Elementary Linear Algebra

Course Description
Vectors and matrices, operations on matrices, determinants, systems of
linear equations, linear independence, linear transformations, applications.

Prerequisites: MATH105 with a minimum grade of C or MATH120 with a
minimum grade of D- or MATH112 or placement

Course Objectives
• The major goal of the course is to study the properties of vectors, vector
spaces, linear transformations, matrices, the connection to the theory of
solving systems of linear equations, independence and basis.
• The material provides a first exposure to abstract mathematical
argumentation (proofs), which is so typical for upper level mathematics
courses.
• Learn the use of technologies to solve standard linear algebra problems.

Topics covered
We will cover most material in the textbook.
Unit 1. Matrices and vectors, linear combinations, systems of linear
equations, Gaussian elimination, the inverse of a matrix, linear
transformations. Applications (Sections 1.1-1.7, 2.1-2.8)
Unit 2. Determinants, vector spaces, subspaces, basis and dimension,
coordinate systems. (Sections 3.1-3.2, 4.1-4.4, 7.1-7.3)
Unit 3. Eigenvalues and Eigenvectors, diagonalization of matrices, the
geometry of vectors, orthogonal vectors, orthogonal projections, Least
squares approximations.(Sections 5.1-5.3, 6.1-6.5)

Class organization and grading
Homework is assigned frequently and the assignments are due on the specified
date and there is a penalty for late work. The points for homework are assigned
as a mixture of correctness and effort. A student may thus receive full points
without having the homework totally correct. Students will be asked to present
their solutions to the class for discussion. Some in-class activities will be based
on students working together in groups and peer reviewing their work.

We will also have several quizzes. They are usually given at the beginning of the
class period; so make sure you come on time. Quizzes cannot be made up after
they are taken in class. The lowest quiz score will be dropped. In case a quiz was
missed this allows for a missed class.

We will have two in-class tests and a final exam. All tests are cumulative since
the material naturally builds up in layers and later concepts rely on the
understanding of earlier ideas.
Rules during exams:
• Use black or blue pen or pencil.
• Don't leave the room without permission.
• You can usually leave the room after you are done. After the first person
leaves the room nobody can go out for a bathroom break. If you leave
while other people are still writing, close the door quietly.
• No hats with visors during tests and quizzes, baseball hats need to be
turned to the back.
• Come on time! I will be early for a test and you can start early if you want.
If you do oversleep, come in even if it is half way through the test, we will
deal with it.
Tentative Exam schedule
Test 1: February 11, covers Chapters 1 and 2
Test 2: March 25, covers Chapters 3,4 and 7
Final Exam : April 20 (starts 30 minutes before regular class time) covers all
sections, including Chapters 5 and 6,which were not covered on the previous
tests.

The grade will be computed by averaging the scores on the 2 tests, the final,
the homework percentage and the quiz percentage with equal weights. In case
that the final exam is better than the lowest of the other 4 scores it can replace
that lowest score and thus count twice the weight of the other components.

My office is in 515 K Pray-Harrold, phone 487-1068
my home phone is 665-2691 (Please, do not call me at home after 8 PM)
Do not leave a message in the office, but on the home answering machine. The
best way to contact me is to write me an e-mail message.

Academic Honesty
I expect all students to abide by the University’s code of conduct, and in
particular to abide by rules concerning academic honesty. In order to assess
how the class is going and what you have learned, I need to see your own work:
your own words and the details of your own computations. You may work with
other students or math tutors on your assignments, but you must do an
independent write-up. I will give failing grades for academic dishonesty.

Special Needs
If you have a learning disability or other physical impairment that may affect
your ability to do the work in this course, please let me know as soon as
possible so that we can make appropriate arrangements.