A Review of Basic Concepts and Skills | |

The Language, Notation, and Numbers of Mathematics | |

Algebraic Expressions and the Properties of Real Numbers | |

Exponents, Scientific Notation, and a Review of Polynomials | |

Factoring Polynomials | |

Rational Expressions | |

Radicals and Rational Exponents | |

Equations and Inequalities | |

Linear Equations, Formulas, and Problem Solving | |

Linear Inequalities in One Variable | |

Absolute Value Equations and Inequalities | |

Complex Numbers | |

Solving Quadratic Equations | |

Solving Other Types of Equation | |

Relations, Functions and Graphs | |

Rectangular Coordinates; Graphing Circles and Relations | |

Graphs of Linear Equations | |

Linear Equations and Rates of Change | |

Functions, Notation, and Graphs of Functions | |

Analyzing the Graph of a Function | |

Toolbox Functions and Transformations | |

Piecewise-Defined Functions | |

The Algebra and Composition of Functions | |

Polynomial and Rational Functions | |

Quadratic Functions and Applications | |

Synthetic Division; The Remainder and Factor Theorems | |

The Zeroes of Polynomial Functions | |

Graphing Polynomial Functions | |

Graphing Rational Functions | |

Additional Insights into Rational Functions | |

Polynomial and Rational Inequalities | |

Variation: Function Models in Action | |

Exponential and Logarithmic Functions | |

One-to-One and Inverse Functions | |

Exponential Functions | |

Logarithms and Logarithmic Functions | |

Properties of Logarithms; Solving Exponential and Logarithmic Equations | |

Applications from Business, Finance, and Science | |

Business, Finance, and Science Applications | |

Systems of Equations and Inequalities | |

Linear Systems in Two Variables with Applications | |

Linear Systems in Three Variables with Applications | |

Nonlinear Systems of Equations and Inequalities | |

Systems of Inequalities and Linear Programming | |

Matrices and Matrix Applications | |

Solving Systems Using Matrices and Row Operations | |

The Algebra of Matrices | |

Solving Linear Systems Using Matrix Equations | |

Applications of Matrices and Determinants: | |

Analytical Geometry and Conic Sections | |

Introduction to Analytic Geometry | |

The Circle and the Ellipse | |

The Hyperbola | |

The Analytic Parabola | |

Additional Topics in Algebra | |

Sequences and Series | |

Arithmetic Sequences | |

Geometric Sequences | |

Mathematical Induction | |

Counting Techniques | |

Introduction to Probability | |

The Binomial Theorem | |

Appendices | |

More on Synthetic Division | |

More on Matrices | |

Deriving the Equation of a Conic | |

Proof Positive | |

A Selection of Proofs from College Algebra | |

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