Course Description

Course:      MAT 472, Intermediate Real Analysis I
Instructor:  Jack Spielberg
Time:        TuTh 12:15 - 1:30
Location:    EDB L1-32
Line #:      66350

This is a rigorous foundation for analysis in metric spaces, with emphasis
on the real line.  Among the most important topics are compactness, uniform
continuity, uniform convergence, and differentiation and integration of
functions of one real variable.  With any luck, we'll also see the Baire
Category Theorem, the Weierstrass Approximation Theorem, and the
Arzela-Ascoli Theorem.
 
This course is the first part of our qualifier sequence in analysis (the
second part being MAT 473).  The final exam also serves as the first half
of the graduate programÕs qualifying exam in Real Analysis.  However, the
use of the final exam in determining final grades for this course is
independent of its use by the graduate program.
 
This course gives an adequate preparation for graduate real analysis (MAT
570 at ASU).
 
Prerequisites: The formal prerequisites are MAT 342 (Linear Algebra) and
MAT 300 (Mathematical Structures, our introduction-to-logic-and-proofs
course).  While MAT 371 (Advanced Calculus) is not formally required, many
students find it essential as a warm-up for this course.  The coverage of
MAT 472 includes that of MAT 371 (and much more), at a significantly more
sophisticated level.

Textbook: The lectures will be self-contained, so that it is not required
to buy a book.  However, it is very useful to have a book (especially if
you don't trust your note-taking ability).  Any text covering topology in
metric spaces and advanced calculus on the real line will be helpful.  I
recommend the text 'Principles of Mathematical Analysis, 3rd edition' by
Walter Rudin.  This is available in a (somewhat) reasonably priced
paperback edition, e.g. from Amazon.

(Try the url:

http://www.amazon.com/gp/product/0070856133/ref=sr_11_1/103-5241456-3887867?%5Fencoding=UTF8

You can also try the British publisher at 

http://www.mcgraw-hill.co.uk/html/0070856133.html 

The ISBN number is 0070856133.  The price will depend on the exchange 
rate.  It's also sometimes possible to find used copies at 
www.bookfinder.com)

Questions should be addressed to the instructor at 965-3286, or by email at
jack.spielberg@asu.edu