Syllabus for Linear Algebra

 

MA 322  - Matrix Algebra and its Applications (Spring 2004)

 

An introductory course in linear algebra

 

Text:  Linear Algebra and Its Applications (2nd Ed.) by David C. Lay

 

Section:                       005

Instructor:                  Dr. Paul Eakin, Professor of Mathematics

                                    777 POT

                                    paul@ms.uky.edu

                                    257-6798 (office)  276-1048 (home)

Office Hours:              8:30-9:20 Tuesday and Thursday in Mathskeller

                                    (and by appointment)

 

Class Meeting:

            Time:              9:30-10:45 A.M.  Tuesday and Thursday

            Room:             CB 345

 

 

Material to be covered (subject to change depending on progress of course) and Examination schedule

 

1.1               Systems of linear equations

1.2               Row reductions and echelon forms

1.3               Vector equations

1.4               The equation AX = B

1.5               Solution sets of linear systems

1.6               Linear independence

1.7               Introduction to Linear Transformations

1.8               The matrix of a linear transformation

 

2.1               Matrix operations

2.2               The inverse of a matrix

2.3               Characterization of invertible matrices

2.4               LU factorization

 

FIRST MIDTERM EXAM:  Feb. 19

3.1                 Introduction to determinants

3.2                 Properties of determinants

3.3                 Cramer's Rule, volume, and linear transformations

3.4                 Vector spaces and subspaces

3.5                 Null spaces, column spaces, and linear transformations

3.6                 Linearly independent sets and bases

3.7                 Coordinate systems

3.8                 Dimension of a vector space

3.9                 The rank of a matrix

3.10              Change of basis

3.11              Difference equations

 

SECOND MID-TERM:  March 30

 

5.1                 Eigenvectors and eigenvalues

5.2                 The characteristic equation

5.3                 Diagonalization

5.4                 Eigenvalues and linear transformations

5.5                 Complex eigenvalues


6.1     Inner products

6.2                 Orthogonal sets

6.3                 Orthogonal projections

6.4                 The Gram-Schmidt algorithm

6.5                 Least squares problems

 

7.1                 Diagonalization of symmetric matrices

7.2                 Quadratic forms

 

FINAL EXAM      Thursday, May  06, 2004 at 8:00 A.M.

 

Grades:

 

There are  450 points in the course

 

First Midterm    100

Second Midterm            100

Final Exam                    150

Class Attendance            25

Homework                      75

To earn an "A" in the course you must accumulate at least  405 points (>=90%)
To earn a  "B" in the course you must accumulate  at least  360 points  (>=80%)

To earn a  "C" in the course you must accumulate  at least  315 points  >=70%)

To earn a  "D" in the course you must accumulate  at least  270 points (>= 60%)
A course total of less than 270 points results in a failing grade.

Homework Grade:       

The homework is a web-based system, found at http://www.mathclass.org It requires an account and registration (within the system) in the section Ma322-005 (Eakin). Accounts have already been created for students pre-registered for the class. For these accounts the  initial login and password are the 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 on www.mathclass.org 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/.


NOTE WELL: Adding the class on the web homework system is not the same as adding it "officially", through the registrar.

 

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.  There is a "Homework Scores" link where one can check the percentage completion for each problem set or group of sets at any time.

·         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. There is always at least a week to work on a set.

The following approach  to the homework assignments 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.

 

There are 25 homework points to be earned before each examination. The number of those points earned is credited at the time the exam is returned.

There is a calculator in the "Homework Scores" section on the web site which will calculate it at any time the average percentage completion of each of the homework sets that have expired since the last examination.  Points are assigned by that value, as follows:

 

90% or more     25 points

80% or more     15 points

70% or more     10 points

60% or more     5 points

 

Attendance:

 

There are 25 attendance points. Attendance credit will be earned as follows.  Students are expected to bring to class  a  3 x 5 inch  card on which they have written:

a.                   Name

b.                   Percentage completed on each problem set for the next exam


These will be taken up at the end of class.  From time to time the instructor will take the last minute or two of class and ask students to respond to a simple (subject-matter) question on the card. 

 

At the end of the course these cards will be counted. The student(s) with the largest number of cards will receive 25 points. If that number is N then a student with M cards will receive  (25M)/(N-3), rounded up to the nearest integer, to a maximum of 25.