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 makeup 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 makeup midterm without a valid reason . In the case of taking the makeup 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 makeup 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, 7858642620. 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 upperleft corner. Write your name on the upperright 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
the midterm review
the final review
Online Resource
Prof. Saul Stahl's webpage.