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Books - Professional & Technical - Professional Science - Mathematics - my favorite Real Analysis books

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    Introduction to Real Analysis, 3rd Edition
    by Robert G.Bartle, Donald R.Sherbert
    Average Customer Review: 4.0 out of 5 stars
    Hardcover (21 September, 1999)
    list price: $113.95 -- our price: $113.95
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    Reviews (15)

    5-0 out of 5 stars Reasonable Introduction, Wealth of Exercises
    A reasonable introduction to analysis on the real line. The authors repeatedly challenge the student by "leaving the proof as an exercise". But the most crucial results are proved in the text. In addition they provide a wealth of exercises and the coverage is enough to make the reader ready to approach the likes of Rudin (Principles of Mathematical Analysis). Finally, I agree with some of the other reviewers that it is not suitable for learning analysis in the absence of an instructor. But I don't agree with one reviewer who says that the authors leave too much for the student to figure out himself/herself. In my view, this is a good practice rather than bad, for otherwise students wouldn't bother to remember what they read before and couldn't solve more difficult problems by themselves.

    2-0 out of 5 stars Not for the first course in Real Analysis
    I cannot recommend this book to beginners. Its hard to understand, and there are very few examples. The only good thing is maybe, that beginners get an intuitive feel of integration, and the underlying ideas, thats all.
    Certainly not what an undergraduate needs. Apostol's book is much better.

    1-0 out of 5 stars For an average person, this book is terrible.
    Before I began my class in real analysis, I was pretty confident with whatever knowledge I had. When I started reading this book, I realized that there were so many places where the author just left the readers to figure out. There are a few examples, but I cannot apply that to solve the problems in the book. Some problems have answers, but they only provide hints so I don't know if I am doing them right or not.

    I think the book should have more examples so the students know what is going on, and it should come with the (instructor's solutions manual) so that the students have something to hold onto when their professors are not available. Spending 3 hours on a problem and getting no answer is nothing but a pain, and generally students do not have that much time.

    Some may say, "you are training your brain by doing that," but I disagree. Thinking hard and getting no improvement just make us tired. If you are a college professor, if you don't want to be the reason why a student stops being a math major, then don't use this textbook if you are not going to be available for them when they need you. ... Read more

    Isbn: 0471321486
    Sales Rank: 69065
    Subjects:  1. Calculus    2. Functions Of Real Variables    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Mathematics / General    7. Mathematics for scientists & engineers    8. Real analysis   


    Introduction to Real Analysis (2nd Edition)
    by Manfred Stoll
    Average Customer Review: 5.0 out of 5 stars
    Paperback (15 November, 2000)
    list price: $111.40 -- our price: $111.40
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    Reviews (1)

    5-0 out of 5 stars Another excellent Real Analysis Text
    The style of this book is a bit like Robert Bartle's Introduction to Real Analysis. It is detailed and rigorous. It is an excellent book for those who want to learn Real Analysis. ... Read more

    Isbn: 0321046250
    Sales Rank: 609295
    Subjects:  1. Advanced    2. Calculus    3. Functions of real variables    4. Mathematical analysis    5. Mathematics    6. Science/Mathematics    7. Mathematics / Advanced   


    Introductory Real Analysis
    by Frank Dangello, Michael Seyfried
    Hardcover (01 July, 1999)
    list price: $122.36 -- our price: $122.36
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    Isbn: 0395959330
    Sales Rank: 128948
    Subjects:  1. Calculus    2. Mathematics    3. Science/Mathematics   


    Understanding Analysis
    by Stephen Abbott
    Average Customer Review: 4.5 out of 5 stars
    Hardcover (12 January, 2001)
    list price: $49.95 -- our price: $43.09
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    Reviews (8)

    3-0 out of 5 stars beware, no solutions
    Good book, but no solutions to any exercises. Usually Springer books do have some solutions, so it was a bit disappointing.

    4-0 out of 5 stars the missing star
    Stephen Abbott is with no doubt a very talented writer in mathematics. The book is a fun to read because
    of its style : each chapter starts describing a basic mathematical question that challenged the human mind
    in history. This always makes you curious to read further to discover the great constructs made by the creative thinkers who solved these problems. Also, each chapter ends with adescription of related topics and some historical notes . I really like this style ....

