MA
108B
MID-TERM EXAMINATION
INSTRUCTOR:
Time:
N.H. KATZ
266 SLOAN
WINTER 2014
x2326
4 hours
This exam should be completed in a standard blue book (or two) within four hours, at one sitting.
Be sure to write your full name on the blue book. If you go over
Problem set 5: due February 27
Turn in one of the following:
choice 1: 4 standard problems and the challenge problem
choice 3: All 6 standard problems.
Standard Problems
Carothers Chapter 17: 11,31 Chapter 18: 4,22,42,51
Challenge problem
1. Let f be a no
Problem set 4: due February 20
Turn in one of the following:
choice 1: 4 standard problems and the challenge problem
choice 3: All 6 standard problems.
Standard Problems
Carothers Chapter 16: 8,16,28,37,44,73
Challenge problem
1. Let E [0, 1] be a measura
Problem set 2: due January 23
Turn in one of the following:
choice 1: 2 standard problems and both Challenging problems.
choice 2: 4 standard problems and 1 Challenging problem.
choice 3: All 6 standard problems.
Standard Problems
Carothers Chapter 14: 5,
Problem set 1: due January 16
Turn in one of the following:
choice 1: 2 standard problems and both Challenging problems.
choice 2: 4 standard problems and 1 Challenging problem.
choice 3: All 6 standard problems.
Standard Problems
Carothers Chapter 13: 5,
PROBLEM SET NO. 7, PART II
Let X = cfw_(xn )nN :
nN
|xn | < and
|xn |
x =
for x = (xn )nN .
nN
Show that is a norm on X and show that X is complete with respect
to the corresponding metric.
Dene G : R2 R by
xy
x2 + y 2
G(x, y) :=
0
, if (x, y) = (0, 0)
PROBLEM SET NO. 7, PART I
Rudin, Ch. 7: Exercises 16, 25 (you dont need to prove the Riemann
integrability in (a)
Problem set due on Wednesday, 11/26, 4:00 PM, in math departments drop
box
1
PROBLEM SET NO. 6
Rudin, Ch. 4: Exercise 20
Rudin, Ch. 7: Exercises 1, 5, 7, 14
Problem set due on Thursday, 11/20, 4:00 PM, in math departments drop box
1
PROBLEM SET NO. 5
Rudin, Ch. 3: Exercise 20, 21 (complete is dened in 3.12)
Rudin, Ch. 4: Exercise 4, 6, 18
Problem set due on Thursday, 11/13, 4:00 PM, in math departments drop box
1
PROBLEM SET NO. 4
Rudin, Ch. 2: Exercise 6, 15, 22, 24
Rudin, Ch. 3: Exercise 1
Problem set due on Tuesday, 10/28, 4:00 PM, in math departments drop box
1
PROBLEM SET NO. 3
Rudin, Ch. 2: Exercise 7, 9, 14, 16
For grading purposes, 9 counts as two problems (parts a,b,c and d,e,f, respectively as one problem).
Problem set due on Thursday, 10/23, 4:00 PM, in math departments drop box
1
PROBLEM SET NO. 1
Rudin, Ch. 1: Exercises 5, 6, 8, 9
Rudin, Appendix to Ch. 1: Fill in the details in Step 6, i.e., verify the
axioms (M) and (D) of Denition 1.12 with R+ in place of F and with 1
in the role of 1.
Problem set due on Thursday, 10/9, 4:00