Department: Math & Computer Science

Discipline: Mathematics

Subject Code: MATH Course #: 220

Course Title: Linear Algebra

HARRISBURG AREA COMMUNITY COLLEGE

FORM 335

Course Form 335 must be updated at least every five years per AP 765 to include, at a minimum, the following elements. [§335.2]

1. Digital Description:

Credit hours: 4.0

Lecture hours: 4.0

Lab hours: 0.0

BL: []⅓ []½ []⅔ [ ] Other (Indicate fraction or percent)

2. Catalog Description:

Linear systems; matrix algebra; finite dimensional vector spaces including function spaces; linear transformations and their matrix representations including coordinates, change-of-basis, real spectral theorem, orthogonal diagonalization, principal axes theorem. (For students of Mathematics, Science and Engineering.)

Minimum Grade Required

3. Prerequisites: MATH 122 C

Corequisites:

Other:

4. Learning Outcomes

[These outcomes are necessary to enable students to attain the essential

knowledge and skills embodied in the program’s educational objectives.]

Upon successful completion of the course the student will be able to:

· Solve systems of equations using matrices

· Perform operations on matrices

· Calculate determinants and apply results to the theory of systems of equations

· Perform basic operations on 2-D and 3-D vectors, including dot products and cross products and use them to solve geometric problems

· Extend geometric properties of 2-D and 3-D vectors to n-dimensional and general vectors

· Investigate connections between properties of linear transformations and matrices

· Investigate connections between the dimension and bases of vector spaces and matrices

· Carry out proofs through abstract thinking and use of logical arguments

5. Planned Sequence of Learning Activities

[These must be designed to help students achieve the learning outcomes.]

Hours

Linear Equations and Matrices 15

Systems of equations

Gaussian Elimination

Matrix operations and properties

Determinants

Real Vector Spaces 26

Linear independence, span bases and dimension

Rank and nullity

Coordinates, change of basis

Inner Product Space

Gram-Schmidt Process

Eigenvalues and Eigenvectors 5

Diagonalization

Orthogonal Diagonalization

Linear Transformations 7

Kernel and Range

Inverse of Linear Transformations

Matrix of Linear Transformations

Other Applications 2

Quadratic Forms

Quadric Surfaces

Tests and Review 5

Total 60

6. Assessment of Student Learning

[Methods of assessment should be appropriate for Learning Outcomes listed above.]

Assessment of student learning outcomes for the course, as required by AP 765, is part of regular curriculum maintenance and/or improvement. The specific plan has been determined by the pertinent faculty involved and is maintained in the College’s assessment management system.

Student assessment includes tests and a comprehensive final exam. Other forms of assessment may include, but are not limited to, the following: class participation, graded assignments, projects, portfolios, and/or quizzes. All assessment instruments cover course competencies on file in the Mathematics and Computer Science Department.

7. List of Texts, References, Selected Library Resources or other Learning Materials (code each item based on instructional use): C-Lecture/Laboratory, A-Lecture, B-Laboratory, LC-Lecture/Clinical, CLN-Clinical, I-Online,

BL-Blended, D-Independent Study, P-Private Lessons, E-Internship,

F-Cooperative Work-Study, FE-Field Experience. [These resources must be easily accessible to students.]

A: Elementary Linear Algebra with Applications, 10th edition by Howard Anton; John Wiley and Sons, Inc.

8. Prepared by Faculty Member: O. Pauline Chow Date: 5/11/10

9. Approved by Department Chairperson: O. Pauline Chow Date: 5/11/10

10. Approved by Academic Division Dean: Juliette Winterer Date: 5/14/10

This course meets all reimbursement requirements of Chapter 335, subchapters A / B.

This course was developed, approved, and offered in accordance with the policies, standards, guidelines, and practices established by the College. It is consistent with the college mission.

If the course described here is a transfer course, it is comparable to similar courses generally accepted for transfer to accredited four-year colleges and universities.

11. Director, Curriculum Compliance: Catherine A. Lencioni Date: 5/17/10

12. Provost & VP, Academic Affairs: Ronald R. Young Date: 5/17/10

13. Original Date of course approval by the college: 197020

14. Date(s) of subsequent reviews [Indicate change: Learning Outcomes; textbook(s)]:

Fall 1997

5/03

12/14/06 (textbook change)

2/13/08 – learning outcomes

3/19/09 – updated textbook

5/11/10 – assessment statement & textbook update

12/1/04

Review and updated: 10/26/07; 1/11/08; 1/16/09; 7/14/09