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MATH 250 Linear Algebra

Students will develop skills in the basic concepts of linear algebra. These skills will cover areas such as vector spaces, systems of linear equations and matrices, determinants, similar matrices, diagonalizations, linear transformations, eigenvalues and eigenvectors, orthogonality, quadratic forms, complex vector spaces, and applications. Use of MATLAB, a computer algebra system, is required. Calculators are not permitted.

Credits

4

Prerequisite

MATH 181 or equivalent with a grade of C or higher

Hours Weekly

4 hours weekly

Course Objectives

  1. Solve systems of linear equations using matrices with elementary row operations and determinant of a matrix.
  2. Do basic vector arithmetic including calculating vector sums, differences, scalar products and inner products, and projections.
  3. Use the basic rules of matrix arithmetic and algebra, and explore matrix LU factorizations.
  4. Identify fundamental vector spaces and subspaces, find a basis for a vector space, and communicate mathematical reasoning symbolically, verbally, and in writing using proofs.
  5. Find orthogonal and orthonormal bases using a Gram-Schmitz process, and coordinate vectors in general vector spaces.
  6. Use concept of a linear transformation and apply it to geometry including matrix representations of linear transformations.
  7. Use real/complex eigenvalues and eigenvectors to diagonalize/factor matrices.
  8. solve applications dealing with quadratic forms.
  9. Use MATLAB to solve problems, such as Markov Chains and Gram-Schmidt processes, and to complete projects.

Course Objectives

  1. Solve systems of linear equations using matrices with elementary row operations and determinant of a matrix.

    Learning Activity Artifact

    • Other (please fill out box below)
    • Final exam

    Program Goal(s)

    Degree: Actuarial Science - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Mathematics - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

  2. Do basic vector arithmetic including calculating vector sums, differences, scalar products and inner products, and projections.

    Learning Activity Artifact

    • Other (please fill out box below)
    • Final exam

    Program Goal(s)

    Degree: Actuarial Science - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Mathematics - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

  3. Use the basic rules of matrix arithmetic and algebra, and explore matrix LU factorizations.

    Learning Activity Artifact

    • Other (please fill out box below)
    • Final exam

    Program Goal(s)

    Degree: Actuarial Science - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Actuarial Science - A.A. Degree (Transfer)

    2. Utilize technology to communicate, collect, display, and analyze information.

    Degree: Mathematics - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Mathematics - A.A. Degree (Transfer)

    2. Utilize technology to communicate, collect, display, and analyze information.

  4. Identify fundamental vector spaces and subspaces, find a basis for a vector space, and communicate mathematical reasoning symbolically, verbally, and in writing using proofs.

    Learning Activity Artifact

    • Other (please fill out box below)
    • Final exam

    Program Goal(s)

    Degree: Actuarial Science - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Actuarial Science - A.A. Degree (Transfer)

    3. Communicate mathematical reasoning symbolically, verbally, and in writing.

    Degree: Mathematics - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Mathematics - A.A. Degree (Transfer)

    3. Communicate mathematical reasoning symbolically, verbally, and in writing.

  5. Find orthogonal and orthonormal bases using a Gram-Schmitz process, and coordinate vectors in general vector spaces.

    Learning Activity Artifact

    • Other (please fill out box below)
    • Final exam

    Program Goal(s)

    Degree: Actuarial Science - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Actuarial Science - A.A. Degree (Transfer)

    2. Utilize technology to communicate, collect, display, and analyze information.

    Degree: Mathematics - A.A. Degree (Transfer)

    2. Utilize technology to communicate, collect, display, and analyze information.

    Degree: Mathematics - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

  6. Use concept of a linear transformation and apply it to geometry including matrix representations of linear transformations.

    Learning Activity Artifact

    • Other (please fill out box below)
    • Final exam

    Program Goal(s)

    Degree: Mathematics - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Actuarial Science - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

  7. Use real/complex eigenvalues and eigenvectors to diagonalize/factor matrices.

    Learning Activity Artifact

    • Other (please fill out box below)
    • Final exam

    Program Goal(s)

    Degree: Actuarial Science - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Mathematics - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

  8. solve applications dealing with quadratic forms.

    Learning Activity Artifact

    • Other (please fill out box below)
    • Final exam

    Program Goal(s)

    Degree: Actuarial Science - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

    Degree: Mathematics - A.A. Degree (Transfer)

    1. Demonstrate core knowledge in Calculus and Linear Algebra.

  9. Use MATLAB to solve problems, such as Markov Chains and Gram-Schmidt processes, and to complete projects.

    Learning Activity Artifact

    • Other (please fill out box below)
    • Project

    Program Goal(s)

    Degree: Actuarial Science - A.A. Degree (Transfer)

    2. Utilize technology to communicate, collect, display, and analyze information.

    Degree: Mathematics - A.A. Degree (Transfer)

    2. Utilize technology to communicate, collect, display, and analyze information.