Jinho Baik
530 Church Street
Dept. of Mathematics
University of Michigan Ann Arbor, MI 48109-1043
Office: 4071 East Hall
email: lastname at umich edu
Tel: (734) 763-2150
Fax: (734) 763-0937
Final Exam: Friday, 4/18, 1:30-3:30 (university schedule)
Make-up class will meet on 4/16 (Wednesday), 1-3pm.
Homework All numbers are from the textbook.
Homework 9 (due Mon 4/11)
Homework 8 (due Fri 4/4):
(sec 6.1) #7, 10, (sec 6.2) #18, (sec 5.1) #10 when k=1, #11(a). (Hint for sec 5.1 #10: Corollary 2.32.) Do not hand in: (sec 6.1) #6, 8, 11, (sec 5.1) #7
Homework 7 (due Fri 3/21):
Hand in: (sec 3.4) #22, (sec 3.5) #30, 31, 40, 42. Do not hand in: (sec 3.4) #23, (sec 2.4) #37, 39.
Homework 6 (Do not hand in):
(sec 2.6) #55, 61. If you like, also do (sec 2.6) #56, 60, (sec 2.7) #63, 65.
Homework 5 (due Fri 2/22):
Hand in: (sec 2.3) #21, 28(a)(b)(c), 30, 31(a)(c), (sec 2.4) #32, 39. 44. Do not hand in: (sec 2.3) #20, 25, 26, 27, 28(d), 31(b)(d)(e), (sec 2.4) #33, 35.
Homework 4 (due Fri 2/15):
Hand in: (sec 2.1) #9, 11, (sec 2.2) #13, 14. Do not hand in: (sec 2.1) #3, 6, 8, 10, (sec 2.2) #12, 16.
Homework 3 (due Fri 2/8):
Hand in: (sec 1.4) #22(a), (sec 1.5) #27, 29, 30. Do not hand in: (sec 1.5) #25, 26, 28, 32
Homework 2 (due Fri 2/1):
Hand in: (sec 1.4) #17, 18(a)-(b), 19, 23 (In #23, assume that A also contains the empty set.) (Hint for #18 (b): consider epsilon=1/N for each natural number N). Do not hand in: (sec 1.4) #24
Homework 1 (due Wed 1/23):
Hand in: (sec 1.2) #5, (sec 1.3) #8, #11, #12, #16 (a)-(d). Do not hand in the following problems: (sec 1.2) #4, (sec 1.3) #10, #13
Office Hours: Wed 3-4, Thur 3-4 or by appoitment
Class: MWF 12:10pm-1:00pm at 3088 East Hall
This is one of the basic courses for the first year graduate students in mathemiatics. The students are expected to have mathematical maturity of first year math graduate students, and have studied advanced calculus (Math 451) and are familiar with rigorous proofs and reasonings. Some familiarity with complex numbers, elementary set theory and linear algebra are also assumed.
Topics to be covered: measures, integration, differentiation, Lp spaces, Radon measures
If time permits, some of the following will also be coverd: point set topology, functional analysis, Fourier analysis, distributions
Text: Real Analysis, Modern Techniques and Their Applications (second edition) by Gerald B. Folland, Wiley-Interscience, 1999
We plan to cover Chapters 0,1,2,3,6,7 and some of 4,5,8,9. We cover roughly 5 pages of the textbook per class.
Other books: The following books have different appeal
Real Analysis (third edition) by Royden, Prentice Hall 1988
Analysis (second edition) by Elliot Lieb and Michael Loss, AMS 2001
Homework: Roughly one homework set per week
Exams: one midterm exam and one final exam
Grading: homework (20%), midterm exam (30%), final exam (50%)
Final Exam: Friday, April 18, 1:30-3:30 (university schedule)