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| Preliminary Contents | |
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| Problem Solving | |
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| Inductive and deductive reasoning | |
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| Problem solving with patterns | |
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| Problem-solving strategies | |
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| Sets | |
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| Basic properties of sets | |
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| Complements, subsets, and venn diagrams | |
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| Set operations | |
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| Applications of sets | |
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| Infinite sets | |
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| Logic | |
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| Logic statements and quantifiers | |
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| Truth tables, equivalent statements, and tautologies | |
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| The conditional and the biconditional | |
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| The conditional and related statements | |
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| Arguments | |
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| Euler diagrams | |
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| Numeration Systems and Number Theory | |
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| Early numeration systems | |
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| Place-value systems | |
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| Different base systems | |
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| Arithmetic in different bases | |
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| Prime numbers | |
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| Topics from number theory | |
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| Applications of Equations | |
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| First-degree equations | |
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| Rate, ratio, and proportion | |
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| Percent | |
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| Second-degree equations | |
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| Applications of Functions | |
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| Rectangular coordinates and functions | |
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| Properties of linear functions | |
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| Finding linear models | |
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| Quadratic functions | |
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| Exponential functions | |
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| Logarithmic functions | |
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| Mathematical Systems | |
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| Modular arithmetic | |
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| Applications of modular arithmetic | |
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| Introduction to group theory | |
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| Geometry | |
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| Basic concepts of Euclidean geometry | |
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| Perimeter and area of plane figures | |
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| Properties of triangles | |
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| Volume and surface area | |
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| Introduction to trigonometry | |
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| Non-Euclidean geometry | |
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| Fractals | |
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| The Mathematics of Graphs | |
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| Traveling roads and visiting cities | |
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| Efficient routes | |
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| Planarity and Euler's formula | |
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| Map coloring and graphs | |
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| The Mathematics of Finance | |
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| Simple interest | |
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| Compound interest | |
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| Credit cards and consumer loans | |
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| Stocks, bonds, and mutual funds | |
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| Home ownership | |
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| Combinatorics and Probability | |
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| The counting principle | |
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| Permutations and combinations | |
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| Probability and odds | |
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| Addition and complement rules | |
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| Conditional probability | |
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| Expectation | |
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| Statistics | |
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| Measures of central tendency | |
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| Measures of dispersion | |
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| Measures of relative position | |
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| Normal distributions | |
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| Linear regression and correlation | |
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| Apportionment and Voting | |
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| Introduction to apportionment | |
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| Introduction to voting | |
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| Weighted voting systems | |