Re: How to learn real analysis-

On Mon, 11 Feb 2008 11:39:37 +0100, JEMebius
<jemebius@xxxxxxxxx> wrote:

Some books I can recommend:
Dieudonné: Modern analysis;
Walter Rudin: Real and complex analysis;
Walter Rudin: Functional analysis;
Riesz and Nagy: Leçons d'analyse fonctionnelle

N.B. None of these is for beginners!

At an introductory level, Spivak's "Calculus" gets a lot of
recommendations, and the third edition was reprinted by
Cambridge University Press in 2006 (at a reasonable price).
(I really must read it myself ...)

An almost arbitrary list of a few others worth considering;

Apostol, "Mathematical Analysis" (out of print)
Beardon, "Limits: A New Approach to Real Analysis"
Bressoud, "A Radical Approach to Real Analysis"
Burkill, "A First Course in Mathematical Analysis"
Carothers, "Real Analysis"
DePree & Swartz, "Introduction to Real Analysis" (expensive!)
Rudin, "Principles of Mathematical Analysis"
Simmons, "Introduction to Topology and Modern Analysis"
(maybe a second course? - it's been a while since I saw it)

Supplementary reading:

Gelbaum & Olmsted, "Counterexamples in Analysis"

--
Angus Rodgers
(twirlip@ eats spam; reply to angusrod@)
Contains mild peril
.