College Algebra

Table of Contents

1. Chapter 1: Algebra and Geometry Review
   1. Algebra
      1. Simplifying Expressions
      2. Solving Equations
      3. Solving Equations in One Variable
      4. Solving Systems of Equations
      5. Inequalities
   2. Geometry
      1. The Pythagorean Theorem
      2. Analytic Geometry
      3. Lines, Circles, and Parabolas
      4. Conic Sections
      5. Trigonometry
   3. Exercises
2. Chapter 2: Real Numbers
   1. Introduction
   2. Sets and Functions
   3. Fields
   4. Ordered Fields
   5. The Natural Numbers and Induction
   6. The Fundamental Theorem of Arithmetic
   7. The Real Numbers
      1. Infinite Decimals
      2. Decimal Expansions
      3. Limits of Sequences
   8. Complex Numbers
      1. The Field of Complex Numbers
      2. Geometric Interpretation of Complex Operations
      3. Applications
         1. Translations, Reflections, and Rotations
         2. Angles and Trigonometry
   9. Exercises
3. Chapter 3: Polynomial Equations
   1. Polynomials
   2. Rational Roots
   3. The Fundamental Theorem of Algebra
   4. Cubic Equations
   5. Quartic Equations
   6. Exercises
4. Chapter 4: The Fundamental Theorem of Algebra
   1. The Overall Strategy for Proving the Fundamental Theorem
   2. Continuity
   3. More Continuous Functions
   4. Theorems of Bolzano and Weierstrass
   5. The Proof of the Fundamental Theorem of Algebra
   6. Exercises
5. Chapter 5: Elementary Functions
   1. Infinite Series and Convergence
   2. The Exponential and Logarithm Functions
   3. The Trigonometric Functions
   4. Exercises