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Title: Treatise on Analysis : Volume 1 by Jean Dieudonne, Paul Smith, Samuel Eilenberg ISBN: 0-12-215550-5 Publisher: Academic Press Pub. Date: 28 August, 1960 Format: Hardcover Volumes: 1 List Price(USD): $99.95 |
Average Customer Rating: 4 (3 reviews)
Rating: 5
Summary: Bring back Bourbaki
Comment: Dieudonne's books are worth the many hundreds of dollars they would cost if they could be bought today. (Does anyone know if the French edition is still available?) They provided a very refined treatment of most of modern analysis, much as the classics of the past, such as Goursat, did in their time. Concerning motivation, this treatment is for those who are motivated to understand. And so is Bourbaki. The precise, formal, careful exposition educates and helps one to mature intellectually (have I spelled that right?).
Rating: 4
Summary: RELATED TO MR BERNARO OPINION!
Comment: MR BERNARDO>
THE ATOMIC NUCLEUS IT'S ABSTRACT!!!
YOUR SINCERELY!!
MAURICE ALLMAN L
Rating: 3
Summary: Abstraction to its last consequences.
Comment: I should be surprised to be the first reviewer of this book, but thinking it again I see the point. Dieudonné's books are just being displaced by more accesible and focused texts, instead of these authoritative Bourbaki-style treatises which are often too abstract to be useful. Bourbaki mathematics accomplished the mission of unifying and standarizing (more or less) the whole of mathematics, but once that was done, their work now turns out to be useless. The point is that when we tackle a problem, be it in pure or applied mathematics, we seldom need the high level of abstraction used by Bourbaki authors. Moreover, what we need are specific results to handle the details of our solututions, and Dieudonné pays almost no attention to them; he prefers to stay at the most general possible setting, making his treatment perspectiveless because he misses completely the goal of abstraction: To use its power when dealing with particular situations. That's why no one has reviewed Dieudonné before me: His books are read no more.
Nevertheless, undergraduate and graduate students may find it useful as a reference, but not as a course text because it presents no motivation to the topics treated and includes only a very short bibliography.
Its contents are: Set theory, real numbers, metric spaces, normed spaces, Hilbert spaces, spaces of continuous functions, differential calculus, analytic functions, existence theorems (for ODE's), and elementary spectral theory.
"Treatise on Analysis" consisted originally on this sole book. Later it was expanded to four and later on to nine.
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