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
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 364
Analysis I
Winter 2016
Course Instructor:
Dr. C. David, Office: LB 927-9 (SGW), Phone: 848-2424, Ext. 3227
Email: chantal.david@concordia.ca
Textbook:
Notes on Real Analysis by L. Larson
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: elie.cohen@concordia.ca
Text:
Linear Algebra, 4th Edition, by S. Friedb
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: galia.dafni@concordia.ca
Lectures:
M-W 13:15-14:30, MB 3.430
O
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: ron.stern@concordia.ca
Class Schedule:
Tuesdays and
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: alina.stancu@concordia.ca
Webpage: http:/alcor.concordia.ca/~a
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: chantal.david@concordia.ca
Office Hours:
To be announced.
Problem 1 [Sec. 5.1: # 2f]
The matrix of T with respect to the basis is
3
0
0
0
0
1
0
0
0
0
1
0
0
0
.
0
1
So is a basis of eigenvectors of T .
Problem 2 [Sec. 5.1: # 3b] Computing f (t) = det(A tI3 ), we nd f (t) = (t 1)(t 2)(t 3). So
the eigenvalues
Problem 1 [Sec. 3.4: # 6] Using Theorem 3.16 in the book, we can deduce the remaining columns of A
by expressing the corresponding columns of the reduced row echelon form of A as linear combinations of its
rst, third and fth columns which are the vectors
Problem 1 [Sec. 3.2: # 2f] By using row reduction, we nd the reduced row echelon form of the matrix is
1 2 0 1 0
0 0 1 1 0
0 0 0 0 1
0 0 0 0 0
Since there are 3 linear independent rows, the rank of the original matrix is 3.
Problem 2 [Sec. 3.2: # 4b] Usin
Math 251 Sec A Midterm Test 15 October 2003
Professor:
Instructions:
Richard Hall
Please answer both questions, which carry equal marks.
Explain your work clearly. Calculators are permitted.
1.
(a) Find the coordinates of the matrix
B=
1
1
1
1
,
0 1
1 1
0
Problem 1 [Sec. 1.2: # 12]
I will show that the sum of two even functions is even and the scalar multiplication too. So, if f, g are
even, then
symmetry
def
def
(f +g)(t) = f (t) + g(t) = f (t) + g(t) = (f +g)(t)
(1)
So the sum of even functions is even.
Problem 1 [Sec. 1.4: # 4(a,c)] We try and express the rst polynomial as a combination of the other two;
we will obtain a system of a certain number of equations (which depends on the example) in less unknowns.
Whether the system can be solved or not deter
Problem 1 [Sec. 1.6: # 4] They cannot possibly generate P3 (R). Indeed dim P3 (R) = 4 but those three
polynomials can generate a subspace of dimension at most 3.
Problem 2 [Sec. 1.6: # 10(b,d)] (b) The points are (4, 24), (1, 9), (3, 3) and thus
(x 1)(x 3
Problem 1 [Sec. 2.1: # 2] To prove linearity we use the criteria that T is linear i T (av + bw) =
aT (v) + bT (w) for any v, w V and a, b R. So, let v = (v1 , v2 , v3 ) and w = (w1 , w2 , w3 ). Then
T (av1 + bw1 , av2 + bw2 , av3 + bw3 ) = (av1 + bw1 ) (a
Note: Theorem X-Y means Theorem Y of Section X.
Problem 1 [Sec. 2.4: # 7] Let A be an nn matrix. For part a our hypothesis is that A2 is the zero matrix
and we have to prove the conclusion that A is not an invertible matrix. We will prove this by contradi
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: alexey.kokotov@concordia.ca
Text:
Basic Pa