COMPUTER SCIENCE

Course Credits: 3 Units

Prerequisites: Math 107

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Math 114 - Linear Algebra

Course Description

This is a course that discusses vector spaces, eigenvalues, linear transformation, and matrices. Linear Algebra has applications in every area of more advanced mathematics courses such as Differential Equations, Modern Geometry, and Probability Theory. It is also widely used in most fields like physics, chemistry, computer science, and engineering. The lectures and discussions will not only focus on computational aspects, but also on the theory of Linear Algebra. Aside from developing your computational abilities, this course will enhance your skills in proving.

Course Learning Outcomes

After completion of the course, the student should be able to:

  1. Discuss basic terms and concepts of linear algebra;
  2. Use matrices to solve systems of linear equations and in linear transformations;
  3. Determine if a set of vectors is a vector space, a subspace, or a basis for a vector space;
  4. Use theorems and techniques to solve the eigenvalue and diagonalization problems; and
  5. Formulate clear and accurate proofs using the concepts of linear algebra.
Course Outline

UNIT 1. Introduction to Systems of Linear Equations

UNIT 2. Matrices

  1. Definition of a Matrix
  2. Using Matrix to Solve Systems of Linear Equations (Gaussian Elimination, Gauss-Jordan Elimination)
  3. Operations with Matrices
  4. Properties of Matrix Operations
  5. The Inverse of a Matrix
  6. Elementary Matrices

UNIT 3. Determinants

  1. Determinant of a Matrix
  2. Determinants and Elementary Operations
  3. Properties of Determinants
  4. Applications of Determinants (Adjoint of a Matrix, Cramer’s Rule)

UNIT 4. Vector Spaces

  1. Definition of Vector Space
  2. Subspaces of Vector Spaces
  3. Spanning Sets and Linear Independence
  4. Basis and Dimension
  5. Rank of a Matrix and Systems of Linear Equations
  6. Coordinates and Change of Basis
  7. Length and Dot Product
  8. Orthonormal Bases: Gram-Schmidt Process

UNIT 5. Linear Transformations

  1. Introduction to Linear Transformations
  2. The Kernel and Range of a Linear Transformation
  3. Matrices for Linear Transformations

UNIT 6. Eigenvalues and Eigenvectors

  1. Eigenvalues and Eigenvectors
  2. Diagonalization
  3. Symmetric Matrices and Orthogonal Diagonalization