Course Information

Course Title:	Linear Algebra
Course Code:	None
Credits:	0 credits
Certificate Provider:	Westcott Courses
Grading Mode:	Standard letter grade
Proctored Final:	No

Textbook Requirement:
An additional textbook/account through Pearson Publishing is required for this course. The textbook is embedded in a Pearson account where you will read the e-text, do your homework and take your quizzes and tests. Once you enroll and log into your Westcott account, you will be given instructions on how to obtain this textbook/account from Pearson. ( Linear Algebra and its Applications - David C. Lay )

Course Description

This course includes the study of vectors in the plane and space, systems of linear equations, matrices, determinants, vector spaces, linear transformations, inner products, eigenvalues, eigenvectors, diagonalization, matrix decomposition, and the Spectral Decomposition theorem.

Prerequisite:   Calculus l with a grade of C or better. Methods of Proof is recommended.

Learning Outcomes

At the conclusion of this course, students should be able to:

1. Perform matrix operations and calculate determinants.
2. Understand the concept of matrices and their role in linear algebra and applied mathematics.
3. Understand linear systems Ax = b and the role of subspaces, linear independence, etc. in the analysis of these systems.
4. Understand eigenvalues, eigenvectors and their role in diagonalization.
5. Understand linear transformations and their properties over Rⁿ.
6. Understand important definitions in Linear Algebra and the ability to do very elementary proofs.

Methods Of Evaluation

Homework 15%
Chapter Tests 60%
Proctored Final Exam 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)

Homework:   Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and using the concepts to solve problems. Each lesson contains a set of homework problems.

Assessment

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

Content Menu

Chapter 1 - Linear Equations in Linear Algebra

Lessons	Homework
1.1 Systems of Linear Equations	1.1
1.2 Row Reduction and Echelon Forms	1.2
1.3 Vector Equations	1.3
1.4 The Matrix Equation Ax = b	1.4
1.5 Solution Sets of Linear Systems	1.5
1.6 Applications of Linear Systems	1.6
1.7 Linear Independence	1.7
1.8 Introduction to Linear Transformations	1.8
1.9 The Matrix of a Linear Transformation	1.9
Exam Chapter 1

Chapter 2 - Matrix Algebra

Lessons	Homework
2.1 Matrix Operations	2.1
2.2 The Inverse of a Matrix	2.2
2.3 Characterizations of Invertible Matrices	2.3
2.4 Partitioned Matrices	2.4
2.5 Matrix Factorizations	2.5
2.8 Subspaces of Rn	2.8
2.9 Dimension and Rank	2.9
Exam Chapter 2

Chapter 3 - Determinants

Lessons	Homework
3.1 Introduction to Determinants	3.1
3.2 Properties of Determinants	3.2
3.3 Cramer's Rule, Volume and Linear Transformations	3.3
Exam Chapter 3

Chapter 4 - Vector Spaces

Lessons	Homework
4.1 Vector Spaces and Subspaces	4.1
4.2 Null Spaces, Column Spaces, and Linear Transformations	4.2
4.3 Linearly Independent Sets; Bases	4.3
4.4 Coordinate System	4.4
4.5 The Dimension of a Vector Space	4.5
4.6 Rank	4.6
4.7 Change of Basis	4.7
Exam Chapter 4

Chapter 5 - Eigenvalues and Eigenvectors

Lessons	Homework
5.1 Eigenvalues and Eigenvectors	5.1
5.2 The Characteristic Equation	5.2
5.3 Diagonalization	5.3
5.4 Eigenvectors and Linear Transformations	5.4
5.5 Complex Eigenvalues	5.5
Exam Chapter 5

Chapter 6 - Orthogonality and Least Squares

Lessons	Homework
6.1 Inner Product, Length, and Orthogonality	6.1
6.2 Orthogonal Sets	6.2
6.3 Orthogonal Projections	6.3
6.4 The Gram-Schmidt Process	6.4
6.5 Least-Squares Problems	6.5
6.6 Applications to Linear Models	6.6
6.7 Inner Product Spaces	6.7
Exam Chapter 6

Chapter 7 - Symmetric Matrices and Quadratic Forms

Lessons	Homework
7.1 Diagonalization of Symmetric Matrices	7.1
7.2 Quadratic Forms	7.2
7.3 Constrained Optimization	7.3
7.4 The Singular Value Decomposition	7.4
Exam Chapter 7
Final Exam

Time on Task

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.

Schedule

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.

Week	Complete Sections
1	1.1 - 1.3
2	1.4 - 1.6
3	1.7 - 1.9
4	2.1 - 2.3
5	2.4 - 2.6
6	2.7 - 2.9
7	3.1 - 3.3
8	4.1 - 4.3
9	4.4 - 4.6
10	4.7 - 5.2
11	5.3 - 5.5
12	6.1 - 6.2
13	6.3 - 6.4
14	6.5 - 6.6
15	6.7 - 7.1
16	7.2 - 7.4
Final Exam

Code of Conduct:

Code of Ethics:

Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

Respectful communications:

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

Grading information and proctored final policies:

The grading rules are put in place to protect the integrity of online education by stopping grade inflation, which is done by demanding a display of competency in exchange for a grade. By agreeing to the terms of service agreement, you agree to read the 'Grading' Policy from within your account, and the 'Proctored Final Information' page, if applicable. You have 24 hours after your first log-in to notify us if you do not agree to the grading policy and proctored final policy ( if applicable ) outlined in the pages inside of your account, otherwise it is assumed that you agree with the policies. There are no exceptions to these policies, and the pretext of not reading the pages will not be deemed as a reasonable excuse to contest the policies.

Examples of academic misconduct:

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.

Unauthorized collaboration:

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

Important Notes:

This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.