Introduction to Linear Algebra

  • Introduction to Linear Algebra

    Course Description: CSUSM: MATH 264 (3 units): Introduction to Linear Algebra.Matrix algebra, systems of linear equations, vector spaces, independence, linear transformations, eigenvalues and eigenvectors, and applications.

    Students must successfully complete AP Calculus AB and AP Calculus BC. In addition to this, all students must pass the AP Calculus BC exam with a 3 or higher.

    Student Expectations: This course is a college level course. The course will be approached as a college level course and students are expected to do college level work. Students will be expected to adhere to all TVUSD behavior policies. Preparation includes being on time with required material including notebook, pencil/eraser, graphing calculator and any other materials designated by the teacher. The Schools tardy policy will be strictly enforced. Be engaged. Please leave all distracting items out of the classroom (i.e. food, drinks, iPods, video games, graphing calculator games, etc.). Cell phones must be turned off during class time and may not be used as calculators.

    Grading: Grades will be based on a combination of tests, quizzes, in class assignments, homework, and a final. Grades will be calculated using weighted categories:
    Tests: 65%
    Final: 15%
    Quizzes: 10%
    Homework: 10%
    The following grading scale will be used to determine letter grades:
    A 90-100%
    B 80-89%
    C 70-79%
    F 00-69%

    Office Hours: I will be available on a regular basis. I will be available most days after school from 2:30-3:30. I will also be available upon request. I am here to help, so if you need help, PLEASE let me know!!!!

    Homework: I am a firm believer in homework. In math, you learn through practice. Homework will be assigned on a weekly basis and students are expected to turn in that homework assignment on the Friday of the week it was assigned. No credit will be given for late work.

    Tests/Quizzes: Quizzes will usually be given midway between units. Tests will be given at the end of each unit. Make-up tests and quizzes will not be given.

    Absences: I expect you to look at the notes from when you are absent and come in with them complete. USE THE WEBSITE.

    Academic Integrity: Academic dishonest will not be tolerated. If you are found to have committed academic dishonesty, a zero will be awarded for that grade and you will not be given the opportunity to make this grade up. Disciplinary action will be taken. If I find anyone copying the work of anyone else all guilty parties will receive zeroes and disciplinary action will be taken. You will not be given the opportunity to make up this grade.

    Textbook: The text we will be using is Howard Anton, Elementary Linea Algebra, Ninth edition, John Wiley & Sons, Inc., c.2005.

    Teacher Contact: The school’s phone number is 294-6450 and my extension is 3603. If it is an emergency during the school day, please contact the school operator. To contact me via e-mail use:

    Introduction to Linear Algebra Course Outline:
    A. Systems of Linear Equations and Matrices
    1. Systems
    2. Gaussian Elimination
    3. Matrices and Matrix Operations
    4. Inverses: Rules of Matrix Arithmetic
    5. Elementary Matrices and a Method for Finding Inverse
    6. Further Results on Systems of Equations and Invertibility
    7. Diagonal, Triangular, and Symmetric Matrices

    B. Determinants
    1. Determinants by Cofactor Expansion
    2. Evaluating Determinants by Row Reduction
    3. Properties of the Determinant Function
    4. A combinatorial Approach to Determinants

    C. Vectors in 2-Space and 3-Space
    1. Vectors (introduction)
    2. Norm of a Vector; Vector Arithmetic
    3. Dot Product
    4. Cross Product
    5. Lines and Planes in 3-Space

    D. Euclidean n Vector Spaces
    1. Euclidean n-Space
    2. Linear Transformations
    3. Properties of Linear Transformations
    4. Linear Transformations and Polynomials

    E. General Vector Spaces
    1. Real Vector Spaces
    2. Subspaces
    3. Linear Independence
    4. Basis and Dimension
    5. Row Space, column Space and Nullspace
    6. Rank and Nullity

    F. Inner Product Spaces
    1. Inner Products
    2. Angle and Orthogonality in Inner Project Spaces
    3. Orthonormal Bases; Gram-Schmidt Process; QR Decomposition
    4. Best Approximation; Least Squares
    5. Change of Basis
    6. Orthogonal Matrices

    G. Eigenvalues, Eigenvectors
    1. Eigenvalues and Eigenvectors
    2. Diagonalization
    3. Orthogonal Diagonalization

    H. Linear Transformations
    1. General Linear Transformations
    2. Kernel and Range
    3. Inverse Linear Transformations
    4. Matrices of General Linear Transformations
    5. Similarity
    6. Isomorphism