MAT 342  Linear Algebra
SPRING 1999*

  *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. 
GO TO:
General
Course Description
Homework Problems
Related Web Sites
Important Info(HW,Labs&Tests)
Back to Suslov's home page


General

Course:           MAT 342, Linear Algebra
Time:              10:40 - 11:30, MWF
Location:         PSH 552
Line #:             88308
Instructor:       Dr. Sergei Suslov
Office:             PSA 643
Phone:             965-8987
E-mail:             sks@asu.edu
Office Hours: 9:30 – 10:25 am and 1:45 – 2:30 pm MWF
Text:                Linear Algebra with Applications, 5th edition,
                         by Steven Leon, 1998
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.



Course Description

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 recommended 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            p. 11, #: 1a, 1c*, 2, 3*, 4, 5a, 5b*, 5c*, 6a, 6c, 6f*, 7, 11*
1.2            p. 25, # 1*, 3*, 4, 5b, 5d*, 5e, 5h, 6b*, 11*, 13, 16
1.3            p. 53, # 1*, 2*, 3, 4*, 8b, 8d*, 12*, 14, 15*, 16, 17*, 22, 31
1.4            p. 65, # 1, 2, 3a, 4c, 7a, 7d, 8*, 9c*,11a, 15a, 21
1.5            p. 74, # 1, 3, 4*, 7, 9*, 11, 13, 14, 15

2.1            p. 90, # 2, 3c, 3e, 3g, 5, 10, 11, 12
2.2            p. 97, # 1c, 2, 3e, 5, 6, 10, 11,13, 16
2.3            p. 103, # 1a-d, 2a-d

3.1            p. 114, # 1, 4, 6, 9, 11, 15, 16
3.2            p. 123, # 2, 3, 4, 5, 9, 11, 14, 17, 18, 19, 20
3.3            p. 135, # 2, 3, 5, 7, 11, 14, 15, 16, 17
3.4            p. 141, # 2, 5, 8, 9, 10, 13, 17
3.5            p. 152, # 1, 2, 5, 7, 8, 11
3.6            p. 159, # 1, 2, 3, 4b, 4d, 4e, 4f, 5, 6, 7, 8, 9, 10, 11, 12, 15, 19

4.1            p. 172, # 1, 3, 4, 6, 7, 8, 9, 11, 12, 16, 19, 20, 21, 22, 24
4.2            p. 184, # 2, 3a-b, 4
4.3            p. 192, # 1, 2, 6

5.1            p. 206, # 1a,1d, 2a, 2d, 3c, 3d, 5, 7b, 8, 10, 11
5.2            p. 215, # 1, 2, 3, 4, 5, 9, 11, 12, 13, 16
5.3            p. 224, # 1, 2, 8, 12, 13, 14, 16, 17, 24, 25, 28, 29

6.1            p. 289, # 1a, 1c, 1f, 1h, 11, 3, 5, 8, 10, 13, 18, 19, 22
6.2            p. 302, # 1a, 1e, 2a, 2b, 4
6.3            p. 316, # 1b, 1e, 2b, 2e, 3a, 3e, 4a, 6, 8c, 13, 15, 20, 24b, 25a
6.4            p. 327, # 1b, 2, 3, 4, 5a, 5d, 7, 9, 11, 12, 16, 19
6.5            p. 342, # 1, 3b, 4, 5, 6a, 6b, 6c, 7e, 7f, 10
6.6            p. 350, # 1, 3, 4a, 4c, 5a, 5c, 8, 13
 
 *homework problem for grading



Related Web Sites:

Leon Linear Algebra Textbook Homepage
Linear Algebra WebNotes by Dr. Mark V. Sapir
Linear Algebra WebNotes by Dr. Beth Novick
Elementary Linear Algebra
(Lecture Notes by Keith Matthews, 1991)
Linear Algebra Website,
Department of Mathematics, Arizona State University
History of Mathematics Archive

I Hate Linear Algebra Home Page
Top Ten Suggestions on Teaching Linear Algebra

The Maple Computer Algebra System


IMPORTANT INFO:

Homework
HW#1, sections 1.1-1.2: due to Monday, Feb 1.
HW#2, sections 1.3-1.5: due to Monday, Feb 15.
HW#3, sections 2.1-2.3: due to Wednesday, Feb 24.
HW#4, sections 3.1-3.3: due to Friday, March 12.
HW#5, sections 3.4-3.6, 4.1-4.3: due to Monday, April 5.
HW#6, sections 5.1-5.3: due to Monday, April 19.
HW#7, sections 6.1 - 6.6: due to Monday, May 3

Computer labs
Lab#1, "Introduction to Maple V"Wednesday, Jan. 27,
room ECA 221, 10:40-11:30 am.
Lab#2, "Gauss-Jordan elimination": Wednesday, Feb. 3,
room ECA 221, 10:40-11:30 am.
Lab#3, "Matrix Algebra": Wednesday, Feb. 10,
room ECA 221, 10:40-11:30 am.
Lab#4, "Matrix Inversion, Determinants, and Cramer's Rule":
Wednesday, Feb. 17, room ECA 221, 10:40-11:30 am
Lab#5, "Vector Spaces, Independence, Basis, and Dimension":
Wednesday, March 10, room ECA 221, 10:40-11:30 am
Lab#6, "Row Space, Column Space, and Nullspace":
Wednesday, March 31, room ECA 221, 10:40-11:30 am
Lab#7, "Gram-Schmidt process, Eigenvalues and Eigenvectors":
Monday,  April 26, room ECA 221, 10:40-11:30 am

Tests
Test#1, Wednesday, Feb. 24; Test Review Monday, Feb 22.
Test#2, Monday, April 5; Test Review, Friday, April 2.
Test#3, Monday, May 3; Test Review, Friday, April 30
Final Exam

HAVE A NICE SEMESTER!