ISBN13:
9780971576612
640 pages, Hardcover, smythesewn binding. June 2006.
Price
$73
Studentfriendly
but rigorous book aimed primarily at third or fourth year
undergraduates. The pace is slow but thorough, with an abundance of
motivations, examples, and counterexamples. Arguments used within
proofs are explicitly cited, with references to where they were first
proved. Many examples have solutions that make use of several results
or concepts, so that students can see how various techniques can blend
together into one.
Includes
solutions to all oddnumbered exercises
"The
author has set himself a monumental task: writing a functional analysis
book that can be read by any wellmotivated student, even one with only
a modest background in analysis. He carried out this task with great
patience and care and he did a
remarkable job....the author has included a great deal of mathe matics
in this book.... all of it is done in complete detail, so a student who
is asked to present some topic, in a seminar, say, will find this book
a valuable source of information....This is a remarkable book, one that
will serve as a valuable reference for anyone."
— from SIAM Review, June 2010, Vol 52, No. 2.
"A thorough ... presentation
of all the standard topics any
introductory functional analysis course might wish to cover ... highly
accessible, selfcontained ... Highly recommended."
— from the March 2007 issue of
Choice:
Current Reviews for Academic Libraries, published by the American Library
Association. See complete review
"The book
contains about 250 examples and counterexamples. It also contains about
800 exercises.... A remarkable feature is an appendix
of 120 pages containing the complete solutions to all oddnumbered
exercises....
The book is carefully written and its index is well
arranged and comprehensive... useful to students from a wide variety of
backgrounds, including graduate students in physics and
engineering...."
— Zentralblatt Math
"Clearly a labour
of love" —
Professor C.S. Ramalingam,
Department of Electrical Engineering, Indian Institute of Technology
Madras
Table of contents (html)
index (in
pdf)
Front
cover (designed
by Leila Joiner)
Look inside this book (sample pages)
Errata and notes (1 page, in pdf)
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information: books shipped within the United States
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information: other countries
From the preface:
This book is designed as an introduction to basic
functional analysis at the senior/graduate level. It has been written
in such a way that a wellmotivated undergraduate student can follow
and appreciate the material without undue difficulties while an
advanced graduate student can also find topics of interest: topological
vector spaces, Kolmogorov's normability criterion, Tychonov's
classification of finitedimensional Hausdorff topological vector
spaces, and the theorems of Korovkin and Muntz, to mention a few.
Textbooks
in functional analysis (or more generally, in mathematics) are often
unnecessarily demanding  written in a concise manner with few
examples and motivations. Proofs in such textbooks are sometimes so
terse that much time and energy are required of students just to verify
their logical correctness, let alone understand the
ideas behind them. This is counterproductive: students are
given the impression that mathematical proofs are mysterious; the
proofs fail to convince readers of the validity of the theorems; and
students are deprived of an opportunity to learn useful techniques and
principles in problem solving.
In
contrast, the pace of this book is deliberately slow but
thorough. I chose to write a textbook that I would like to
have studied from as a student  one that is mathematically rigorous
but leisurely, with lots of motivations and examples. This is
a studentfriendly book that can be read and enjoyed by a reasonably
wellmotivated undergrad. Proofs are developed in detail,
with all steps justified. Almost all previously proven results used
within proofs and solutions to examples are explicitly cited, and
referred to by number. This eliminates unnecessary time and frustration
spent figuring out exactly which results were used and where they were
first proved.
see the
complete preface
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shipped within the United States
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countries
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