    However I did not give this book a five star rating for the following reasons :

    -Some proofs contain gaps that are left as an exercise to the reader. Not all of these exercises are
    staightforward however. It sometimes took me several hours to find a solution for these exercises ...
    This is OK for real exercises, though it is no fun to have to spend this time filling up some basic proofs..
    Sometimes I also had the impression that the hints were misleading. For example, I completed the proof on the double summation bit did not at all understood why we needed the hint prooved in exercise 2.8.4. Also when I tried to complete the
    proof of the sequential criterium for nonuniform continuity (theorem 4.4.6), I did not see why we would need the hint
    to take values 1/n for epsilon...
    -Some explanations are missing, (maybe this will be solved in second edition). For instance :
    a)please give a clear definition of what an interval is before using the name interval throughout the book.
    b)In baires theorem, the author claims that every open set is either a finite or countable union of open intervals .... Please explain why ...
    -Especially the 'more advanced' topics like baire 's theorem, fourier analysis, metric spaces, ... are rather presented as one big exercise. If you want to learn these topics, there are better books, providing you with much more information....
    -This book only covers a limited range of topics. All the analysis is done for real variables in one dimension.

    I think we need a broader scope, even for an introductionary course. My opinion is that modern analysis should start from the beginnigwith n-dimensional metric spaces, conveying your mind to the beautifull theories of normed linear spaces and banach spaces.
    -Since the book is targeted to the beginning student of abstract math, it would be good idea to include some pages
    (appendix) on logic reasoning like second order predicate calculus, and some basic set theory ....

    So, no five stars for this edition (maybe for a next edition ??)...
    Giving this beautifull book less then four stars however would be unfair, since it definitely has it strengths : the things that are explained are explained very clear and the narrative style of the author always keeps the reader interested!!! Nobody could have done that better !!

    5-0 out of 5 stars A Joy to Read
    This is my first analysis book.So, I have no basis for camparing it as an analysis book.But, as a math book, it is honestly the most readable and enjoyable I have ever read. ... Read more

    Isbn: 0387950605
    Sales Rank: 132749
    Subjects:  1. Calculus    2. Functional Analysis    3. Functions Of Real Variables    4. Mathematical Analysis    5. Mathematics    6. Science/Mathematics    7. Mathematics / Mathematical Analysis   


    A Course of Pure Mathematics (Cambridge Mathematical Library)
    by G.H. Hardy
    Average Customer Review: 5.0 out of 5 stars
    Paperback (04 March, 1993)
    list price: $37.99 -- our price: $37.99
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    Reviews (11)

    5-0 out of 5 stars My God? What a book!
    Godfred Harold Hardy is one of the greatest mathematicians of the 20th century. A Course of Pure Mathematics is an introduction to Analysis, but he only starts Limits on page 110. Until there he talks about real numbers, Dedekind cuts and complex numbers as vectors. I have no words to describe his style: it seems that he is talking with you. If you are looking about a book of Calculus, stop here in buy it.

    5-0 out of 5 stars Best introduction to mathematical analysis
    This book is simply beyond any rating whatsoever. Giving 5 stars is to undermine the value of this classic.
    The first time I got this book, I was neither aware of it not of its author. I just picked it up randomly from school library. From the contents I figured it was a book on calculus. I immediately searched for the proof that "every continuous function is integrable." This was the first book I encountered which had a rigorous proof of this.
    Then I began reading the chapters sequentially thinking that this seems to be a good book on calculus. The book went much beyond my expectation and it satisfied all my mathematical curiousities. All the mysteries of calculus were revelaed. Hardy demystified calculus in the first chapter itself by creating reals out ot rationals.
    The Dedekind's construction of reals as presented in this book is the best I have seen. The properties of reals were not stated as axioms (common approach in books on analysis) but rather deduced from those of rationals.
    The concepts of functions, limits, continuity, derivative etc. were explained in a prosaic style which has no parallel. This was also my first book on maths which had far more english words than mathematical symbols.
    After finishing the entire book I was wondering who was this guy G. H. Hardy who has written such a masterpiece.
    Only a few months later I came to know that he was one of the greatest British mathematicians of the century and was responsible for making our Indian Ramanujan famous. After that I read most of his books including "A Mathematician's Apology" and "An Introduction to Theory of Numbers"
    Any persons who thinks maths is dull should just read few pages from this book and I bet his old beliefs would be shattered.

    5-0 out of 5 stars 1900 yrs from now....
    ...people will look at this like we look at Euclid's Elements today, it's just one of those immortal books. Hardy starts by constructing the real numbers & then doing all the calculus you'd ever want to know, and with a bunch of math 'trivia' that can't be found anywhere. I can't add much to what the other reviewers have said, except this book has some evil integrals from old Cambridge Tripos exams that would make some Putnam problems look easy. lol At least, if you're only allowed to use real variables (& not complex variables & residues). Get this book for an excellent reference no matter what level you're at. ... Read more

    Isbn: 0521092272
    Sales Rank: 47141
    Subjects:  1. Calculus    2. Functions    3. Mathematical Analysis    4. Mathematics    5. Mathematics (General)    6. Probability & Statistics - General    7. Science/Mathematics    8. Mathematics / Probability   


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