Spring 2016, Math 766, Real Analysis

Course Information

• Course Coverage: This course is the second part of real analysis at the graduate level; the first part is Math 765. It continues with the following topics from Chapters 7, 8, 10, 11: infinite series of functions, the Topology in the Euclidean spaces, Metric spaces, and Differentiability on R^n. We skip Chapter 9 because Chapter 10 covers the topics of Chapter 9 in a more general setting.
 
• Time: MWF 11:00 ---11:50 AM
 
• Location: Snow Hall 302
 
• Text: An Introduction to Analysis, William R. Wade
 
• Prerequisite: Math 290 and Math 500. Math 765 is preferred.
 
• Instructor: Shuanglin Shao
 
• Office: Snow Hall 615
 
• Email: slshao@ku.edu
 
• Office Hour: MWF: 1-2 PM or by appointment.

Grade Policy

• Homework: There will be 10 homework. Each homework consists of roughly 10 problems; only 3 of them will be graded, which will be decided after you turn in homework. The lowest homework grade will be dropped.
 
• Quizzes: There will be 5 quizzes in class; the date will be annouced one week in advance in class or by email.
 
• Midterm: There will one midterm of 50 minutes in class. The date is 03/11/2016 in class.
 
• Final Exam: There is a comprehensive final exam in class. The time is 10:30 AM -- 1 PM on 05/11/2016.
 
• Grade Percentage: homework (30 %) + midterm (20 %) + quizzes (10 %) + final (40 %).

Homework

• HW 1. (due by February 5th in class.) # 7.1.2, # 7.1.3,#7.1.6, # 7.1.8, # 7.1.10, # 7.1.11, #7.2.1, # 7.2.4, # 7.2.7, # 7.2.10 HW 1 solutions.
 
• HW 2. (due by February 17th in class.) # 7.3.2, # 7.3.5, # 7.3.10, # 7.4.1 (a) (c), # 7.4.4, # 7.4.6, # 7.4.8. HW 2 solutions.
 
• HW 3. (due by Feb. 24th in class.) # 8.1.2, # 8.1.9, # 8.2.4, # 8.2.11, # 8.3.4, # 8.3.6, # 8.3.7, # 8.3.8, # 8.3.9. HW 3 solutions.
 
• HW 4. (due by March 7th in class.) # 8.4.2, # 8.4.4, # 8.4.6, # 8.4.9, # 10.1.2, # 10.1.5, # 10.1.7, # 10.1.8, # 10.1.10. HW 4 solutions.
 
• HW 5. (due by March 21st in class.) # 10.2.3, # 10.2.8, # 10.2.9, # 10.3.5, # 10.3.8, # 10.4.1, # 10.4.3, # 10.4.5, # 10.4.7, # 10.4.8. HW 5 solutions.
 
• HW 6. (due by April 1st in class.) # 10.5.4, # 10.5.6, # 10.5.7, # 10.6.1, # 10.6.3, # 10.6.5, # 10.6.6, # 10.6.9. HW 6 solutions.
 
• HW 7. (due by April 8th in class.) # 11.1.2, # 11.1.4, # 11.1.5, # 11.2.2, # 11.2.3, # 11.2.4, # 11.2.5, # 11.2.8, # 11.2.11 HW 7 solutions.
 
• HW 8. (due by April 15th in class.) # 11.3.1 (a)(b), # 11.3.2 (a)(b), # 11.4.1, # 11.4.4, # 11.4.6, # 11.4.10, # 11.4.11. HW 8 solutions.
 
• HW 9. (due by April 22nd in class.) # 11.5.1 (a)(c), # 11.5.2, # 11.5.5, # 11.5.6, # 11.5.8, # 11.5.11, # 11.5.12 (a)(b). HW 9 solutions.
 
• HW 10. (due by April 29th in class.) # 11.6.1 (a)(b), # 11.6.2 (a) (b), # 11.6.3, # 11.6.7, # 11.6.10. HW 10 solutions.
 
• List_Questions_Math766. Bonus questions to present during the last five classes in 4 groups. The bonus (additional 10 points ) will be added to final grades. Solutions will not be provided; in case of need, consult the individual presenter.