Problem Solving | |
The Nature of Mathematical Reasoning | |
Estimation and Interpreting Graphs | |
Problem Solving | |
Chapter 1 Review | |
Sets | |
The Nature of Sets | |
Subsets and Set Operations | |
Venn Diagrams | |
Using Sets to Solve Problems | |
Infinite Sets | |
Chapter 2 Review | |
Logic | |
Statements and Quantifiers | |
Truth Tables | |
Types of Statements | |
Logical Arguments | |
Euler Circles | |
Chapter 3 Review | |
Numeration Systems | |
Early and Modern Numeration Systems | |
Tools and Algorithms in Arithmetic | |
Base Number Systems | |
Operations in Base Number Systems | |
Chapter 4 Review | |
The Real Number System | |
The Natural Numbers | |
The Integers | |
The Rational Numbers | |
The Irrational Numbers | |
The Real Numbers | |
Exponents and Scientific Notation | |
Arithmetic and Geometric Sequences | |
Chapter 5 Review | |
Topics in Algebra | |
The Fundamentals of Algebra | |
Solving Linear Equations | |
Applications of Linear Equations | |
Ratio, Proportion, and Variation | |
Solving Linear Inequalities | |
Solving Quadratic Equations | |
Chapter 6 Review | |
Additional Topics in Algebra | |
The Rectangular Coordinate System and Linear Equations in Two Variables | |
Systems of Linear Equations | |
Solving Systems of Linear Equations Using Matrices | |
Linear Inequalities | |
Linear Programming | |
Functions | |
Linear, Quadratic, and Exponential Functions | |
Supplement: An Application of Functions--Sound | |
Chapter 7 Review | |
Consumer Mathematics | |
Percents | |
Simple Interest | |
Compound Interest | |
Installment Buying | |
Home Ownership | |
Stocks and Bonds | |
Chapter 8 Review | |
Measurement | |
Measures of Length: Converting Units and the Metric System | |
Measures of Area, Volume, and Capacity | |
Measures of Weight and Temperature | |
Chapter 9 Review | |
Geometry | |
Points, Lines, Planes and Angles | |
Triangles | |
Polygons and Perimeter | |
Areas of Polygons and Circles | |
Volume and Surface Area | |
Right Triangle Trigonometry | |
A Brief Survey of Non-Euclidean and Transformational Geometries | |
Chapter 10 Review | |
Probability and Counting Techniques | |
The Fundamental Counting Rule and Permutations | |
Combinations | |
Basic Concepts of Probability | |
Tree Diagrams, Tables, and Sample Spaces | |
Probability Using Permutations and Combinations | |
Odds and Expectation | |
The Addition Rules for Probability | |
The Multiplication Rules and Conditional Probability | |
The Binomial Distribution | |
Chapter 11 Review | |
Statistics | |
The Nature of Statistics and Organizing Data | |
Picturing Data | |
Measures of Average | |
Measures of Variation | |
Measures of Position | |
The Normal Distribution | |
Applications of the Normal Distribution | |
Correlation and Regression Analysis | |
Supplement: Misuses of Statistics | |
Chapter 12 Review | |
Other Mathematical Systems | |
Mathematical Systems and Groups | |
Clock Arithmetic | |
Modular Systems | |
Chapter 13 Review | |
Voting Methods | |
Preference Tables and the Plurality Method | |
The Borda Count Method and the Plurality-with-Elimination Method | |
The Pairwise Comparison Method and Approval Voting | |
Apportionment | |
Apportionment Flaws | |
Chapter 14 Review | |
Graph Theory | |
Basic Concepts of Graph Theory | |
Euler's Theorem | |
Hamilton Paths and Circuits | |
Trees | |
Chapter 15 Review | |
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