Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 3


COURSE DESCRIPTION
3 Linear Algebra Units: 3.00
 
Prerequisite(s): MAT 1B: Calculus II
Introduction to matrix algebra, determinants, systems of linear equations, vector spaces, linear independence, linear transformations, eigenvalues and eigenvectors, and applications. 54 hours lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
Introduction to matrix algebra with vector spaces and linear transformations.
 
ADVISORY ENTRY SKILLS
None.

STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

1.  Solve systems of linear algebraic equations using Gaussian elimination or Cramer’s rule.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

2.  Calculate and apply determinants to a variety of problems including but not limited to areas, volumes, and cross products.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

3.  Determine the rank and the dimension of the kernel for a matrix operator.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

4.  Find bases for the range and the kernel of linear operators.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

5.  Find Eigenvalues and related Eigenvectors for a square matrix.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

6.  Use the Gram-Schmidt process to produce an orthonormal.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

7.  Use an orthonormal basis to diagonalize a square matrix.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

8.  Prove fundamental theorems in linear algebra.
   

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Construct sound arguments and evaluate arguments of others
  3. Critical Thinking - Generalize appropriately from specific contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace
 
COURSE CONTENT
  TOPICS
 

   1.   Systems of Linear Equations
         a.   Gauss Eliminations, Application of Systems
   2.   Matrices.
         a.   Operations, Properties, Inverses, Applications
   3.   Determinants.
         a.   Evaluation, Properties, Applications
   4.   Vector Spaces.
         a.   Subspaces, Linear Independence, Basis and Dimension, 
               Range of a Matrix, Applications
   5.   Linear Transformations.
         a.   Kernal and Range, Matrices for Transformations, Similarity, 
               Applications
   6.   Eigenvalues and Eigenvectors
         a.   Diagonalization, Applications.
   7.   Proofs of Fundamental Theorems in linear algebra.
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  • Class lectures/discussions/demonstrations
  • Drills and pattern practices
  • Videos/films/slides/audio tapes
  • Pair and small group activities/discussion
  • Class exercises
  • Reports and papers
  • Handouts
  • Cooperative learning tasks
  • Online/distance education and technology based
 
METHODS OF EVALUATION
 Students will be evaluated for progress in and/or mastery of learning outcomes by methods of evaluation which may include, but are not limited to:

  • Oral reports/presentations/performance
  • Written reports/presentations
  • Quizzes/examinations
  • Written assignments
  • Class and individual projects
  • Laboratory projects/performance
  • Final examination

 
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
COURSE MATERIALS
 All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include:

  • Larson and Edwards. Elementary Linear Algebra. 4th ed. Houghton Mifflin, 2000.
  • Fraleigh and Beauregard. Linear Algebra. 3rd ed. Addison Wesley Longman, Inc., 1998.
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