Fall 2012, Math 765, Real Analysis

Course Information

• Course Coverage: This course intends to cover some basic topics of real analysis: the real number system, sequences and functions on R, differentiability and integrability on R, infinite series of real numbers. Tentatively, the following chapters and sections will be covered: 1.3---1.6 of chapter 1, chapter 2, 3,4, 5.1---5.4 of chapter 5, 6.1---6.4 of chapter 6. If time permits, some topics in chapter 7 will be also discussed.
 
• Time: MWF 10:00 --- 10:50 AM
 
• Location: Strong Hall 339
 
• Text: An Introduction to Real Analysis (4th edition) by William R. Wade
 
• Prerequisite: Math 223, Math 290, math 500 or equivalent
 
• 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 15 problems. 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 be one midterm of 50 minutes in class. The date is tentatively scheduled to Oct. 22 (Monday) in class.
 
• Final Exam: There is a comprehensive final exam for this course. It is scheduled to be on Dec. 11, 7:30 am -- 10 am in class.
 
• Grade Percentage: homework (30 %) + midterm (20 %) + quizzes (10 %) + final (40 %).

Class Policy

• Lecture attendance is strongly recommended.
 
• Group study and discussion are encouraged, however, the homework must be completed independently. You are also strongly encouraged to work on as many exercises as possible.
 
• Please go through carefully the class schedule and mark all the important dates for exams and homework in your calender to avoid any conflict.

Students with disabilities

• If you have a disability for which you may request accomodation in KU classes, please contact the office of the staff of Services for Students with Disabilities (SSD), 135 Strong, 785-864-2620. Please also see the instructor privately in regard to this course.

Policy on religious observances

• All students in this course who plan to observe a religious holiday which conflicts in any way with the course schedule or requirements should contact the instructor as soon as possible to discuss alternative accomodations.

Instructions on turning in homework

• Put a cover page on top of your homework and staple all pages in the upper-left corner. Write your name on the upper-right corner and underline the last name. Please do not write your student ID number on the cover page. Fold your homework in halves. Your homework may not be graded if you do not follow these instructions.

Homework

• Homework 1 (due on Aug. 29th in class): P22. 1.3.1, 1.3.3, 1.3.6; P23. 1.3.11; P40. 1.6.1, 1.6.2, 1.6.3, 1.6.6. Solutions to Homework 1
 
• Homework 2 (due on Sept. 17th in class): P45. 2.1.1 a). d)., 2.1.2 a). c). 2.15; P51. 2.2.1; P52. 2.2.5. P57. 2.3.1, 2.3.2, 2.3.8. P61. 2.4.1, 2.4.4,2.4.6; P65. 2.5.2, 2.5.3; P66. 2.5.4. 2.5.5, 2.5.6 Solutions to Homework 2
 
• Homework 3 (due on Sept. 24th in class): P74. #3.1.2; P75. #3.1.6, #3.1.7; P76. #3.1.8; P81. #3.2.1; P82. #3.2.4, #3.2.6, #3.2.7; P83. #3.2.8. Solutions to Homework 3
 
• Homework 4 (due on Oct. 1st in class): P91. #3.3.3, #3.3.4, #3.3.5,#3.3.8, #3.3.10. P96. #3.4.2, #3.4.4, #3.4.5, P97. #3.4.7, #3.4.8, #3.4.9. Solutions to Homework 4
 
• Homework 5 (due on Oct. 12th in class; extended to Oct. 15th.): P104. #4.1.1, #4.1.4, #4.1.6, #4.1.7. P105. #4.1.8, #4.1.9. P107. #4.2.2, #4.2.5. P108. #4.2.6, #4.2.8. P116. #4.3.4, #4.3.6, #4.3.8, #4.3.11, #4.3.12 Solutions to Homework 5
 
• Homework 6 (due on Oct. 22nd in class.): P 123. #4.4.1 (a) (b). P124. #4.4.3, #4.4.5 (b)(d)(f)(h), #4.4.6 (a). P 125. #4.4.7, #4.4.8, #4.4.11. P 128. #4.5.2, #4.5.4 (a)(b)(c). P129 # 4.5.6, #4.5.9.#4.5.11 Solutions to Homework 6
 
• Homework 7 (due on Nov. 5th in class.): P139. #5.1.2, #5.1.3, #5.1.4, #5.1.5; P140. #5.1.6, #5.1.7; P141. #5.1.9. P151. #5.2.2, #5.2.4, #5.2.5, #5.2.6, #5.2.7, #5.2.8.Solutions to Homework 7
 
• Homework 8 (due on Nov. 16th in class.): P161. #5.3.3, #5.3.4; P162. #5.3.5, #5.3.6; P163. #5.3.9, #5.3.10.P168. #5.4.1 (a), (d); P169. #5.4.6, #5.4.7; P170. #5.4.8
Solutions to Homework 8  
• Homework 9 (due on Nov. 28th in class.): P190. #6.1.4, #6.1.5, #6.1.7; P191. #6.1.9, #6.1.11; P192. #6.1.12; P197. #6.2.1 (a), (d); #6.2.2 (a), (d). #6.2.3; P198. #6.2.5, #6.2.7, #6.2.9. Solutions to Homework 9
 
• Homework 10 (due on Dec. 5th in class.): P207. #6.3.3 (a) (c) (e), #6.3.5, #6.3.6; P208 #6.3.8; P213. #6.4.3, #6.4.4, #6.4.5, P214. #6.4.6. Solutions to Homework 10
 

Online Resource

• Prof. Stefanov's webpage and Prof. Torres's webpage, which contain some information of this course in the previous years.