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Title: Introduction to Analysis (2nd Edition) by William R. Wade ISBN: 0-13-014409-6 Publisher: Prentice Hall Pub. Date: 06 July, 1999 Format: Hardcover Volumes: 1 List Price(USD): $101.33 |
Average Customer Rating: 3.6 (5 reviews)
Rating: 5
Summary: Wonderful book on Analysis
Comment: One of the best and clearest book on analysis of all times. Modern introduction. I would like to have a solutions manual so it would be perfect for self study.
Rating: 1
Summary: The worst book I have never seen before
Comment: I have studied this book for a semester. My professor chose this book because he thinks it easy for us to understand analysis. He professed that every student must learn Math step by step and whether the books are good or bad, any student could not understand concepts on Euclidean n space or metric space unless the concepts on R, the set of real numbers, are comprehended first.
However, this book is a counterexample. Chapter 1 to 7 discuss theorems on R including concepts of sequence, continuity, uniform contunuity, integral, convergence, series.... There is nothing about metric space or vector space until chapter 8. How could a book of analysis not mention these spaces in half of its content? I cite my professor's point of view. any student could not understand concepts on Euclidean n space or metric space unless the concepts on R, the set of real numbers, are comprehended first. It is a specious argument. Whether a student can understand or not depends on that the book chosen is easy for the student or not . It does not depend on what is learn first or second. Obviously, this book is difficult to read and understand not only for me but also for the reader who ever read the book, Elementary classical analysis 2nd edition by Jerrold E. Marsden.
I here give an example. In page 191 is theorem 7.15, Weierstrass M test. The proof uses uniform Cauchy criterion of series of function but it is not mentioned in the previous passage. Looking for it in the preceding pages, uniform Cauchy criterion of sequence of function is found in page 187 which is far away from the page of Weierstrass M test. It means that the reader can't connect the concepts used in the proof of Weierstrass M test. The book by Marsden does perfectly in this point. In page 244 in Marsden's book, Weierstrass M test follows the uniform Cauchy criterion of sequence of function immediately. Uniform Cauchy criterion of series of function is also mentioned between them. The way that Marsden wrote the book makes me connect concepts and feel easy to comprehend.
Marsden's book explains why Weierstrass M test is introduced in the passage preceding to the passage of Weierstrass M test. It also gives an intuitive interpretation to let the reader have insight into the theorem and its proof in a natural point of view, not merely a syntatic point of view like Wade's book. It applies to every theorem in Marsden's book. I could not understand the proof of Weierstrass M test in Wade's book after I read it 10 times, but I comprehended it immediately and derived the proof by myself after I read Marsden's book.
I can't comprehend Math only in syntax. I comprehend Math intuitively by reason. And I think every Math learner does in this way. A proof like the proof of Weierstrass M test can be comprehended as an a priori analytic judgement or an a priori synthetic judgement. It is said analytic because it uses Uniform Cauchy criterion. It is said synthetic because the reader can think of some examples of the theroem which are consistent with the phenomena in the real world. Thus the concepts and the theorems have objective references which can be found in our experience of phenomena. A Math learner can't merely check the validity of the process of a proof syntatically and then says he comprehends the theorem.
Rating: 5
Summary: A Great Textbook for mathematics lover
Comment: It has a lot of problems and concise anwsers and hints. It is a very good book to challeng your mind and push you to think more. I've read Apostol's, Rudin's and Courant John's Analysis textbook. Wade's is even easier and also clear.
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Title: Linear Algebra Done Right by Sheldon Axler ISBN: 0387982582 Publisher: Springer Verlag Pub. Date: 18 July, 1997 List Price(USD): $34.95 |
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Title: Complex Variables and Applications by James Ward Brown, Ruel Vance Churchill ISBN: 0072872527 Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 26 February, 2003 List Price(USD): $125.70 |
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Title: Introductory Real Analysis by A. N. Kolmogorov, S. V. Fomin ISBN: 0486612260 Publisher: Dover Pubns Pub. Date: 01 June, 1975 List Price(USD): $15.95 |
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Title: A First Course in Abstract Algebra, Seventh Edition by John B. Fraleigh ISBN: 0201763907 Publisher: Pearson Addison Wesley Pub. Date: 06 November, 2002 List Price(USD): $108.00 |
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Title: Applied Multivariate Statistical Analysis by Richard A. Johnson, Dean W. Wichern ISBN: 0130925535 Publisher: Prentice Hall Pub. Date: 15 January, 2002 List Price(USD): $111.33 |
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