Instructor:
Dr. Sergei Suslov
Office:
PSA 643
Phone:
965-8987
E-mail:
suslov@math.la.asu.edu
Office Hours: 9:40 – 10:15
am and 1:15 – 2:00 pm MWF
Text:
A First Course in Linear Algebra, 2nd edition,
by Moore & Yaqub, 1996
Prerequisite: MAT 272
or equivalent
Exams:
There will be three regular in class exams (3*100);
homework and/computer labs (100);
and a comprehensive final exam (200)
Grading Policy:
A = 90 - 100%
B = 80 - 89%
C = 70 - 79%
D = 60 - 69%
E = 0 - 59%
Material to be covered: Except
for a few sections, the entire text will be covered
Make-up policy: No make-up
exams will be given without notification.
Also, no late homework will be accepted for grading.
MAT 342 is a linear algebra course at the sophomore/junior level, intended primarily for mathematics, science and engineering students. The goal of the course is to impart the concepts and techniques of modern linear algebra (over the real scalar field) with a significant level of rigor. The prerequisite is coregistration in MAT 272.
The successful student will be able to write clearly about the concepts of linear algebra, (definitions, counterexamples, simple proofs), and to apply the theory to examples. Some exposure to the practical nature of solutions of linear algebra problems is healthy. On the other hands, sophisticated numerical algorithms should not be presented.
Use of computers to work numerous problems often can enhance the student’s understanding of the material. It is suggested that a software package be made available to the students, but that classroom discussion of computers be limited. Instructors are encouraged, but not required, to make use of computers in the course.
Below is a list of required topics,
together with approximate class times for each section.
If time permits, applications (e.
g. least-squares, LU decomposition, difference equations,
dense vs. sparse matrices, etc.),
or an introduction to complex vector spaces may be included.
# Systems of linear equations and
matrices
(6 50-minute classes)
Gauss-Jordan elimination, homogeneous
systems, matrix algebra, elementary matrices, inverses
# Determinants
(3 50-minutes classes)
by row reduction and cofactor
expansions, Cramer’s rule
# Vector Spaces
(9 50-minutes classes)
Euclidean space, general (real)
vector spaces, subspaces, linear independence, dimension, row, column and
null spaces
# Inner products
(5 50-minutes classes)
norms, orthogonal bases and Gram-Schmidt
orthogonalization
# Linear transformations
(8 50-minutes classes)
Kernel and range, inverse transformations,
matrices of linear transformations, change of basis, similarity
# Eigenvalues and eigenvectors
(7 50-minutes classes)
diagonalization, orthogonal diagonalization
and symmetric matrices, quadratic forms
Suggested
MAT 342 Homework Problems
Section
Problems
1.1
1, 6, 13, 14, 16, 20, 31, 41, 42, 53, 54, 55
1.2
7, 8, 9, 10, 11, 12, 17, 20, 32, 33, 34
1.3
1*, 3, 7, 9*, 10, 11, 12, 13, 22*
1.4
1, 2, 3, 4, 5, 6, 9*, 10, 16*, 21, 22, 23*
1.5
1, 2, 3, 4*, 5, 7, 15*, 20, 25, 29*, 31, 39
2.1
1, 2, 3, 8*, 9, 17, 18, 21, 24, 25, 27*, 29*, 30, 41
2.2
1, 2, 3*, 4*, 5, 6, 15*, 17, 18, 19, 44
2.3
1*, 2*, 4, 8*, 10, 11*, 14*, 15, 18, 36, 37
2.4
2, 3, 4, 5*, 12*, 13, 14*
3.1
6, 10, 12*, 16, 18*, 29, 31*, 34, 37, 38, 39*, 40
3.2
12*, 25, 26, 28*, 29*, 35, 39*, 42, 43
3.3
2, 5*, 8, 10, 11*, 12, 13, 14*, 15, 21, 23*, 24, 46
3.4
1*, 2, 3, 4*, 13, 14*, 16, 17, 21*, 26
4.1
11, 15, 28*
4.2
1, 10*, 42, 43
4.3
7*, 12, 14*, 24, 25*, 26, 31, 34*, 42*, 51*, 53
4.4
8, 16, 24*, 28, 29*, 38, 40 (should read p(x)=x2), 44
4.5
1*, 5, 9*, 14, 16, 20*, 26
4.6
1, 6*, 9, 11*, 26
5.1
1 – 8*, 10, 16, 31*, 32, 42
5.2
1 – 6*, 20*, 25, 28*, 29
5.3
9*, 11, 12*, 29, 33*, 35
5.4
1 – 16*, 24, 25, 43
5.5
1 – 5*, 9, 37*
5.6
1 – 6*, 10, 12*, 22
6.1
1*, 7*, 28*, 29*, 30*, 31, 43*
6.2
1, 6, 7, 10, 12, 14, 29
6.3
2*, 9*, 11*, 16, 23*, 27
6.4
19, 25, 57 – 59
6.6
1, 3, 7, 8, 33
*homework problem for grading
Linear
Algebra WebNotes by Dr. Mark V. Sapir
Linear
Algebra WebNotes by Dr. Beth Novick
Elementary
Linear Algebra
(Lecture
Notes by Keith Matthews, 1991)
I
Hate Linear Algebra Home Page
Top
Ten Suggestions on Teaching Linear Algebra
Linear
Algebra Website,
Department
of Mathematics, Arizona State University
The
Maple Computer Algebra System
Homework
HW#1, sections 1.1-1.2: due
to Monday, Feb 2.
