Course Descriptions & Syllabi

Course Descriptions & Syllabi

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Note: some or all of the courses in the subjects marked as "Transfer" can be used towards a transfer degree: Associate of Science and Arts or Associate of Engineering Science at DACC. Transferability for specific institutions and majors varies. Consult a counselor for this information.

Areas of Study | | MATH137 syllabus

COURSE TITLE:Introduction to Linear Algebra

This course is a study of introductory linear algebra. Basic techniques are introduced involving vectors and matrices; vector spaces and subspaces; linear dependence, independence, and transformations and dimension; determinants; and orthogonality.

Place into MATH137 with approved and documented math placement test scores or by completing MATH111 with a grade of C or better.

NOTES: This course is a basis for a first undergraduate course in linear algebra. Because linear algebra provides the tools to deal with many problems in fields ranging from forestry to nuclear physics, it is desirable to make the subject accessible to students from a variety of disciplines. There is a blend of intuition and rigor in the presentation. It is anticipated that the student will attain at least 70% accuracy in meeting these objectives. MATLAB and Mathmatica are utilized as a tools for working with tedious problems.

Students are expected to achieve strong critical thinking skills in terms of problem solving skills. Students are expected to be able to determine from any initial question of any of the following that apply:
  1. the meaning and importance of all given information
  2. the primary unknown for which a solution is desired
  3. all secondary unknowns that will be needed to determine the primary unknown
  4. all formulas and/or theorems that are applicable to a solution, and/or
  5. a proper understanding of the meaning/interpretation of the solution
Upon completion of this course, students will be able to:
  • Clearly show work or provide clear explanation as how to setup and generate a solution for application problems
  • Correctly make computer software to provide solution to problems involving large matrix systems
  • Achieve strong critical thinking skills in terms of problem solving
  • Use basic vector terminology correctly in discussions (oral or written)
  • Use, understand and write all required algebraic symbols and abbreviations, primarily those that relate to matrices, vectors, and systems of equations
  • Clearly show work or provide clear explanation as how to both setup and generate a solution for application problems
  • Strengthen critical thinking skills in terms of problem solving. Students will learn to be able to determine, from any initial question, the techniques needed to deconstruct the information provided in a problem as it relates to solution
  • Clearly relate interpretation of solution to give real-world meaning to numeric answers, and to properly interpret abstract answers
Topic Specific Learning Outcomes
  • Determine the sum and product of matrices
  • Determine the reduced form of an augmented matrix using Gauss-Jordan operations
  • Calculate the inverse of a square matrix
  • Use the inverse of a matrix to solve a linear system of equations
  • Use the inverse of matrix to distinguish between an independent and a dependent system
  • Use the inverse of a matrix to distinguish between systems that have no solution, finite solutions, or infinite solutions
  • Use Markov Chains to determine both near and stable solutions to iterative processes
  • Calculate determinants for square matrices
  • Use Cofactor Expansion to calculate the determinant of large square matrices
  • Use the properties of determinants to simplify matrix expressions
  • Use Gauss-Jordan row operations to simplify matrices prior to determinate calculation
  • Use the axioms of Vector Spaces to determine whether a rule does or does not define a Space
  • Determine the dot product of two vectors
  • Determine the angular measure between two vectors
  • Determine the magnitude of a vector
  • Determine whether or not a rule does or does not define a subspace
  • Determine the linear combination of a set of vectors
  • Distinguish between an independent and a dependent set of vectors
  • Determine the dimension of a Space
  • Determine the Rank of a matrix
  • Determine the projection of one vector onto another
  • Determine the projection of a vector onto a subspace
  • Generate an orthogonal basis using the Gram-Schmidt Orthogonalization process
  • Caculate the eigenvalues and eigenvectors of a square matrix
  • Conduct a Linear Transformation on a matrix
  • Generate the kernel and the range of a transformation
  • Determine whether or not a transform is one-to-one
  • Determine whether a transform is or is not invertible
  • Determine the coordinate vectors in a linear combination
  • List the axioms defining an inner product space
  • Draw a space-time diagram based on the Minkowski inner product space
  • Apply the Minkowski inner product space to calculate time dilation values
  • Apply appropriate technology to find solutions to problems involving large matrix systems

  • Introduction to Linear Systems 12%
    • Matrices and Their Algebra
    • Gauss-Jordan Elimination
    • Basis and Dimension
    • Inverses of Square Matrices
    • The Linear Transformation T (x) = Ax
  • Vector Spaces 20%
    • The Geometry of Rn
    • Vector Spaces
    • Dot Product
    • Linear Combinations and Subspaces
    • Independence
    • Bases, Rank, and Kernel
    • Dimension and Rank
    • Coordinatization of Vectors
    • Linear Transformations
    • Inner Product Spaces
  • Determinants 12%
    • Areas, Volumes, and Cross Products
    • The Determinant of a Square Matrix
    • Computation of Determinants
  • Eigenvalues and Eigenvectors 18%
    • Eigenvalues and Eigenvectors
    • Diagonalization
  • Orthogonality 18%
    • Projections
    • The Gram-Schmidt Process
    • Orthogonal Matrices
  • Linear Transformations and Similarity 16%
    • Properties of Linear Transformations
    • Matrix Representations
    • Change of Basis and Similarity


Linear Algebra with Applications, by Gareth Williams, WCB Publishing, 8th Edition, Alternate Edition 2014.

See bookstore website for current book(s) at


The student should obtain 70% competency in the above as measured by exams, assignments, and a comprehensive final.

"Assignments" will be 15 items composed of 10 homework sets from the text, 4 homework sets from the instructor, and 1 long term project.

The course grade will be determined by:
Grading Scale:
A= 90-100%
B= 80-89%
C= 70-79%
D= 60-69%
F= Under 60%


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Spring 2019

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