Dear Students,

I will be teaching Functional Analysis in Fall 2018 to be continued in

Spring 2019. After an extensive search for a
suitable textbook, I have

made my decision. The textbook for the course will
be "Functional

Analysis (Methods of Modern Mathematical
Physics)" by Michael Reed and

Barry Simon.

https://www.amazon.com/Functional-Analysis-Methods-Mathematical-Physics/dp/0125850506

The following quote is from the Amazon page
above

This book is the first of a multivolume series
devoted to an

exposition of functional analysis methods in modern
mathematical

physics. It describes the fundamental principles of
functional

analysis and is essentially self-contained...

The following quote is from the review by J.
A. Goldstein

The American Mathematical Monthly

Vol. 80, No. 10 (Dec., 1973), pp. 1152-1153

"The book has many strong features,
including

the selection of topics, the notes, the
exercises, the applications,

the chapter on

locally convex spaces, etc. Even the students who had
no knowledge of

(or interest in)

physics appreciated the fact that the analysis they
were studying is

useful outside of

mathematics, and this is an important motivating
factor."

Quote from a review on Amazon

"Books on mathematical methods "for
physicists" are often criticized

by their superficiality, a sacrifice deemed
necessary for achieving

completeness. This one is a glaring exception: the first
of a set of 4

(!) volumes dealing
with the finest tools for dealing with the

delicate mathematical questions in quantum theory -
namely, functional

analysis. Of course, this sounds rather vague, since
quantum physics

makes use of functional-analytic tools as diverse
as distributions,

Hilbert, Banach and
locally convex spaces, spectral theory, semigroup

theory, operator algebras, etc.

However, do not expect ready-brew formulae and
cookbook recipes: this

book gets his job done at least as well as Rudin, Yosida and

Riesz-Sz.Nagy, just to mention the classics. Most theorems
are

rigorously proved, and although the book becomes more
and more biased

towards mathematical physics [...] this
particular volume has

precisely the most useful stuff: metric, Banach, topological, locally

convex, and Hilbert spaces, bounded and unbounded
operators. A

supplement extracted from the second volume with the
basics of Fourier

transforms makes it self-contained as a monograph.

However, the best things, that make this book
nearly unbeatable, are

the several wisely chosen examples and
counterexamples, the notes at

the end of each chapter and the wonderful - and
useful - exercises.

[...]"

Sincerely,

Jerzy Wojciechowski