x 235 x 35 mm
Greutate: 0.96 kg
Ediția:2nd ed. 2014
Editura: Springer
Colecția Birkhäuser
Locul publicării:New York, NY, United States
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Cuprins
Preface.- Set Theory.- Sequences and Series of Real Numbers.- Limits of Functions.- Topology of R and Continuity.- Metric Spaces.- The Derivative.- The Riemann Integral.- Sequences and Series of Functions.- Normed and Function Spaces.- The Lebesgue Integral.- Lebesgue Measure.- General Measure and Probability.- Appendix A: Construction of Real Numbers.- References.- Index.
Notă biografică
Houshang H. Sohrab is a Professor of Mathematics at Towson University.
Textul de pe ultima copertă
This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language.
The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus.
With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition, is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide.
Reviews of first edition:
The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis.
—Zentralblatt MATH
The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest.
—Mathematical Reviews
[This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear.
—CHOICE Reviews
The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus.
With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition, is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide.
Reviews of first edition:
The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis.
—Zentralblatt MATH
The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest.
—Mathematical Reviews
[This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear.
—CHOICE Reviews
Caracteristici
The second edition includes three expanded chapters, additional problems, and an application to fixed-point theory
New solutions manual available to instructors upon request
Elegant proofs and excellent choice of topics
Numerous examples and exercises to enforce methodology; exercises integrated into the main text, as well as at the end of each chapter
Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis
Solid preparation for deeper study of functional analysis
Request lecturer material: sn.pub/lecturer-material
New solutions manual available to instructors upon request
Elegant proofs and excellent choice of topics
Numerous examples and exercises to enforce methodology; exercises integrated into the main text, as well as at the end of each chapter
Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis
Solid preparation for deeper study of functional analysis
Request lecturer material: sn.pub/lecturer-material
Recenzii
"Students who find Goffman's ‘Real Functions’ (1953), Halmos's ‘Measure Theory’ (1950), Hewitt and Stromberg's ‘Real and Abstract Analysis’ (1965), Lang's (1969) or Royden's ‘Real Analysis’ (1963), or Rudin's (1973) or Yosida's ‘Functional Analysis’ (1965) to be too hard, or too easy, may find Sohrab's presentation just right. Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. . . . Recommended."
—CHOICE
"This book is intended as a text for a one-year course for senior undergraduates or beginning graduate students, though it seems to the reviewer that it contains more than enough material for one year's study. . . . The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest."
—MATHEMATICAL REVIEWS
"The book is a clear and well structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. . . . The author managed to confine within a reasonable size book, all the basic concepts in real analysis and also some developed topics . . . The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact this textbook can serve as a source of examples and exercises in real analysis. . . . This book can behighly recommended as a good reference on real analysis."
—ZENTRALBLATT MATH
—CHOICE
"This book is intended as a text for a one-year course for senior undergraduates or beginning graduate students, though it seems to the reviewer that it contains more than enough material for one year's study. . . . The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest."
—MATHEMATICAL REVIEWS
"The book is a clear and well structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. . . . The author managed to confine within a reasonable size book, all the basic concepts in real analysis and also some developed topics . . . The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact this textbook can serve as a source of examples and exercises in real analysis. . . . This book can behighly recommended as a good reference on real analysis."
—ZENTRALBLATT MATH