Preliminary Contents | |

Problem Solving | |

Inductive and deductive reasoning | |

Problem solving with patterns | |

Problem-solving strategies | |

Sets | |

Basic properties of sets | |

Complements, subsets, and venn diagrams | |

Set operations | |

Applications of sets | |

Infinite sets | |

Logic | |

Logic statements and quantifiers | |

Truth tables, equivalent statements, and tautologies | |

The conditional and the biconditional | |

The conditional and related statements | |

Arguments | |

Euler diagrams | |

Numeration Systems and Number Theory | |

Early numeration systems | |

Place-value systems | |

Different base systems | |

Arithmetic in different bases | |

Prime numbers | |

Topics from number theory | |

Applications of Equations | |

First-degree equations | |

Rate, ratio, and proportion | |

Percent | |

Second-degree equations | |

Applications of Functions | |

Rectangular coordinates and functions | |

Properties of linear functions | |

Finding linear models | |

Quadratic functions | |

Exponential functions | |

Logarithmic functions | |

Mathematical Systems | |

Modular arithmetic | |

Applications of modular arithmetic | |

Introduction to group theory | |

Geometry | |

Basic concepts of Euclidean geometry | |

Perimeter and area of plane figures | |

Properties of triangles | |

Volume and surface area | |

Introduction to trigonometry | |

Non-Euclidean geometry | |

Fractals | |

The Mathematics of Graphs | |

Traveling roads and visiting cities | |

Efficient routes | |

Planarity and Euler's formula | |

Map coloring and graphs | |

The Mathematics of Finance | |

Simple interest | |

Compound interest | |

Credit cards and consumer loans | |

Stocks, bonds, and mutual funds | |

Home ownership | |

Combinatorics and Probability | |

The counting principle | |

Permutations and combinations | |

Probability and odds | |

Addition and complement rules | |

Conditional probability | |

Expectation | |

Statistics | |

Measures of central tendency | |

Measures of dispersion | |

Measures of relative position | |

Normal distributions | |

Linear regression and correlation | |

Apportionment and Voting | |

Introduction to apportionment | |

Introduction to voting | |

Weighted voting systems | |

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