Linear Algebra

Course Material: The central topics of study for this course are: systems of linear equations,
matrices, determinants, algebra and geometry of finite-dimensional vector spaces, linear transformations.

Grading: The course grade will be determined using a 90-80-70-60 scale applied to the total
number of points earned on homework, three regular exams, and the final exam. The relative
weights of homework and exams are as follows:

Homework: Homework will be collected nearly every day. Please note the following policies
regarding homework:

(a.) Work must be shown for credit. Answers alone are generally not sufficient.
(b.) Use only standard size (8.5'' * 11'') notebook paper with smooth edges (i.e., not ripped out of
a spiral notebook, unless edges are trimmed). Write neatly, with problems in order and with pages
stapled. Fold papers in half lengthwise, and write your name on the back.
(c.) Homework is due at the beginning of each class period. If you arrive late to class, you should
turn in your homework immediately upon arrival. I will often work some of the homework problems
at the beginning of class, but no credit will be given for these problems if your paper is turned in
afterward. Also, any papers turned in after class will be considered late and will not be accepted
for grading. (See additional information on homework policies under the section on Attendance
and Absences.)

Exams: Dates for the three regular exams will usually be announced as the term progresses. I
generally do not give makeup exams (see below), but your lowest regular exam score will be replaced
by your final exam score if this is to your advantage. The final exam will be cumulative, and
is scheduled for Monday, May 11, 10:30 - 12:30.

Attendance & Absences:
(a.) In order to comply with University regulations, I will check attendance daily. Attendance does
not contribute directly toward your grade. It is, however, important for your success - you should
attend class regularly, take good notes, and do all of the homework if you hope to do well in this
class.

(b.) Absence from class, even for illness or family emergency, does not automatically entitle you to
make up a missed exam or to turn in late homework papers. In general, no late homework papers
will be accepted. No makeup exams will be administered except possibly in documented cases of
extreme illness or emergency. However, I will replace your lowest exam grade (a 0 if the exam is
missed) by your score on the final exam, if this is to your advantage, and I will also drop your three
lowest homework scores.

(c.) If you miss class for any reason, even for University-sponsored activities, such as athletic events,
performances, etc., it is still your responsibility to get your homework turned in (ahead of time if
necessary), and to obtain the assignment for the next class period. I intend to post assignments
on the web in order to make this easier for you, but this is done only as a service - each student
is ultimately responsible for remaining informed about current homework assignments and exam
dates. If for some reason this information doesn't appear on the course web site, you may need to
call me or contact a classmate.

Classroom Expectations and Policies:

(1.) Students are expected to be present when class begins - habitual tardiness is discourteous and
distracting.
(2.) Students who sleep during class may be invited to leave.
(3.) No electronic communication or entertainment devices are allowed during class - turn o® and
put away your cell phones, iPods and other MP3 players, PDAs, etc.

Some University Policies:

(1.) Angelo State University expects its students to maintain complete honesty and integrity in
their academic pursuits. Violators will be penalized in accordance with University policy.

(2.) Persons with disabilities which may warrant academic accommodations must contact the
Student Life Office, Room 112 University Center, in order to request such accommodations prior
to any accommodations being implemented. You are encouraged to make this request early in the
semester so that appropriate arrangements can be made.

Miscellaneous Remarks:

(1.) This course covers a lot of material at a rapid pace. You should plan on allocating 10-12 hours
per week for study in order to do well. Some students may need to spend more time than this.
(2.) Most of work in this course will be done without calculators, and calculators will not be allowed
on exams.
(3.) Because I drop three homework scores and allow you to replace one regular exam score by the
final exam score, I do not then again curve grades at the end of the semester. My 90-80-70-60 scale
means exactly what it says.
(4.) Please feel free to come by during Office Hours if you need extra help with the material or if
you need to discuss anything pertaining to the course. However, please also note that my Office
Hours are not intended as personal tutoring sessions for students who intentionally miss class.
(5.) The main keys to success in this course are : attending class regularly, taking good notes,
completing all assigned homework, reviewing material on a continuous basis, and asking for help
when you need it; do all of these, and you will probably do well in this class!

Student Learning Outcomes

1. The students will demonstrate factual knowledge including the mathematical notation and
terminology used in this course. Students will read, interpret, and use the vocabulary, symbolism and
basic definitions used in linear algebra , including vectors, matrices, vector spaces, subspaces, linear
independence, span, basis, dimension, linear transformation , inner product, eigenvalue and eigenvector.

2. The students will describe the fundamental principles including the laws and theorems arising from
the concepts covered in this course. Students will identify and apply the theorems about and the
characteristics of linear spaces and linear transformations. Determine bases, compute dimensions, evaluate
linear transformations, solve systems of linear equations and find determinants.

3. The students will apply course material along with techniques and procedures covered in this course
to solve problems . Students will apply properties and theorems about linear spaces to specific
mathematical structures that satisfy the linear space axioms.

4. The students will develop specific skills, competencies and thought processes sufficient to support
further study or work in this or related fields. Students will acquire a level of proficiency in the
fundamental concepts and applications necessary for further study in academic areas requiring linear algebra
as a prerequisite or for work in occupational fields requiring a background in linear algebra. These fields
might include the physical sciences and engineering as well as mathematics.

Course Content

Textbook: Linear Algebra and Its Applications, Third Edition, by David Lay.

1. Linear Equations in Linear Algebra: Systems of Linear Equations; Row Reduction and Echelon
Forms; Vector Equations; The Matrix Equation Ax = b; Solution Sets of Linear Systems; Linear
Independence; Introduction to Linear Transformations; The Matrix of a Linear Transformation.

2. Matrix Algebra: Matrix Operations; The Inverse of a Matrix; Characterizations of Invertible Matrices

3. Determinants: Introduction to Determinants

4. Vector Spaces: Vector Spaces and Subspaces; Null Spaces, Column Spaces, and Linear
Transformations; Linearly Independent Sets, Bases; Coordinate Systems ; The Dimension of a Vector
Space; Rank.

5. Eigenvalues and Eigenvectors: Eigenvectors and Eigenvalues; The Characteristic Equation;
Diagonalization.

6. Orthogonality and Least Squares : Inner Product, Length, and Orthogonality; Orthogonal Sets;
Orthogonal Projections; the Gram-Schmidt Process; Least- Squares Problems .

Additional topics include partitioned matrices, matrix factorizations , change of basis , topics from Chapter 7
(Symmetric Matrices and Quadratic Forms ), and applications.