For the exclusive use of T. Banguel, 2016.
W13377
A-CAT CORP.: FORECASTING
Jitendra Sharma wrote this case solely to provide material for class discussion. The author does not intend to illustrate either
effective or ineffective handling of a managerial s
Solutions Homework Assignment 10
Concordia MATH 364/626 Fall 2016
Problem 1. Let g(x) =
p
|x|.
definition of continuity to prove that g(x) is continuous for every x 2 R.
p
p
Proof. Fix x0 2 R. Let > 0 be given. We have to find > 0 so that |x x0 | < ) | |x
Solutions to Homework Assignment 12
Concordia MATH 364 Fall 2016
Problem 1. A function f : D R is called Lipschitz continuous (or just Lipschitz) if there exists a constant
M such that
x, y D |f (x) f (y)| M |x y|.
(i) Prove that a Lipschitz function is u
Homework Assignment 2
Concordia MATH 364/626/2
SOLUTIONS:
Problem 1:
(a) Does the the subset cfw_(x, y) R R : x3 = y 4 define a function ? If yes: is it
injective? , is it surjective?
Solution: No, it is not a function since for every positive x we have t
Homework Assignment 2
Concordia MATH 364/626/2
due Wednesday, September 28, 2016 in class
Solutions should be handwritten and submitted on paper, in class, not electronically. Solve the following 5 problems
in detail, making sure that the proofs are rigor
Homework Assignment 3
Concordia MATH 364/626/2
due Wednesday, October 5, 2016 in class
Solutions should be handwritten and submitted on paper, in class, not electronically. Solve the following 5
problems in detail, making sure that the proofs are rigorous
Homework Assignment 6
Concordia MATH 364/626/2
SOLUTIONS:
Solutions should be handwritten and submitted on paper, in class, not electronically. Solve the following 5 problems
in detail, making sure that the proofs are rigorous and complete and the calcula
MATH 364, December 2012 Final, SOLUTIONS:
Problem 1: Let S be a non-empty subset of R which is bounded above and
denote = sup S.
(a) Prove that for any > 0, there exists s S such that < s .
Solution: By contradiction. Let us assume that this is not true,
Homework Assignment 9
Concordia MATH 364/626/2
SOLUTIONS:
Solutions should be handwritten and submitted on paper, in class, not electronically. Solve the following 5 problems
in detail, making sure that the proofs are rigorous and complete and the calcula
Solutions to Homework Assignment 1
Concordia MATH 364/626/2, Fall 2016
Problem 1. Determine which of the following are mathematical statements, and write their negation:
(i) Please pass the salt.
This is not a mathematical statement since it cannot be ass
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
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 , ,
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)
[( ) ( )] ( ),
[( ) (
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
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
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
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
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.
(
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 # 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
The old midterms are posted with the caution that there
is no guarantee that the questions on the midterm will
be in the same style, since they will be based on the
homework assignments from this year and some of them
are significantly different from thos
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
Mathematics
Number
MATH 364/MATH 626
Examination
Midterm
Date
October 2016
Section(s)
A
Time
1 14 hours
Instructor
Pawel G
ora
Pages
3
Course Examiner
Galia Dafni
Special Instructions: A
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
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
Homework Assignment 11
Concordia MATH 364/626/2
due Wednesday, November 30, 2016 in class
Solutions should be handwritten and submitted on paper, in class, not electronically. Solve the following 5 problems
in detail, making sure that the proofs are rigor
Homework Assignment 10
Concordia MATH 364/626/2
due Wednesday, November 23, 2016 in class
Solutions should be handwritten and submitted on paper, in class, not electronically. Solve the following 5
problems in detail, making sure that the proofs are rigor
Homework Assignment 5
Concordia MATH 364/626/2
due Wednesday, October 19, 2016 in class
Solutions should be handwritten and submitted on paper, in class, not electronically. Solve the following 5
problems in detail, making sure that the proofs are rigorou
Homework Assignment 1
Concordia MATH 364/626/2
due Wednesday, September 21, 2016 in class
Solutions should be handwritten and submitted on paper, in class, not electronically. Solve the following 5
problems in detail, making sure that the proofs are rigor
Homework Assignment 4
Concordia MATH 364/626/2
due Wednesday, October 12, 2016 in class
Solutions should be handwritten and submitted on paper, in class, not electronically. Solve the following 5 problems
in detail, making sure that the proofs are rigorou