MATH260 Linear Algebra

Department of Science, Technology, Engineering & Mathematics: Mathematics

1. Course Number and Title

   MATH260 Linear Algebra

2. Number of Credits

   3 credits

3. Minimum Number of Instructional Minutes Per Semester

   2250 minutes

4. Prerequisites

   MATH140 (C or better)

   Corequisites

   None

5. Other Pertinent Information

   None

6. Catalog Course Description

   Topics for this course include: vector spaces, linear transformations, matrix algebra, change of bases, similarity, diagonalization, eigenvalues and vectors; with application to solutions of systems of linear equations, linear programming, Leontief models, Markov chains, codes, and quadratic forms.

7. Required Course Content and Direction

   1. Learning Goals:

      Course Specific:
      The student will be able to:
      1. solve a system of linear equations.
      2. reduce a matrix to reduced echelon form.
      3. solve a matrix equation.
      4. recognize a vector space, subspace.
      5. determine a basis for a vector space and the dimension of a vector space.
      6. determine coordinates for a vector relative to a given basis.
      7. perform dot product and apply to defining norm and orthogonality.
      8. recognize a linear mapping.
      9. determine domain, null space, and range for a given linear mapping and relate the dimensions of these three vector spaces.
      10. find a matrix for a linear mapping.
      11. perform matrix products (composition of mappings),
      12. find an inverse of a nonsingular matrix (inverse of a mapping).
      13. apply matrix algebra to Leontief model, population model.
      14. evaluate determinant and relate to theory.
      15. recognize similar matrices.
      16. determine eigenvalues and eigenvectors.
      17. determine diganonability.
      18. apply theory of eigenvalues to Markov model.

   2. Planned Sequence of Topics and/or Learning Activities:

      1. Systems of Equations (8 lessons)
      
      
      
      Solutions using matrices
      Row reduction
      Existence and uniqueness of solutions
      Set of solutions as an example of a vector space
      Matrices
      Matrix equations
      
      
      
      2. Vector Spaces (12 lessons)
      
      
      
      Definitions
      Examples: Rn, C[0,1]
      Subspaces
      Independence and spanning
      Bases and coordinates
      
      
      
      3. Geometric Examples (2 lessons)
      
      
      
      R2 and R3
      Dot product
      Norm
      Orthogonality
      
      
      
      4. Linear Mappings (20 lessons)
      
      
      
      Homomorphisms, isomorphisms
      Null space of mapping
      Linear mappings
      Composition of mappings
      Product of matrices
      Inverse of a mapping
      Inverse of a matrix
      Algebra of matrices
      Determinants
      Leontief models
      Similar matrices
      Eigen vectors and values
      Diagonability
      Invariant subspaces
      Markov chains
      Quadratic forms - optional
      

   3. Assessment Methods for Core Learning Goals:

      All Discipline-Specific Course Objectives will be assessed as follows:

      The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment will consist of open-ended questions reflecting theoretical and applied situations.

   4. Reference, Resource, or Learning Materials to be used by Students:

      Departmentally selected textbook. Details provided by the instructor of each course section. See Course Format.

8. Teaching Methods Employed

   Use of lecture, class discussion, and WebCT.

Review/Approval Date - 4/06