Functional analysis arose in the early twentieth century and
gradually, conquering one stronghold after another, became a nearly
universal mathematical doctrine, not merely a new area of
mathematics, but a new mathematical world view. Its appearance was
the inevitable consequence of the evolution of all of
nineteenth-century mathematics, in particular classical analysis
and mathematical physics. Its original basis was formed by Cantor's
theory of sets and linear algebra. Its existence answered the
question of how to state general principles of a broadly
interpreted analysis in a way suitable for the most diverse
situations. A.M. Vershik ( 45], p. 438). This text evolved from the
content of a one semester introductory course in fu- tional
analysis that I have taught a number of times since 1996 at the
University of Virginia. My students have included ?rst and second
year graduate students prep- ing for thesis work in analysis,
algebra, or topology, graduate students in various departments in
the School of Engineering and Applied Science, and several und-
graduate mathematics or physics majors. After a ?rst draft of the
manuscript was completed, it was also used for an independent
reading course for several und- graduates preparing for graduate
Springer-Verlag New York
|Country of origin:
||Graduate Texts in Mathematics, 253
Barbara D. MacCluer
||235 x 155 x 11mm (L x W x T)
||Softcover reprint of hardcover 1st ed. 2009
Science & Mathematics >
Calculus & mathematical analysis >
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