Real Analysis I : Math 623
Meeting : TuTh 9:30--10:45 LGRT 1234
Instructor : Luc Rey-Bellet
Office : 1423 J LGRT
Phone : 545-6020
E-Mail : email@example.com
Office Hours :
M 1:30--2:30, Tu 2:00--4:00pm, Th 11:30--12:30 , or by appointment.
Text: The text book for the class is
Real Analysis. Measure Theory, Integration & Hilbert Spaces,
by E. M. Stein & R. Shakarchi. Princeton Lecture Notes in Analysis III, Princeton University
Erratum: Correct proof of Theorem 4.2, Chapter 1
SUP#2 PDF file
Other very useful references:
My all-time favourite undegraduate analysis text:
Real Analysis: Modern Techniques and their applications,
by G.B. Folland. 2nd ed. Wiley 1999.
Real Analysis, by H.L. Royden. 3rd ed. Collier Macmillan 1988
Measure and Integral: An Introduction to Real Analysis,
by R.L. Wheeden and A. Zygmund. M Dekker 1977.
A Radical Approach to Lebesgue's Theory of Integration,
by D. M. Bressound. (MAA textbooks) Cambridge University Press 2008.
Analysis by its History,
by E. Hairer and G. Wanner. Undergraduate Texts in Mathematics. Springer
This is the first part of a 2-semester introduction to real analysis
(Math 623-624). The prerequisites for this class is a working knowledge of
the basics of analysis taught in a class like M523, see for example Chapter 3
and 4 of Analysis by its History.
1) Measure theory: Lebesgue measure and Integrable functions
2) Integration theory: Lebesgue integral, convergence theorems and Fubini theorem
3) Differentiation and Integration. Functions of bounded variation.
4) Hilbert spaces and Banach spaces . Examples and Applications. Inequalities.
5) Abstract measure theory.
Grade: There will be a midterm and a final.
Homework will be assigned regularly.
- Midterm: Room:
- Final: Room:
Homework #1 (due on September 28):
Homework #2 (due on October 19 ):
Homework #3 (due on November 9):
Homework #4 (due on November 30 ):
Homework #5 (due on December 13 ):