# 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.