Spring 2012, Math 500, Real Analysis

Course Information

• Course Coverage: This course intends to cover some basic topics of real analysis at the undergraduate level: the real number system, limits, sequences, series of numbers, series of functions, continuity, differentiability, and Riemann integrals. Tentatively, we will quickly go over the first five chapters of the book; then starting from the 6th chapter, we will discuss the following chapters and sections: 6.1, 6.3, 6.5 and part of 6.2 in Chapter 6, Chapter 7, Chapter 8, 9.1, 9.2, 9.3 in Chapter 9, Chapter 10, Chapter 11, Chapter 12, and Chapter 15.
 
• Time: MWF 12:00 ---12:50 PM
 
• Location: Snow Hall 301
 
• Text: Real Analysis: A Historical Approach (2nd Edition), By Saul Stahl
 
• Prerequisite: Math 223 and Math 290
 
• Instructor: Shuanglin Shao
 
• Office: Snow Hall 615
 
• Email: slshao@ku.edu
 
• Office Hour: MWF: 1:30 --- 2:30 PM, or by appointment

Grade Policy

• Homework: There will be 10 homework. Each homework consists of roughly 20 problems; only 3 of them will be graded, which will be decided after you turn in homework. The lowest homework grade will be dropped. No late homework will be accepted.
 
• Quizzes: There will be 5 quizzes in class; the date will be annouced one week in advance in class or by email. No make-up quizzes.
 
• Midterm: There will one midterm of 50 minutes in class. The date is tentatively scheduled to be the time after we finish Chapter 9. No make-up midterm without a valid reason . In the case of taking the make-up midterm, you should submit a written and signed notice to the instructor in advance.
 
• Final Exam: There is a comprehensive final exam for this course. The date and location are to be determined. No make-up final.
 
• Grade Percentage: homework (30 %) + midterm (20 %) + quizzes (10 %) + final (40 %). Tentatively, a total of 85% will be in the A range, 75% in the B range, 60 % in the C range, and 45% in the D range.

Class Policy

• Calculators are not allowed in either exams or homework unless specified. But crib sheets are allowed in exams. For midterm, a sheet is allowed at one side of a half page of 8.5*11 inch; for final, one side of a full page of 8.5*11 inch is allowed.
 
• 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 in Class on Feb. 1): P6, 1(a) (b). P7. 4. P17, 1(a), 2(b). P23, 1(a) (k). P39, 1(a)(d). P57 1(a) (b). Solutions to Homework 1
 
• Homework 2 (due in Class on Feb. 8): P63, 1,3. P64. 8,9. P75, (a), (b), (c), (d), (e), (f), (r), (t), (v). P76, 4,8. Solutions to Homework 2
 
• Homework 3 (due in Class on Feb. 15; extended: Feb. 22): P91, 1, (b), (d), (f), (h), (j), (l), 2,4,6. P 99, 1, (b), (d), (f), (h), (j), (l), (n), (p). 3, 5,7. P 100, 10,12,13. P101. 25, 27,28, 35,36. Solutions to Homework 3
 
• Homework 4 (due in Class on Feb. 29): P108, 1,4,5. P 109, 15; P 113, 1; p 114, 2,7. Solutions to Homework 4
 
• Homework 5 (due in Class on Mar. 7): P119, 1, b), f). P120, 2, b), d), f), h). 3, 7, 11,12,13. P 123, 1, a), d),g),j),l),n),p). 2, 3. Solutions to Homework 5
 
• Homework 6 (due in Class on Mar. 14; extended: Mar. 26): P129, 1. b,d,f,h,j,l,n,p,r. P130. 3,4. P131, 6,8,9,12,14,15,16,17,18. Solutions to Homework 6
 
• Homework 7 (due in Class on Mar. 28; extended: March 30): P143, 1. b), h),n). 2,4,8,9. P144, 15,16. P146, 1. b),d),f). 2. a), c), e), g). Solutions to Homework 7
 
• Homework 8 (due in Class on April 11): P154. 1,2,8; P155. 13; P159. 1; P160, 2,11; P161. 14; P162. 23,31; P166. 1,3; P167. 7. Solutions to Homework 8
 
• Homework 9 (due in Class on April 25): P175. Ex. 1,4,6; P 176. Ex. 15, 17,22. P177. 25; P181. Ex. 2, 4,9,12,13,14,15; P 182. Ex. 17; P 184. Ex. 2,4,5. Solutions to Homework 9
 
• Homework 10 (due in Class on May 2): P221. Ex.1,3,5; P 226. Ex. 2. P234. 3; P235. Ex.5,6,7,8,10,15. Solutions to Homework 10
 

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