CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Number
251/2
Problem assignment
7
Instructor I. Cojocaru
Due date
November 3
Week no.
8
Instructions.
Answer all questions. The value for each part is indicated in square
brackets i
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Assignment
4
Number
251
Section
AA
Due date
February 9 (beginning of the class)
Course Instructor
I. Cojocaru
Instructions. Late assignments will not be accepted. Solutions must be
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Assignment
5
Number
251
Section
AA
Due date
February 16 (beginning of the class)
Course Instructor
I. Cojocaru
Instructions. Late assignments will not be accepted. Solutions must be
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Number
251
Assignment
1
Section
AA
Due date
January 19 (beginning of the class)
Course Instructor
I. Cojocaru
Instructions. Late assignments will not be accepted. Solutions must be
Midterm MATH 251, March 2, 2017
Justify all answers
Problem 1 [5 pt] Let V = P4 (R) Determine whether the following set
S = cfw_1 + x, 1 2x2 + x3 , 5 + 2x 6x2 + 3x3 , x2 , 2x4
(1)
is linearly independent. Justify your answer.
Problem 2 [5pt] Let V = M22
Solution to Problem 1 First case. We try to write them as a linear combination (in column form for brevity)
1
a + b + 2c
2
b+c+d
=
(1)
0 a + b + 2c
1
a + b + 2c + e
The system clearly has no solution because the two equations marked in red are inco
Midterm MATH 251, Fall 2015
Justify all answers
Problem 1 [5 pt] Let V be the vector space indicated below, case by case. In each case find if the specified vector v
belongs to the span of the given set S.
V = R4 ;
S := cfw_(1, 0, 1, 1), (1, 1, 1, 1), (2,
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Number
251/2
Sections
Problem solutions
Assignment 5
Due date
October 13
Instructor
J. Harnad
Solutions.
[2]
Course examiner
J. Harnad
1.
0 2 1
M = 1 0 2
1 1 0
[2]
2.
0
0
M =
0
0
[2
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Number
251/2
Problem assignment
10
1. Solution: We have
Week no.
11
Due date
November 24
1
0
[T ] =
0
0
0
1
0
0
0
0
1
0
0
0
,
0
1
and hence, is a basis of eigenvectors of T .
2. So
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Number
251/2
Week no.
11
Problem assignment
Due date
10
November 24
Instructor
Instructions.
Answer all questions. The value for each part is indicated in square
brackets in the mar
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Number
251/2
Week no.
3
Instructor
Course examiner
J. Harnad
Instructions. Answer all five questions. The value for each part is indicated in square
brackets in the margin (out of a
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Number
251/2
Week no.
6
Instructor
Course examiner
J. Harnad
Instructions.
Answer all questions. The value for each part is indicated in square
brackets in the margin (out of a poss
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Number
251/2
Problem assignment
2
Sections
Due date
September 22
Instructor
Course examiner
J. Harnad
J. Harnad
Instructions. Answer all five questions. The value for each part is i
Department of Mathematics and Statistics
Concordia University
MATH 251
Linear Algebra I
Winter 2017
Instructor:
Dr. I. Cojocaru, Office: LB 1036 (SGW), Phone: 848-2424, Ext. 8656
Email: [email protected]
Text:
Linear Algebra, 4th Editio
Theorems
Theorem 1.1 (Cancellation Law for Vector Addition). If 3;, y,
and z- are Vectors in a vector space V such that a: + z = y + 2, then a: = y.
Proof. There exists a vector v in V such that 2 +1: = 0 (VS 4). Thus
x=m+0=m+(z+v]=(m+z)'+v
=(y+23+v=y+(z+
Theorems
Theorem 1.1 (Cancellation Law for Vector Addition). If 3;, y,
and z- are Vectors in a vector space V such that a: + z = y + 2, then a: = y.
