Assignment # 2 MATH 364 , Fall 2015
Due date: September 30, 2015
Problem 1:
Let S be the set of all squares in R2 such that: the sides are parallel to
the coordinate axes, the center has rational coordinates, the length of the side is a
rational number. P
Assignment # 3 MATH 364 , Fall 2015
Due date: October 7, 2015
Problem 1:
Sketch graphs of
a) f(x) = x E(x)
b) g(x) = 1/x E(1/x)
c) h(x) = sin(1/x). E(x) denotes the largest integer smaller or equal to x. For
example: E(1.2) = 1, E(0.35) = 0, E(1) = 1, E(1
Assignment # 4 MATH 364 , Fall 2015
Due date: October 14, 2015
Problem 1:
(a) Let f : X Y be a surjective map. Show that there exists an
injective map g : Y X such that f g : Y Y is the identity map, f g = IdY .
The function g is called a right inverse.
(
Sample questions for MATH 364
October 2012
Section A only
This is a representative list of problems. The actual midterm will consist in 6 (or less) questions.
Problem 1. Rewrite the following statements using only the symbols , , and brackets
a. (A A) A
b
Department of Mathematics & Statistics
Concordia University
MATH 364 (MATH 626)
Analysis I
Fall 2015
Instructor*:
Office/Tel No:
Office Hours:
*Students should get the above information from their instructor during class time. The instructor is the person
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
Mathematics
Number
MATH 364
Examination
Midterm
Date
October 2012
Section(s)
A
Time
1 1 hours
4
Instructors
Pawel Gra
o
Pages
4
Course Examiner
Ronald Stern
Special Instructions: Approve
CONCORDIA UNIVERSITY
Course
Mathematics
Department of Mathematics and Statistics
Number
MATH 364
Examination
Midterm
Date
February 2013
Section(s)
AA
Time
1 1 hours
4
Instructor
Pawel Gra
o
Pages
4
Course Examiner
Ronald Stern
Special Instructions: Approv
Assignment # 1, Math 364, Fall 2015
1. Express the sentence ( ) using symbols , and .
2. Write negation of the sentence
( ).
3. Prove that the following sentences are theorems, i.e., are true for all choices of
sentences , , .
a)
b)
[( ) ( )] ( ),
[( ) (
Assignment # 1, Math 364, Fall 2015
Due date: September 23, 2015
1. Express the sentence ( ) using symbols , and .
2. Write negation of the sentence
( ).
3. Prove that the following sentences are theorems, i.e., are true for all choices of
sentences , ,
40 CHAPTER 4. CON TINUITY
0 => f = f(:c); and so, by induction, = (-1)f(:z:) V n E N.
Suppose f is continuous at 0. Since 5: -> O, f + f(0) = 0. Hence
(1)"f(z) -> 0, and so f(:r) = 0. We have just shown that if f(:z:)+f(2x) =
O V a: e R and f is cont
30 CHAPTER 3. SEQUENCES
by Theorem 3.10, (3410,3531 (and hence (3n)neN) has a subsequence
(2n)neN which converges to some M E R. Since. [21,, L] 2 a Vn e N,
M % L. Thus, M and L are 2 distinct subsequential limits .of (xn)neN .
4. R since R \ Q is dens
1.3.
6.
FUNCTIONS ' 5
For the other containment, let y E f(A) U f(B). If y E f(A), then
y = f(a:) for some :1: E A C AUB. Ify E f(B)7 then y = f(x) for
some a: E B CAUB. Thus, 3/ e f(AUB).
By drawing the graph of f (this needs to be stressed to studen
Sample questions for MATH 364
October 2008
Instructors: Dr. Marco Bertola
This is a representative list of problems. The actual midterm will consist in 6 (or less) questions.
Problem 1. Rewrite the following statements using only the symbols , , and brack