HW#2, sections 1.3-1.5: due
to Monday, Feb 16.
HW#3, sections 2.1-2.4: due
to Wednesday, Feb 25.
HW#4, sections 3.1-3.3: due
to Friday, March 13.
HW#5, sections 3.4-3.5, 4.1-4.6:
due to Monday, April 6.
HW#6, sections 5.1-5.3: due
to Monday, April 20.
HW#7, sections 5.4
- 5.6, 6.1, 6.3: due to Monday,
May 4
Computer labs
Lab#1,
"Introduction to Maple V": Wednesday, Jan. 28,
room ECA 221, 8:40-9:30 am.
Lab#2,
"Gauss-Jordan elimination": Wednesday,
Feb. 4,
room ECA 221, 8:40-9:30 am.
Lab#3,
"Matrix Algebra": Wednesday,
Feb. 11,
room ECA 221, 8:40-9:30 am.
Lab#4,
"Matrix Inversion, Determinants, and Cramer's Rule":
Wednesday, Feb. 18,
room ECA 221, 8:40-9:30 am
Lab#5,
"Vector Spaces, Independence, Basis, and Dimension":
Wednesday, March 11,
room ECA 221, 8:40-9:30 am
Lab#6,
"Row Space, Column Space, and Nullspace":
Wednesday, April 1,
room ECA 221, 8:40-9:30 am
Lab#7,
"Gram-Schmidt process, Eigenvalues and Eigenvectors":
Monday, April 27,
room ECA 221, 8:40-9:30 am
Tests
Test#1,
Wednesday, Feb. 25;
Test Review, Monday,
Feb 23.
Sections 1.1-1.5 and 2.1-2.4
of Chs 1&2 are on the test.
This test does not require a calculator,
but you may use one if you wish.
Homework, sections 2.1-2.4,
will be collected right after the test.
Problems
to review:
Chapter I, Review Exercises on p.
97: #1, 3, 7, 9, 10;
Chapter 2, Review Exercises on p.
141: #1, 2, 3, 5, 10;
and your homework problems!
Test#2,
Monday, April 6; Test Review, Friday, April 3.
Sections 3.1-3.5 and 4.1-4.6 of Chs 3&4 are on
test.
This test does not require a calculator, but you may use one if you
wish.
Homework, sections 3.4 - 3.5, 4.1 - 4.6, will be collected right
after the test.
Problems to review:
Chapter 3, Review Exercises on p. 206: #1, 2, 3, 5, 7, 9, 11,
12, 14
Chapter 4, Review Exercises on p. 289: #1, 2, 3, 5, 7, 8, 10,
and your homework problems!
Test#3,
Monday, May 4; Test Review, Friday, May 1.
Sections 5.1-5.6 and 6.1, 6.3 of Chs 5&6 are
on test.
This test does not require a calculator, but you may use one if you
wish.
Homework, sections 5.4 - 5.6, 6.1, 6.3, will be collected
right after the test.
Problems to review:
Chapter 5, Review Exercises on p. 366: #1-10
Chapter 6, Review Exercises on p. 455: #1-4, 7,
and your homework problems!
Final
Exam, Tuesday, May 12, 7:40-9:30,
PSA 109
Reviews: Wednesday,
May 6, PSA 109, 8:40-9:30 am;
Thursday, May 7, PSA 106, 8:40-9:30 am.
HAVE A NICE SUMMER!!!