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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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