Real Variables (39163) - Spring 98
MWF 1:30-2:20 in CLBR 302
- Instructor.
Dr. H. Knaust, Bell Hall 219, tel. 747-7002,
e-mail: helmut@math.utep.edu,
- Office Hours.
MWF 10:30-11:30, or by appointment.
- Textbook.
H.L. Royden, Real Analysis,
3rd ed., Macmillan.
- Prerequisites.
The instructor assumes that are thoroughly
familiar with the standard contents of a Classical Analysis course,
in particular the theory of differentiation and Riemann-integration of
one-variable functions.
- Contents.
The course will "uncover" the first part
of the textbook; selected topics from Part 2 and 3 or
other interesting topics will be covered as time permits.
- Bibliography. A multitude of books covering Lebesgue's theory and related topics
can be found at
QA 300 in the library.
Lebesgue's Theory of Integration started with:
- Henri Lebesgue,
Leçons sur l'integration et la recherche des fonctions
primitives.
Chelsea. (1904)
The following books give an in-depth treatment of integration
theory; they serve as standard references:
-
Constantin Carathéodory,
Vorlesungen über Reelle Funktionen.
Chelsea. (1918)
-
Paul R. Halmos,
Measure Theory.
Springer-Verlag. (1950)
-
Edwin Hewitt & Karl Stromberg,
Real and Abstract Analysis.
Springer-Verlag. (1965)
-
Frigyes Riesz & Béla Szökefalvi-Nagy,
Functional Analysis.
Dover. (1955)
-
Walter Rudin,
Real & Complex Analysis.
McGraw-Hill. (1966)
An excellent historical account of the developments leading to Lebesgue's
discovery can be found in:
-
Thomas Hawkins,
Lebesgue's Theory of Integration.
Chelsea. (1970)
- Tests.
A mid-term
in-class exam will be given on Friday March 13.
The comprehensive final exam will be on Friday, May 8, 4:00-6:45.
- Homework.
Working on the assigned homework problems is by far the most
important part of your participation in this course. The
instructor assumes that you will spend a considerable amount of time
on obtaining solutions to the homework assignments. Your homework
will be collected in class and graded by the instructor.
Late homework will not be accepted!
- Information on the Web.This syllabus and other ancillary material can be found on my homepage
http://helmut.knaust.info.
December 14, 1997