Spring 2015, 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 and sequences, sequences and series of functions, continuity and differentiability of functions, Riemann integrals. Tentatively, we will cover Chapter 1 to Chapter 6.
 
• Time: MWF 11:00 --- 11:50 AM
 
• Location: Snow Hall 301
 
• Text: Elementary Analysis, the theory of Calculus, (2nd edition), By Kenneth A. Ross
 
• Prerequisite: Math 223 and Math 290
 
• Instructor: Shuanglin Shao
 
• Office: Snow Hall 615
 
• Email: slshao@ku.edu
 
• Office Hour: MWF: 1:00 --- 2:00 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.
 
• 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 on March 11, 2015.
 
• Final Exam: There is a comprehensive final exam on May 11, 10:30 AM --- 1:00 PM. The location is 301 Snow Hall.
 
• Grade Percentage: homework (30 %) + midterm (20 %) + quizzes (10 %) + final (40 %).

Homework

• Homework 1.(due by Feb. 2nd in class.): #1.1,#1.7,#1.12,#2.3,#2.7,#3.1.#3.5,#3.8,#4.3,$4.4,$4.5,#4.9,#4.10,#4.12,#4.14, #4.16,#5.4.Solutions to homework 1
 
• Homework 2.(due by Feb. 16th in class;rescheduled to be due by Feb. 20th in class.): #7.3(b)(d)(f)(h)(j)(l)(n)(p)(r)(t);#7.4,#8.2(b)(d),#8.4,#8.5(a)(b),#8.6,#8.8; #9.4,#9.5,#9.9,#9.11,#9.15,#9.18,#10.1,#10.3,#10.6,#10.7,#10.9,#10.12.Solutions to homework 2
 
• Homework 3.(due by March 9th in class.extended to March 13 in class): #11.2, # 11.3, # 11.6, #11.8, # 11.11, # 14.1, # 14.2, # 14.5, # 14.6, # 14.8, # 14.12, # 14.13, # 14.14, # 15.1, # 15.2, # 15.3, # 15.6, # 15.7. Solutions to homework 3
 
• Homework 4.(due by March 30th in class.): #17.1, #17.4,# 17.9 (a), # 17.10 (b), # 17.11, # 17.13(a), # 18.1, #18.2,#18.4,#18.5,#18.8,#18.12. Solutions to homework 4
 
• Homework 5.(due by April 1st in class.): #19.1,#19.2 (a)(b), #19.3(a), #19.4, #19.6,#19.7,#19.9; # 20.1,#20.2,#20.5,#20.6,#20.11,#20.11,#20.12,#20.16,#20.17,#20.20. Solutions to homework 5
 
• Homework 6.(due by April 10th in class.): #23.1(b)(d)(f)(h), # 23.2, #23.4, #23.5, #23.6; #28.1 (a)(c)(e), #28.2, #28.3, #28.4,#28.7,#28.11,#28.12, #28.14,#28.16 Solutions to homework 6
 
• Homework 7.(due by April 13th in class.): #29.1(a)(c)(e), # 29.2. # 29.3, # 29.4, # 29.7, # 29.9, # 29.11, #29.18. Solutions to homework 7
 
• Homework 8.(due by April 20th in class.): #32.1, #32.2, #32.3, #32.4, #32.6. Solutions to homework 8
 
• Homework 9.(due by April 27th in class.): # 33.1, # 33.2, # 33.4, # 33.5, # 33.7. Solutions to homework 9
 
• Homework 10.(due by May 4th in class.): # 34.1, # 34.2, # 34.5, # 34.6, # 34.7, # 34.11. Solutions to homework 10