## Spring 2013, 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.
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• Time: MWF 10:00 ---10:50 AM
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• Location: Snow Hall 301
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• Text: Real Analysis: A Historical Approach (2nd Edition), By Saul Stahl
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• Prerequisite: Math 223 and Math 290
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• Instructor: Shuanglin Shao
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• Office: Snow Hall 615
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• Email: slshao@ku.edu
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• Office Hour: M, F: 2:00 --- 3:00 PM, W: 1-2 PM, or by appointment

• 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.
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• Quizzes: There will be 5 quizzes in class; the date will be annouced one week in advance in class or by email.
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• Midterm: There will one midterm of 50 minutes in class on March 15, 2013.
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• Final Exam: There is a comprehensive final exam on May 15, 7:30 AM--- 10:00 AM. The location is 301 Snow Hall.
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• Grade Percentage: homework (30 %) + midterm (20 %) + quizzes (10 %) + final (40 %).

#### Homework

• Homework 1 (due in Class on Feb. 8): 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
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• Homework 2 (due in Class on Feb. 15): P63. 1,3. P64. 8,9. P75. (a), (b), (c), (d), (e), (f), (r), (t), (v). P76. 2, 4, 7, 8. Solutions to homework 2
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• Homework 3 (due in Class on Feb. 25): P91, #1, (b), (d), (f), (h), (j), (l), #2; P92. #4,#6; P 99. #1, (b), (d), (f), (h), (j), (l), (n), (p). #3,#5,#7; P100. #10, #12, #13; P101. #25,#27,#28,#35,#36.Solutions to homework 3
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• Homework 4 (due in Class on Mar. 4): P108, 1,4,5. P 109, 15; P 113, 1; p 114, 2,7. Solutions to homework 4
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• Homework 5 (due in Class on Mar. 15): P119, 1, b), f). P120, 2, b), d), f), h). 7,11,12,13. P 123, 1, a), d),g),j),l),n),p). 2, 3. Solutions to homework 5
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• Homework 6 (due in Class on Mar. 27): P129, 1. b,d,f,h,j,l,n,p,r. P130. 3,4. P131, 6,8,9,12,14,17,18. Solutions to homework 6
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• Homework 7 (due in Class on Apr. 5): 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
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• Homework 8 (due in Class on Apr. 17): P154. 1,2; P155. 8, 13; P159. 1; P160, 2,11; P161. 14; P162. 23,31; P166. 1,3; P167. 7.Solutions to homework 8
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• Homework 9 (due in Class on May 1): P175. Ex. 1,4,7; P 176. Ex. 15,17,22. P181. Ex. 2,3,4,12,13,14,15; P 182. Ex. 17; Solutions to homework 9
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• Homework 10 (due in Class on May 8): P221. Ex.1,2,3,5; P 226. Ex. 2. P234. 3; P235. Ex.5,6,7,8,10. Solutions to homework 10
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