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This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level. It provides a rigorous and comprehensive treatment of the theoretical concepts of analysis. The book contains most of the topics covered in a text of this nature, but it also includes many topics not normally encountered in comparable texts. These include the Riemann-Stieltjes integral, the Lebesgue integral, Fourier series, the Weiestrass approximation theorem, and an introduction to normal linear spaces.
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The Real Number System; Sequence Of Real Numbers; Structure Of Point Sets; Limits And Continuity; Differentiation; The Riemann And Riemann-Stieltjes Integral; Series of Real Numbers; Sequences And Series Of Functions; Orthogonal Functions And Fourier Series; Lebesgue Measure And Integration; Logic and Proofs; Propositions and Connectives
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For all readers interested in real analysis.
- Sales Rank: #734711 in Books
- Published on: 2000-11-25
- Original language: English
- Number of items: 1
- Dimensions: 9.40" h x 1.10" w x 7.40" l, 2.20 pounds
- Binding: Paperback
- 550 pages
Most helpful customer reviews
8 of 8 people found the following review helpful.
A Competent, but Unremarkable Text
By ws
The first two reviews are not very helpful, so I thought I would to write a better review.
The organization of the text is perfectly adequate. The author asserts the completeness axiom of the real numbers and then proves that the reals are the limits of Cauchy sequences and then Heine-Borel, etc. This a very common approach. Like most analysis books, it mostly overlooks that there are other ways of constructing the real numbers. I think it's important for neophyte mathematicians to understand that the choices made by their textbook are not the only choices and that other approaches are equally valid. The book progresses in a typical fashion from there. It ends with a good chapter on measure theory and Lebesgue integration.
Like many mathematics textbooks, it appears at first blush to be a list of definitions, theorems, and properties. However, the author does actually take a good bit of time to explain the significance of some the important results. Theorems are stated clearly with standard notations. He also restates some theorems in plain words to make them clearer. The end of chapter summaries are quite helpful in pulling together what was covered and why it is important. He takes some time to explain to students that some of the results, that initially seem arcane, are profound and indispensable in later chapters.
If your department assigns this book, don't hesitate to buy it. It is much better than many other analysis books. Though I would also recommend Understanding Analysis by Steven Abbott or the book known as "Baby Rudin" (google it). The first gives very lucid explanations of abstract concepts. The second is notable for its subtle and well-chosen "gaps", which are often left in math books for students to read between the lines and discover some depth on their own.
13 of 18 people found the following review helpful.
Professors Should Choose Another Book
By R. J. Thomas
This was my undergraduate textbook for Advanced Calculus I and II (as they were called at my school). I am returning to school to start my master's degree this next term and am going through the book to refresh my memory.
Wow, it is just the way I remember it. Frankly, I can't believe the other reviewers ratings. So, I thought I'd balance the average rating a bit with a review of my own.
When I was in college, this was my most dreaded reading material. It is a difficult subject to master, sure, but the author does not help matters by using failing to use a clear structure with emphasis on key points. Instead, there is barely any structure at all. Headings consist of unenlightening phrases such as "Theorem." Pragraphs are downplayed by the typesetting style as well, making each section almost an undifferentiated block of information. (The author has not even used an end-of-proof symbol!)
And not only is this book unfriendly, it is dry. The author tends to use strictly symbolic language when explaining in words would be so much clearer. In fact, he frequently skips the explanatory material altogether and moves straight to the examples. What is the context or object for these examples? The reader is mystified.
If you are a professor, please do not choose this book for your analysis class. I have a feeling it is only comprehensible to those who already thouroughly understand the material.
If you are a student who has come here to buy this book, you have my sympathy.
0 of 0 people found the following review helpful.
Not a beginner text
By Erik K.
Examples are very difficult to understand. Proofs are also confusing because the author doesn't stray from writing everything in strict symbolic notations. The text itself is dry and lacks any clear explanation for students with no background in real analysis. This book may be treated as a good reference for professors, but it is a genuinely horrendous learning material for students. I suggest you buy a different text unless you have a prior knowledge in the subject.
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