Office Hours for the
remainder of the semester:
|
Friday May 3 |
1:00 - 2:00 |
|
Monday May 6 |
9:00 - 10:00 |
|
Tuesday May 7 |
9:30 - 11:00 |
|
Wednesday May 8 |
9:00 - 10:00 |
|
Thursday May 9 |
9:30 - 11:00 |
Homework and Reading
Assignments: Homework
is to be turned at the beginning of class on the days indicted below. Soon
after class each day the homework assignments will be posted here. You
should do all the homework listed, but turn in only the problems listed in bold
face type. The reading assignments are to be completed by the beginning of
class on the days indicated. The class discussion will focus on the reading
assignment. The schedule below is subject to change.
o January
14
Introduction to Real Analysis
o Janaury 16
Read Section 13
through the middle of page 131
Read Section 2
o January
18
Read the rest of
Section 13
o January
23
Read Section 1
Page 134 13.1 a, b, c, d, e, f, g, 13.2 a, b, 13.3 a, b (Turn in all of these.)
o January
25
Read Section 5
o January
28
Continue with Section
5
o January
30
Negating statements with quantifiers
o February
1
Page 8 1.1, 1.2, 1.3, 1.4, 1.7, 1.9, 1.10, 1.11
Page 15 2.2, 2.3, 2.5, 2.8
Page 47 5.2, 5.3, 5.4, 5.5, 5.8, 5.15,
5.16
o February
4
Review Section 13
o February
6
Continue Section 13
o February
8
Continue Section 13
Page 135 13.5 a, b, d, e, f, 13.8, 13.11 (Hint: think of a set difference as an
intersection.), 13.21 a
Page 49 5.19, 5.25
o February
11
Read the remainder of
Section 13
o February
13
Review for Exam 1
o February
15
Review for Exam 1
Work on the proofs of the lemma I stated in class, Part 2) of the theorem I
stated in class, and problems 13.20 b,c,d, 13.22 a,b,c, and 13.23 a,b,c
o February
18
Exam 1
Page 136 13.12, 13.13, 13.20a
o February
20
Continue Section 13
o February
22
Continue Section 13
Read Section 11
o February
25
Read Section 14
through Lemma 14.4 and read the statement of the Heine-Borel
Theorem
Read Section 12
o February
27
Continue Section 12
Turn in the “Fill in the Reasons” handout
and Page 115 11.3 h,i
o March
1
Continue Section 12
o March
4
Read Section 14
Page 126 12.1, 12.2, 12.3 a,c,d,f,i, 12.4 a,c,d,f,I
Page 135 13.3 c,d 13.4 c,d
o March
6
Continue Section 14
o March
8
Continue Section 14
Page 126 12.6, 12.8, 12.9, 12.13
Page 136 13.19
o March
18
Continue Section 14
o March
20
Read Section 6 through the middle of page 53
Read Section 7
o March
22
Continue Section 7
Page 143 14.1, 14.2, 14.4, 14.5
Page 73 7.1, 7.2 a,b,c,d, 7.3, 7.4, 7.7
o March
25
Review for Exam 2
o March
27
Review for Exam 2
o March
29
Exam 2
o April
1
Continue Section 7
o April
3
Definition of continuous functions
o April
5
Continue discussion of continuous functions
o April
8
Proof of Intermediate Value Theorem
o April
10
Proof that continuous functions with domain [a,b]
attain a maximum
o April
12
Consequences of the two theorems
o April
15
Read Section 10 – Induction
Homework on continuous functions due today.
o April
17
Continue induction proofs
o April
19
More Induction
o April
22
Still more induction
Homework 2 on continuous functions due today
o April
24
Cardinality
Read Section 8
o April
26
Review for Exam 3
o April
29
Exam 3
Page 104 10.3,
10.4, 10,6, 10.8, 10.10,10.13, and use induction to prove that the union of any
finite number of closed sets is closed (You may assume that the union of two
closed sets is closed since we proved this before.)
o May
1
Review for Final
o May
6
Final exam (10:30 in classroom)