Instructor:
Dr. Sergei Suslov
Office:
PSA 643
Phone:
965-8987
E-mail:
suslov@math.la.asu.edu
Office Hours: 10:40 – 11:40
am MWF, 1:00 – 2:00 pm TTh
*Important Note: All
items on this syllabus are subject to change.
Any in-class
announcement, verbal or written, is considered official addendum to this
syllabus.
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
IMPORTANT INFO:
Test 1 was on Monday,
September 29. Sections 1.1-1.5 and 2.1-2.4 of
Chs 1&2
were on the test. Review for the
test was on Friday, Sept. 26. Hope you were there!
This test did not require a calculator,
but you could use one if you wished.
Homework, sections 1.3 - 1.5, 2.1
- 2.4, was 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
Test 2 will be on Friday,
October 31. Sections 3.1-3.5 and 4.1-4.6 of Chs
3&4
were on test. Review for the test
will be on Wednesday, Oct. 29.
This test does not require a calculator,
but you may use one if you wish.
Homework, sections 3.3 - 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
Test 3 will be on Friday,
December 5. Sections 5.1-5.6 and 6.1, 6.3 of
Chs 5&6
are on test. Review for the test
will be on Wednesday, Dec. 3. Be there!
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