Notes on integration and measure
P. B. Kronheimer, for Math 114
Revised, September 12, 2010
These are some outline notes on integration and measure, based on the book by Stein and Sharkarchi
that we are using in class, but adapted to the approach we will
A note on compactness
P. B. Kronheimer, for Math 114
September 1, 2010
These notes are supposed to ll a potential gap, for those who have not seen compactness in the
context of Math 131 or similar.
1. The Bolzano-Weierstrass theorem
All the courses that s
MATH 135
Assignment #1
Winter 2009
Due: Wednesday 14 January 2009, 8:20 a.m.
N.B. Assignments 3 to 9 will not be distributed in class. You must download them from the course
Web site.
Hand-In Problems
1. Disprove the statement “There is no integer n > 3 s
MATH 135
Section
LEC 001
LEC 002
LEC 003
LEC 004
Time
1:30 MWF
10:30 MWF
9:30 MWF
12:30 MWF
ALGEBRA
Location
MC 2034
MC 2034
MC 2034
MC 4021
Instructor
S. Laishram
J. Lawrence
B. Ferguson
M. Eden
Oﬃce
MC 5054
MC 5057
MC 5100B
MC 5102
WINTER 2009
Phone
x33
MATH 135
Winter 2009
Assignment #2
Due: Wednesday 21 January 2009, 8:20 a.m.
Hand-In Problems
1. Express each statement as a logical expression using quantiﬁers. State the Universe of discourse.
(a) There is a smallest positive integer.
(b) There is no sm
MATH 135
Assignment #4
Winter 2009
Due: Wednesday 4 February 2009, 8:20 a.m.
Hand-In Problems
1. For each pair a and b, state the quotient and remainder when a is divided by b.
(a) a = 387, b = 11
(b) a = −387, b = 11
(c) a = 387, b = 121
(d) a = −387, b
MATH 135
Assignment #5
Winter 2009
Due: Wednesday 25 February 2009, 8:20 a.m.
Hand-In Problems
1. In each part, state the answer. No justiﬁcation is necessary.
(a) Determine all non-negative solutions to the linear Diophantine equation 133x + 315y =
98000