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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 303
Course Title: Linear Algebra
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description: Vector spaces, linear transformations, matrices and determinants, with applications to systems of linear equations, geometry and other selected topics. Prerequisite: Grade of C or higher in MATH 201.
Prerequisite(s) / Corequisite(s): Grade of C or higher in MATH 201.
Course Rotation for Day Program: Offered odd Fall.
Text(s): Most current editions of the following:

Elementary Linear Algebra with Applications
By Anton & Rorres (Wiley)
Linear Algebra, A Modern Introduction
By Poole (Brooks-Cole)
Course Learning Outcomes
  1. Demonstrate an understanding of concepts related to matrix solution of systems of linear equations. 

  2. Perform operations on vectors such as dot and cross products and interpret them geometrically.

  3. Perform operations on matrices and classify them.

  4. Demonstrate an understanding of basic concepts of linear transformation including eigenvalues, eigenvectors, kernel, rank, and nullity.

  5. Demonstrate an understanding of basic concepts related to of vector spaces and bases.

  6. Apply methods of linear algebra to solve problems in other branches of mathematics and in other disciplines. 

Major Topics/Skills to be Covered:
  • Use matrices to solve systems of linear equations and interpret cases where solutions fail to exist.
  • Compute determinants and use them to solve systems of linear equations.
  • Compute the room, dot product and cross products of vectors and interpret these quantities geometrically.
  • Classify transformations as linear or nonlinear.
  • Verify the properties of a real vector space for specific examples.
  • Determine if a set of vectors is linearly independent or dependent.
  • Construct a basis for and compute the dimension of a vector space.
  • Analyze the relationship between row space, column space and null space of a coefficient matrix and its transpose with respect to solutions of a linear system of equations.
  • Use the Euclidean inner product to compute lengths, distances and angles.
  • Determine if bases are orthonormal or orthogonal.
  • Use properties of orthogonal matrices to change bases.
  • Compute eigenvalues and eigenvectors of linear transformations.
  • Use the theory of eigenvalues to diagonalize matrices.
  • Compute the kernel, rank and nullity of a linear transformation.
  • Determine if matrices are similar to each other.
Culminating Experience Statement:

Material from this course may be tested on the Major Field Test (MFT) administered during the Culminating Experience course for the degree. 
During this course the ETS Proficiency Profile may be administered.  This 40-minute standardized test measures learning in general education courses.  The results of the tests are used by faculty to improve the general education curriculum at the College.


Recommended maximum class size for this course: 30

Library Resources:

Online databases are available at You may access them from off-campus using your CougarTrack login and password when prompted.

Prepared by: Suzanne Tourville Date: August 26, 2015
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course learning outcomes and cover the subjects listed in the Major Topics/Skills to be Covered section. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.

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