School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160
(404) 894-9231
h e i l @ m a t h . g a t e c h . e d u
MATH 6337 (Real Analysis I),
Fall 2007
Fill out the online
Course Evaluation (open November 26 through December 16)
Course Syllabus
Some related supplementary materials:
Lecture notes following the text
"Real Analysis," 2nd ed., by Gerald Folland, Wiley, 1999:
-
Chapter 0
- Chapter 1:
- Chapter 2:
- Chapter 3:
-
Section 3.1: Signed measures
-
Section 3.2: The Lebesgue-Radon-Nikodym Theorem
-
Section 3.3: Complex measures
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Section 3.4: Differentiation on Euclidean space (corrected 12/6/07)
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Section 3.5, part a: Functions of bounded variation (corrected 12/7/07)
-
Section 3.5, part b: Singular and absolutely continuous functions
(updated 12/2/07)
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Section 3.5, part c: Convex functions and Jensen's inequality
(not included on final exam)
Homework:
Exams:
-
Exam 1 is scheduled for September 25, 2007 (in class).
The exam will cover Sections 1.1-1.5 in Folland's text, and the
corresponding posted lecture notes.
You are allowed to bring one 8.5x11 sheet of notes to the exam
(you can write on both sides).
-
Exam 2 has been rescheduled for November 1, 2007 (in class).
The exam will cover Sections 2.1-2.5 in Folland's text, and the
corresponding posted lecture notes.
You are allowed to bring one 8.5x11 sheet of notes to the exam
(you can write on both sides).
- Our
Final Exam is scheduled for 8:00-10:50, December 12, 2007
(in our usual classroom).
The exam is comprehensive, covering Sections 1.1-1.5, 2.1-2.5,
3.1-3.5 in Folland's text, and the corresponding posted lecture notes.
You are allowed to bring one 8.5x11 sheet of notes to the exam
(you can write on both sides).
Recommended practice homework problems from Folland:
- 1.2 #2, 3 (part a is hard), 4
- 1.3 #6, 7, 8, 9, 10, 11, 12, 13, 14, 15
- 1.4 #17, 18, 19, 20, 23, 24
- 1.5 #25, 26, 28, 29, 31
- 2.1 #2, 3, 4, 5, 6, 8, 9, 10
- 2.2 #12, 13, 14, 15, 16, 17
- 2.3 #18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30
- 2.4 #32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 44
- 2.5 #46, 48, 50, 51
- 2.6 #55, 56, 57, 58, 59
- 3.1 #1, 2, 3, 4, 5, 6, 7
- 3.2 #8, 9, 10, 11, 12, 13, 16
- 3.3 #18, 19, 20, 21
- 3.4 #22, 23, 24, 25
- 3.5 #27, 31, 33, 35, 37
Recommended practice homework problems from the recommended text
by Wheeden and Zygmund:
- Chapter 2 (Functions of bounded variation): #1, 2, 3, 4, 5, 6, 7, 8
- Chapter 3 (Lebesgue measure):
#4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 23
- Chapter 4 (Measurable functions):
#1, 2, 4, 5, 6, 12, 15, 16, 17
- Chapter 5 (The Lebesgue integral):
#1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 13, 20, 21
- Chapter 6 (Repeated integration): #1, 2, 3, 4, 6, 11
- Chapter 7 (Differentiation): #2, 6, 7, 8, 9, 10, 11
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