Math 337 Winter 09, Problem set 1
Due Wed. Jan. 21
All problems are from the text. Hand in:
2.4 A(f), K
2.5 D, E, I Hint for I above: Start by showing that if n + m 2 = n + m 2
then n = n and m = m . Then follow the hint in the text.
2.6 B, D
2.7 H
2.8 B.
Math 337 Winter 09, Problem set 2
Due Fri. Feb. 6
All problems are from the text. Problems to do. Hand in only the starred ones.
2.9 E , L
3.1 D, F
Note: for 3.1 F, the aim is to prove that k=0 (k + 1)ak converges, nd a
formula for it and then apply it do
Math 337 Winter 09, Problem set 3
Due Fri. Feb. 27
All problems are from the text. Problems to do. Hand in only the starred ones.
4.4 C, D, E . Referring to E , also show that if A and B are compact then
A + B is compact, and hand this in as well.
5.1 E,
Math 337 Winter 09, Problem set 3
Due Mon. Mar. 16
Do the following. Hand in only the starred problems.
5.5
5.6
5.7
6.1
6.2
6.3
6.4
A, H, I*
D, F, H*
A*, H
R*, U
I*, N
M, R*
A
Also suggested:
5.5 C
5.6 A, E
6.4 C
1
Math 337 Winter 09, Problem set 5
Due Mon. Mar. 30
Hand in the following.
7.1 A, C
7.2 D, J. If you want to get a feeling for why D is true think about the
case where A is a line segment in R2 and U is an open ball in R2 . (Dont
consider this as a hint fo
Math 337 Winter 09, Problem set 6
NOT TO BE HANDED IN
Do the following.
8.3 B and I. Hint for I: ignore the hint in the book, you only need 6.3.5,
Riemanns integrability criterion.
8.4 C, J. The hint given for J doesnt help as far as I can see, you can us