Product Overview

Note: Each chapter concludes with a Summary, Research Questions, a Practice Test, and Answers to Practice Test.
1. Problem Solving
1.1 Inductive Reasoning
1.2 Estimation: A Problem-Solving Tool
1.3 Graph Interpretation: A Problem-Solving Tool
2. Sets
2.1 Sets: A Problem-Solving Tool
2.2 Set Operations
2.3 Venn Diagrams
2.4 The Number of Elements in a Set: A Problem-Solving Tool
2.5 Infinite Sets
3. Logic
3.1 Statements
3.2 Truth Tables: A Problem-Solving Tool
3.3 The Conditional and the Biconditional
3.4 Variations of the Conditional and Implications
3.5 Euler Diagrams: A Problem-Solving Tool
3.6 Truth Tables and Validity of Arguments
3.7 Switching Networks: A Problem-Solving Tool
4. Numeration Systems
4.1 Egyptian, Babylonian, and Roman Numeration Systems
4.2 The Hindu-Arabic (Decimal) System
4.3 Number Systems with Bases Other Than 10
4.4 Binary Arithmetic
4.5 Octal and Hexadecimal Arithmetic
5. Number Theory and the Real Numbers
5.1 Number Theory: Primes and Composites
5.2 Whole Numbers, Integers, and Order of Operations
5.3 The Rational Numbers
5.4 Decimals, Scientific Notation, Significant Digits
5.5 Rationals as Decimals: Percents
5.6 Real Numbers, Square Roots, and Decimal Representation
5.7 Radicals
5.8 Number Sequences
6. Equations, Inequalities, and Problem Solving
6.1 Solutions of First-Degree Sentences
6.2 Graphs of Algebraic Sentences
6.3 Sentences Involving Absolute Values
6.4 Quadratic Equations
6.5 Modeling and Problem Solving
6.6 Ratio, Proportion, and Variation
7. Functions and Graphs
7.1 Graphing Relations and Functions
7.2 Linear Functions, Relations, and Applications
7.3 Slopes and Equations of a Line
7.4 Quadratic Functions and Their Graphs
7.5 Exponential and Logarithmic Functions
7.6 Two Linear Equations in Two Variables
7.7 Linear Inequalities
7.8 Linear Programming
8. Geometry
8.1 Points, Lines, Planes, and Angles
8.2 Triangles and Other Polygons
8.3 Perimeter and Circumference
8.4 Area Measure and the Pythagorean Theorem
8.5 Volume and Surface Area
8.6 Networks, Non-Euclidean Geometry, and Topology
8.7 Chaos and Fractals
9. Mathematical Systems and Matrices
9.1 Matrix Operations
9.2 Solving Systems of Linear Equations with Matrices
9.3 Clock and Modular Arithmetic
9.4 Abstract Mathematical Systems: Groups and Fields
9.5 Game Theory
10. Counting Techniques
10.1 The Sequential Counting Principle (SCP): A Problem-Solving Tool
10.2 Permutations
10.3 Combinations
10.4 Miscellaneous Counting Methods
11. Probability
11.1 Sample Spaces and Probability
11.2 Counting Techniques and Probability
11.3 Computation of Probabilities
11.4 Conditional Probability
11.5 Independent Events
11.6 Odds and Mathematical Expectation
12. Statistics
12.1 Sampling and Frequency Distributions
12.2 Measures of Central Tendency: The Mean, Median, and Mode
12.3 Measures of Dispersion: The Range and Standard Deviation
12.4 The Normal Distribution: A Problem-Solving Tool
12.5 Statistical Graphs: A Problem-Solving Tool
12.6 Making Predictions: Linear Regression
12.7 Scattergrams and Correlation
13. Your Money and Your Math
13.1 Interest, Taxes, and Discounts
13.2 Credit Cards and Consumer Credit
13.3 Annual Percentage Rate (APR) and the Rule of 78
13.4 Buying a House
14. Voting and Apportionment
14.1 Voting Systems
14.2 Voting Objections
14.3 Apportionment Methods
14.4 Apportionment Objections
15. Graph Theory
15.1 Introduction to Graph Theory
15.2 Euler Paths and Euler Circuits
15.3 Hamilton Paths and Hamilton Circuits
15.4 Trees
Appendix: The Metric System
Answers to Odd-Numbered Problems
Research Bibliography
Acknowledgments
Photo Credits
Index