Real Analysis II : Math 624
Meeting : TuTh 9:30--10:45 LGRT 1322
Instructor : Luc Rey-Bellet
Office : 1423 J LGRT
Phone : 545-6020
E-Mail : luc@math.umass.edu
Office Hours :
TuTh 2:45--3:45, or by appointment.
Text: The text book for the class is the two-volume set
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Real Analysis. Measure Theory, Integration & Hilbert Spaces,
by E. M. Stein & R. Shakarchi. Princeton Lecture Notes in Analysis III, Princeton University
Press 2005.
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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
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Real Analysis: Modern Techniques and their applications,
by G.B. Folland. 2nd ed. Wiley 1999.
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Real Analysis, by H.L. Royden. 3rd ed. Collier Macmillan 1988
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Measure and Integral: An Introduction to Real Analysis,
by R.L. Wheeden and A. Zygmund. M Dekker 1977.
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Real and Abstract Analysis,
by E. Hewitt and K. Stromberg. Graduate Text in Mathematics. Springer.
Two undergraduate analysis texts for further references
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Analysis by its History,
by E. Hairer and G. Wanner. Undergraduate Texts in Mathematics. Springer 2008.
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The Way of Analysis,
by R.S. Strichartz, Jones & Bartlett Learning 2000.
Syllabus:
This is the second part of a 2-semester introduction to real analysis
(Math 623-624). The prerequisites for this class is Math 623 or equivalent. Among the topics covered in this class are
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1) Fourier Analysis: Fourier Series and Fourier Transform.
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2) Abstract measure theory. Integration, Fubini theorem, Absolute continuity and the Radon-Nykodym theorem.
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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