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Real Analysis (Dover Books on Mathematics), by Norman B. Haaser, Joseph A. Sullivan, Mathematics
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This book is a text for a first course in abstract analysis. Although this topic is traditionally treated in first-year graduate courses, the present volume is so clear and accessible, it is suitable for undergraduates with a good background in the calculus of functions of one and several variables.
In outline, the course consists of a study of the familiar concepts of calculus such as convergence, continuity, differentiation, and integration in a more general and abstract setting. This serves to reinforce and deepen the reader's understanding of the basic concepts of analysis and, at the same time, to provide a familiarity with the abstract approach to analysis which is valuable in many areas of applied mathematics and essential to the study of advanced analysis.
After introductory chapters on sets and relations, the real number system and linear spaces, the book offers easily followed discussions of normed spaces, normed linear spaces, inner product spaces, and a complete development of the Lebesgue integral, as well as important topics involving approximation theory, the Banach fixed-point theorem, and its applications and Stieltjes integrals.
Thorough, well-conceived, and well-written, Real Analysis is abundantly furnished with problem material—each chapter includes a carefully chosen selection of stimulating problems.
- Sales Rank: #595147 in Books
- Published on: 1991-01-01
- Released on: 1991-01-01
- Original language: English
- Number of items: 1
- Dimensions: 8.49" h x .72" w x 5.41" l, .70 pounds
- Binding: Paperback
- 352 pages
About the Author
Michael J. Sullivan is an author and sports writer living in New York who graduated from St. John's University, and is a member of the McDonald's All-American Selection Boys Basketball Committee and the Parade All-American Selection Committee.? Michael hosted sports radio shows on WGBB on Long Island, NY, and WEVD 1050AM in New York City, as well as worked with ESPN and Sporting News.? In addition to writing the When Time Forgets series, Michael covers high school and college sports for Fox-owned Scout.com, which involves daily activity on ten to twelve message boards as well as writing approximately 100 articles each month
Michael has published a number of books through established trade houses, including the trivia book "So You Think You're a New Yorker", which was an iconic work lauded by columnist Cindy Adams.? In addition, ?he published seven sports-themed books for children through Enslow, and a volume of a children's book series through HarperCollins.
Most helpful customer reviews
20 of 22 people found the following review helpful.
A thorough and rigorous introduction and exposition
By A Customer
As an undergraduate math major with knowledge of only some linear algebra and elementary calculus of one and several variables, I found this text to be interesting and challenging. The chapter on metric spaces serves as a good introduction to concepts in point-set topology, while providing motivation for such studies. While the proofs are rigorous and complete, sometimes the developments seem to lack motivation. This can be annoying when attempting the exercises, but motivation for such developments could easily be provided by examples from other texts or a professor. After studying Stewart's "Calculus" and Bartle and Sherbert's introductory analysis text, I find the rigor and thoroughness of this text most refreshing. For instance, rather than assuming the completeness property of the reals, the authors develop the reals as an equvalence class on the rationals, and proceed to prove the completeness property. I am certain that anyone interested in learning analysis could benefit greatly from this text, especially in combination with other analysis texts.
12 of 13 people found the following review helpful.
Great Book
By MathGeek741
I don't see why everyone buys other books on the subject for ten times the price when they can just get this one. This book is REALLY good. It really teaches the material in a way which is both clear and understandable and completely rigorous. Moreover, the excercizes, which range from easy to difficult, are all quite instructive. I'd recommend this book to anyone.
17 of 20 people found the following review helpful.
Excellent preparation for books like Big Rudin
By Michael Rauh
This book can serve as an important bridge between books like baby Rudin and big Rudin. Like baby Rudin, this book assumes only the basics from calculus and linear algebra (it is fairly self-contained) and covers the basics on convergence, continuity, differentiation, uniform convergence, etc. It then goes on to cover many topics in the first half of big Rudin like Lebesgue integration, Banach spaces, and Hilbert spaces. The style and tone of the book is sophisticated, and prepares the reader for the arid tone of big Rudin. On the other hand, this book always tries to develop topics in the most elementary way. For example, the Lebesgue theory is developed via the Daniell method on R^n and then, in a brief separate section, the general theory is sketched, leaving many proofs to the reader. I liked this approach, because working in R^n is comfortable and the proofs extend to the general case in an obvious way. Another example is the Riesz representation theorem, which is done on the real line with a very intuitive proof. In contrast, big Rudin is really a book to marvel at once you already know something about its contents. This book is ideal preparation for big Rudin because after reading it, you will know in essence what Rudin wants to say and basically why it is true. But big Rudin will show you how these results extend to more general settings with extremely elegant (although sometimes baffling) proofs. You should also note that when I was at Chicago they were using this book, so the big guys and gals must like it too.
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