MA 322 - Matrix Algebra and its Applications (Fall
2005)
Section 004 taught by Uwe Nagel
at the University of Kentucky.
Overview
Basic Information
Time and Place: 1:00-1:50 pm MWF, CB 243
Students are expected to attend all lectures.
Instructor: Uwe Nagel, POT 763, 257-6793,
uwenagel@ms.uky.edu and
www.ms.uky.edu/~uwenagel.
Office Hours: 3:00-3:50 MWF in POT 763, or by appointment.
You can also consult me by email.
Exams: There will be two midterms and one final exam.
-
Exam 1 (CB 243, September 26, 1:00-1:50 pm)
-
Exam 2 (CB 243, October 31, 1:00-1:50 pm)
-
Final exam (CB 243, December 14, 1:00-3:00 pm).
All exams are cumulative in the sense that students are expected to
know also the material that has been on previous exams.
Material
Textbook: Linear algebra and its applications (3rd
edition) by David C. Lay,
ISBN 0-321-28713-4.
Matrix algebra has its roots in the study of simultaneous linear
equations in several variables. The development of systematic methods
to find and to discuss the solutions of linear equations has lead to
fundamental concepts and methods such as matrix, Gaussian elimination,
vector space, dimension, linear transformation, determinant,
eigenvalue, inner product. The goal of the course is to become very
familiar with all these objects.
Ideas, methods, and the language of matrix algebra are widely used in
all areas of mathematics and most other sciences. The course will
basically cover Chapters 1-7 of the textbook.
Tentative Schedule
- Jan 14:
1.1 Systems of linear equations
- Jan 16:
1.2 Row reductions and echelon forms
- Jan 21:
1.3 Vector equations
- Jan 23:
1.4 The equation Ax = b
- Jan 26:
1.5 Solution sets of linear systems
- Jan 28:
1.6 Linear independence
- Jan 30:
1.7 Introduction to linear transformations
- Feb 2:
1.8 The matrix of a linear transformation
- Feb 4:
2.1 Matrix operations
- Feb 6:
2.2 The inverse of a matrix
- Feb 9:
2.3 Characterizations of invertible matrices
- Feb 11:
2.5 LU factorization
- Feb 13:
Review
- Feb 16:
Review
- Feb 18:
First Midterm
- Feb 20:
3.1 Introduction to determinants
- Feb 23:
3.2 Properties of determinants
- Feb 25:
3.3 Cramer's rule, volume, and linear transformations
- Feb 27:
4.1 Vector spaces and subspaces
- Mar 1:
4.2 Null spaces, columns spaces, and linear transformations
- Mar 3:
4.3 Linearly independent sets and bases
- Mar 5:
4.4 Coordinate systems
- Mar 8:
4.5 The dimension of a vector space
- Mar 10:
4.6 The rank of a matrix
- Mar 12:
4.7 Change of basis
- Mar 22:
4.8 Difference equations
- Mar 24:
4.7 Review
- Mar 26:
4.7 Review
- Mar 29:
Second Midterm
- Mar 31:
5.1 Eigenvectors and eigenvalues
- Apr 2:
5.2 The characteristic equation
- Apr 5:
5.3 Diagonalization
- Apr 7:
5.4 Eigenvalues and linear transformations
- Apr 9:
5.5 Complex eigenvalues
- Apr 12:
6.1 Inner products
- Apr 14:
6.2 Orthogonal sets
- Apr 16:
6.3 Orthogonal projections
- Apr 19:
6.4 The Gram-Schmidt algorithm
- Apr 21:
6.5 Least-squares problems
- Apr 23:
7.1 Diagonalization of symmetric matrices
- Apr 26:
7.2 Quadratic forms
- Apr 28:
Review
- Apr 30:
Review
May 5:
Final Exam
A short quizz will be given during the last 10 minutes of each Friday
lecture beginning September 2, except during exam weeks. Make-up
quizzes will not be given without an excused absence.
Homework problems will be regularly
assigned using a web-based homework system (WHS). Each student has an
individual, Personal Version of the web-based homework
assignments which he or she
is expected to work on and to submit the answers on the web. For
each problem
set there is also a Common Version of problems similar to the personal
version. Everyone gets the same common version. Problems on the common version
are the ones most likely to be discussed in class.
Credit is only given for correct solutions of problems appearing in
the student’s
Personal
Version according to the following rules:
-
A student can submit answers to an assignment any number of
times. The system
maintains a complete record of all submissions.
- A student
receives credit
for a problem if he or she submits the correct answer before the homework set
expiration date passes.
-
Until the expiration
date the homework system will inform students
whether their submitted
answer to a problem is correct. After the
expiration date the system will also provide the expected answer.
This homework system is reached at
http://www.mathclass.org.
There are links which provide information.
Accounts already exist for pre-registered students. Your initial login
and password is your student number.
Please change your login immediately to your complete email address
and change your password to whatever you prefer.
You may also use a non-university email address.
Students who are not pre-registered will need to follow the initial
instructions at the "For Students" link to get started.
Subsequent sections of the "For Students" link describe how to use the system.
If you have problems with your account, there will be student
staff in the Mathskeller to help you. The Mathskeller is room
65 in the basement of the White Hall Classroom Building. A schedule can be
found at http://www.mathskeller.com/.
I strongly recommend to approach the homework assigments via
the following rules.
- Start on an assignment as early as possible.
- Print out copies of your personal and of the common assignments
(it is free in the Mathskeller, the student staff will show you how to
do so) and put them in a notebook.
- Get together with classmates to work on the problems via the
printouts.
- Write down the solutions in your notebook and only thereafter enter your
solutions on the webpage.
Only correct solutions to the personal version of the
homework assignment give you homework credit!
- Bring the notebook with you when going to office hours.
- Bring copies of the common problems to class, they are the ones
that are most likely to
be discussed.
You are encouraged to discuss homework problems and the course
material with each other.
However, when it comes time for you to write up or enter the
solutions, I expect you to do this completely on your own.
It would be the best for your understanding if you put aside your
notes from the discussions with your classmates and wrote up the
solutions entirely from scratch.
Working together on the exams, of course, is expressly forbidden.
(no longer available)
Grades
There is a total of 450 points in the course which is distributed as
follows:
| Attendance | 25 points |
| Homework | 50 points |
| Quizzes | 50 points |
| First Midterm | 100 points |
| Second Midterm | 100 points |
| Final Exam | 125 points |
In this model an A requires at least 405 points (90% or more), B at least
360 (80% or more), C at least 315 (70% or more), D at least 270
(60% or more), E for anything else.
Last Up-date: September 23, 2005