# Real Analysis

Course DescriptionCourse Information Syllabus Homework Assignments

Homework Assignments

Usually on Fridays, we will post the homework due the next Friday. Note that normally you will be handing in homework that goes from Friday of one week through Wednesday of the next week. Here is the homework to date. Note: Homework will be updated on Wednesdays to take into account where we actually are.

Week Number Section Homework Due Date
Week #1
1/5, 1/7
1.1 p. 8: 2, 3, 4, 9 Jan. 9
Week #1
1/9
Week #2
1/12, 1/14
1.2; 1.3
Prob. No. 1 below;
p. 17: 1, 3, 7, 8;
p. 17: 12, 14, 16;
p. 27: 1, 3, 4, 6, 11, 13
Jan. 16
Week #2
1/16
Week #3
[no class Mon 1/19: MLK Day],
1/21
1.4 p. 27: 19, 20;
p. 35: 2, 5, 8
Jan. 23
Week #3
1/23
Week #4
1/26, 1/28
1.4; 2.1 p. 35: 1abcd, 20;
p. 58: 1, 2, 4;
p. 58: 10, 13
Midterm: thr. hwk. due 1/30.
Jan. 30
Week #4
1/30
Week #5
2/2, 2/4
Midterm Exam 2/4-2/6
2.2 p. 58: 7abd;
p. 66: 3, 16, 26;
p. 66: 24, 36, 37
Feb. 11
Week #5
2/6
Week #6
2/9
[No class Fri 2/13: Winter Carnival]
2.3 p. 74: 1, 3ad, 6, 14; Feb. 11
Week #6
2/11
Week #7
2/16, 2/18
3.1, 3.2 p. 90: 3, 9 (Hint: Thms 3.2, 2.7);
p. 90: 27, 32, 38;
p. 97: 7, 25
Feb. 20
Week #7
2/20
Week #8
2/23, 2/25
3.3; 3.5, 3.4 p. 97: 11a, 19;
p. 106: 1, 5 [Hint: IVT],
9 [Hint: consider fctn g(x) = f(x) - x], 13;
p. 121: 8, 9abc; p. 114: 4, 5
Feb. 27
Week #8
2/27
Week #9
3/2, 3/4
6.1, 6.2, 6.3; 7.1, 7.2 p. 214: 1c, 4, 19, 20;
p. 219: 7, 8b,
14acd [comparison test only];
p. 226: 5a, 6;
p. 246: 3 [Also, is convergence uniform?]
pp. 251, 256 [as possible]
Mar. 6:
Do not hand in; take to:
Tutorial Session
Th 3/5 6:00-8:00
105 Kemeny
Week #9
3/6, 3/9
7.2, 7.3 Give out final Mon. 3/9. Fri. Mar. 13: final due
11:00 am, 102A Kemeny

• 1. Prove that in a field F, the element 0 in axiom 4 of Definition 1.1 is unique. (Hint: Assume that there are two elements 0 and 0' in F such that x + 0 = x and x + 0' = x for all x in F. Show that 0 = 0' using a field axiom from Definition 1.1 in each step of your proof.