V.  OUTLINE

1. Introduction
   1. Course requirements
   2. Grading
   
   
2. Basic Algebraic Operations
   1. Review of elementary algebra
   2. Real numbers
   3. Polynomials
   4. Factoring
   5. Rational expressions
   6. Exponents
      1. integer
      2. rational
      3. radicals
   
   
3. Equations
   1. Linear equations
   2. Absolute values
   3. Complex numbers
   4. Quadratic equations
   
   
4. Inequalities
   1. Linear
   2. Absolute values
   
   
5. Functions
   1. Domain and Range
   2. Rational functions
   3. Composition
   4. Inverse functions
   
   
6. Graphs
   1. Straight lines
   2. Circles
   3. Graphing functions
      1. parabolas
      2. rational functions
   
   
7. Polynomial Functions
   1. Long division
   2. Synthetic Division
   3. Remainder Theorem
   4. Factor Theorem
   5. Fundamental Theorem of Algebra
   6. Zeros of polynomials
      1. rational
      2. complex
   
   
8. Exponential and Logarithmic Functions
   1. Exponential functions
   2. Logarithmic functions
   3. Logarithms
   
   
9. Systems of Equations
   1. Linear equations
   2. Elementary solutions
   3. Cramer's Rule
   
   
10. Matrices
    1. Augmented matrices
    2. Gauss-Jordan Elimination
    3. Operations
       1. addition
       2. multiplication by constant
       3. matrix multiplication
    4. Inverse
    5. Matrix equations
    6. Determinants