Proof. There exists a vector v in V such that 2 +1: = 0 (VS 4). Thus
x=m+0=m+(z+v]=(m+z)'+v
=(y+23+v=y+(z+
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Assignment
2
Number
251
Section
AA
Due date
January 26 (beginning of the class)
Course Instructor
I. Cojocaru
Instructions. Late assignments will not be accepted. Solutions must be
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Assignment
6
Number
251
Section
AA
Due date
March 9 (beginning of the class)
Course Instructor
I. Cojocaru
Instructions.
Late assignments will not be accepted. Solutions must be wri
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course Number
MATH
251/2
Week no. 10
Problem assignment 9
Due date: November 17
SOLUTIONS
Solution to no.1 The RREF of
student)
1
0
0
and hence
x1 = 1 +
the augmented matrix is (the steps are
Midterm MATH 251, October 17, 2013
Justify all answers
Problem 1 [5 pt] Are the following subsets of P(R) (space of polynomials) subspaces? Justify your
answer.
(a) W1 := cfw_p(x) : p(4) = 0, p(3) = 0
(b) W2 := cfw_p(x) : p(2) = 1
(1)
Problem 2 [5 pt] Fi
Department of Mathematics & Statistics
Concordia University
MATH 473 (MAST 666)
Partial Differential Equations
Winter 2016
Instructor:
Dr. A. Kokotov, Office: LB 921-5 (SGW), Phone: 514-848-2424, Ext. 3471
Email: [email protected]
Text:
Basic Pa
Department of Mathematics and Statistics
Concordia University
MATH 470 (MAST 692)
Abstract Algebra II
Winter 2016
Instructor:
Dr. C. David, Office: LB 927-9 (SGW), Phone: 848-2424, Ext. 3227
Email: [email protected]
Office Hours:
To be announced.
Department of Mathematics & Statistics
Concordia University
MATH 467 (MAST 669)
Measure Theory
Winter 2016
Instructor:
Dr. A. Stancu, Office: LB 927-21 (SGW), Phone: 848-2424, Ext. 5345
Email: [email protected]
Webpage: http:/alcor.concordia.ca/~a
Department of Mathematics & Statistics
Concordia University
MATH 361 (MATH 601)
Operations Research I
Winter 2016
Instructor:
Prof. R.J. Stern, Office: LB 901-19 (SGW), Phone: 848-2424, Ext. 3255
Email: [email protected]
Class Schedule:
Tuesdays and
Department of Mathematics & Statistics
Concordia University
MATH 365 (MATH 627)
Analysis II
Winter 2016
Instructor:
Dr. G. Dafni, Office: LB 927-15 (SGW), Phone: 514-848-2424, Ext. 3216
Email: [email protected]
Lectures:
M-W 13:15-14:30, MB 3.430
O
Department of Mathematics and Statistics
Concordia University
MATH 251
Linear Algebra I
Winter 2016
Instructor:
Dr. E. Cohen, Office: LB 921-1 (SGW), Phone: 848-2424, Ext. 3219
Email: [email protected]
Text:
Linear Algebra, 4th Edition, by S. Friedb
Department of Mathematics & Statistics
Concordia University
MATH 364
Analysis I
Winter 2016
Course Instructor:
Dr. C. David, Office: LB 927-9 (SGW), Phone: 848-2424, Ext. 3227
Email: [email protected]
Textbook:
Notes on Real Analysis by L. Larson
Department of Mathematics and Statistics
Concordia University
MATH 252
Linear Algebra II
Winter 2016
Instructor*:
_
Office/Tel No.:
_
Office hours:
_
*Students should get the above information from their instructor during class time. The instructor is the
Department of Mathematics & Statistics
Concordia University
MATH 265
Advanced Calculus II
Winter 2016
Instructor*:
_
Office/Tel No.:
_
Office Hours:
_
* Students should get all the above information from their own instructor. The instructor is the person
CONCORDIA UNIVERSITY
Department of Mathematics and Statistics
Course
MATH
Number
251/2
Assignment 6: solutions
Due: Thursday, Oct. 20
Week no.
6
Course examiner
J. Harnad
Solution to no.1 Let n = dim V (finite dimensional). Let k = dim Ker(T ) and
= cfw_