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 : luc@math.umass.edu
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
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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.
Erratum: Correct proof of Theorem 4.2, Chapter 1
SUP#2 PDF file
Other very useful references:
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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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A Radical Approach to Lebesgue's Theory of Integration,
by D. M. Bressound. (MAA textbooks) Cambridge University Press 2008.
My all-time favourite undegraduate analysis text:
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Analysis by its History,
by E. Hairer and G. Wanner. Undergraduate Texts in Mathematics. Springer
Syllabus:
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.
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1) Measure theory: Lebesgue measure and Integrable functions
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2) Integration theory: Lebesgue integral, convergence theorems and Fubini theorem
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3) Differentiation and Integration. Functions of bounded variation.
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4) Hilbert spaces and Banach spaces . Examples and Applications. Inequalities.
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5) Abstract measure theory.
Grade: There will be a midterm and a final.
Homework will be assigned regularly.
Exams:
- Midterm: Room:
- Final: Room:
Homework :
Homework #1 (due on September 28):
Set #1
Homework #2 (due on October 19 ):
Set #2
Homework #3 (due on November 9):
Set #3
Homework #4 (due on November 30 ):
Set #4
Homework #5 (due on December 13 ):
Set #5