Real Analysis II : Math 624
Meeting : TuTh 9:3010:45 LGRT 1322
Instructor : Luc ReyBellet
Office : 1423 J LGRT
Phone : 5456020
EMail : luc@math.umass.edu
Office Hours :
TuTh 2:453:45, or by appointment.
Text: The text book for the class is the twovolume set

Real Analysis. Measure Theory, Integration & Hilbert Spaces,
by E. M. Stein & R. Shakarchi. Princeton Lecture Notes in Analysis III, Princeton University
Press 2005.

Functional Analysis. Introduction to Further Topics in Analysis,
by E. M. Stein & R. Shakarchi. Princeton Lecture Notes in Analysis IV, Princeton University
Press 2011.
Other very useful references for this class are

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.

Real and Abstract Analysis,
by E. Hewitt and K. Stromberg. Graduate Text in Mathematics. Springer.
Two undergraduate analysis texts for further references

Analysis by its History,
by E. Hairer and G. Wanner. Undergraduate Texts in Mathematics. Springer 2008.

The Way of Analysis,
by R.S. Strichartz, Jones & Bartlett Learning 2000.
Syllabus:
This is the second part of a 2semester introduction to real analysis
(Math 623624). The prerequisites for this class is Math 623 or equivalent. Among the topics covered in this class are

1) Fourier Analysis: Fourier Series and Fourier Transform.

2) Abstract measure theory. Integration, Fubini theorem, Absolute continuity and the RadonNykodym theorem.

3) Banach spaces and L^p space theory.
Grade: There will be a midterm and a final.
Homework will be assigned regularly and graded.
Exams:
Homework :
Homework #1 (due on 2/14 ):
HWK #1 PDF file
Homework #2 (due on 2/28 ):
HWK #2 PDF file
Homework #3 (due on 3/15):
HWK #3 PDF file
Homework #4 (due on 4/12 ):
HWK #4 PDF file
Homework #5 (due on 5/1):
HWK #5 PDF file