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Basic Real Analysis, by Houshang H. Sohrab
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Basic Real Analysis demonstrates the richness of real analysis, giving students an introduction both to mathematical rigor and to the deep theorems and counter examples that arise from such rigor. In this modern and systematic text, all the touchstone results and fundamentals are carefully presented in a style that requires little prior familiarity with proofs or mathematical language. With its many examples, exercises and broad view of analysis, this work is ideal for senior undergraduates and beginning graduate students, either in the classroom or for self-study.
- Sales Rank: #3159755 in Books
- Brand: Brand: Birkhäuser
- Published on: 2003-06-03
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.25" w x 6.14" l, 2.05 pounds
- Binding: Hardcover
- 568 pages
- Used Book in Good Condition
Review
"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 be highly recommended as a good reference on real analysis."
—ZENTRALBLATT MATH
From the Back Cover
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
About the Author
Houshang H. Sohrab is a Professor of Mathematics at Towson University.
Most helpful customer reviews
20 of 20 people found the following review helpful.
Thorough treatment of undergraduate analysis
By Stephen Desalvo
I first learned analysis using (baby) Rudin. I had the worst instructor and had a hard time making the leap from calculus courses to mature mathematical topics.
Now that I'm in graduate school I need to have a solid background in analysis and fill in the gaps, and I needed a book on analysis that I could study on my own. This book is perfect! It assumes no real mathematical maturity (though perhaps I am biased since by now I have developed some) and takes INCREMENTAL STEPS to introducing new material.
Let me repeat. INCREMENTAL STEPS. It doesn't just throw you into a proof like Rudin without any examples and without any intuition. Most of the theorems and new definitions are complemented with concrete examples, most of which appeal to the real line and baby calculus concepts.
The other important aspect of the book is its breadth. Rudin is a great reference for the main results in analysis, but this book has a breadth of topics that I haven't seen anywhere else, and I've looked! It is very THOROUGH.
It also includes a few chapters on measure theory and probability, which is a definite plus.
If you're looking for an analysis textbook that is self-explanatory or even a reference book (I've used it for that too!) then this is it! I wish they had used this textbook in my undergraduate courses.
(My excitement over this book is after having spent quite a lot of time studying different analysis texts and not really "getting it." I'm finally starting to get it after reading this book. Thank you Sohrab for writing it!)
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