Mathematical Ideas 15E

Contents
Preface
Acknowledgements
About the Authors
Chapter 1: The Art of Problem Solving
	Chapter Opener
	1.1: Solving Problems by Inductive Reasoning
	1.2: An Application of Inductive Reasoning: Number Patterns
	1.3: Strategies for Problem Solving
	1.4: Numeracy in Today's World
	Chapter 1 Summary
	Chapter 1 Test
Chapter 2: The Basic Concepts of Set Theory
	Chapter Opener
	2.1: Symbols and Terminology
	2.2: Subsets and Diagrams
	2.3: Set Operations
	2.4: Surveys and Cardinal Numbers
	Chapter 2 Summary
	Chapter 2 Test
	Extension: Infinite Sets and Their Cardinalities (Online)
Chapter 3: Introduction to Logic
	Chapter Opener
	3.1: Statements and Quantifiers
	3.2: Truth Tables and Equivalent Statements
	3.3: The Conditional and Circuits
	3.4: The Conditional and Related Statements
	3.5: Analyzing Arguments with Euler Diagrams
	3.6: Analyzing Arguments with Truth Tables
	Chapter 3 Summary
	Chapter 3 Test
Chapter 4: Numeration Systems
	Chapter Opener
	4.1: Historical Numeration Systems
	4.2: More Historical Numeration Systems
	4.3: Arithmetic in the Hindu-Arabic System
	4.4: Conversion between Number Bases
	4.5: Arithmetic in Other Bases
	Chapter 4 Summary
	Chapter 4 Test
	Extension: Modular Systems (Online)
Chapter 5: Number Theory
	Chapter Opener
	5.1: Prime and Composite Numbers
	5.2: Large Prime Numbers
	5.3: Selected Topics from Number Theory
	5.4: Greatest Common Factor and Least Common Multiple
	5.5: The Fibonacci Sequence and the Golden Ratio
	Chapter 5 Summary
	Chapter 5 Test
	Extension: Magic Squares (Online)
	Extension: Modern Cryptography (Online)
Chapter 6: The Real Numbers and Their Representations
	Chapter Opener
	6.1: Real Numbers, Order, and Absolute Value
	6.2: Operations, Properties, and Applications of Real Numbers
	6.3: Rational Numbers and Decimal Representation
	6.4: Irrational Numbers and Decimal Representation
	6.5: Applications of Decimals and Percents
	Chapter 6 Summary
	Chapter 6 Test
	Extension: Complex Numbers (Online)
Chapter 7: The Basic Concepts of Algebra
	Chapter Opener
	7.1: Linear Equations
	7.2: Applications of Linear Equations
	7.3: Ratio, Proportion, and Variation
	7.4: Linear Inequalities
	7.5: Properties of Exponents and Scientific Notation
	7.6: Polynomials and Factoring
	7.7: Quadratic Equations and Applications
	Chapter 7 Summary
	Chapter 7 Test
	Extension: Complex Solutions of Quadratic Equations (Online)
Chapter 8: Graphs, Functions, and Systems of Equations and Inequalities
	Chapter Opener
	8.1: The Rectangular Coordinate System and Circles
	8.2: Lines, Slope, and Average Rate of Change
	8.3: Equation of Lines
	8.4: Linear Functions, Graphs, and Models
	8.5: Quadratic Functions, Graphs, and Models
	8.6: Exponential and Logarithmic Functions, Graphs, and Models
	8.7: Systems of Linear Equations
	8.8: Applications of Linear Systems
	8.9: Linear Inequalities, Systems, and Linear Programming
	Chapter 8 Summary
	Chapter 8 Test
	Extension: Using Matrix Row Operations to Solve Systems (Online)
Chapter 9: Geometry
	Chapter Opener
	9.1: Points, Lines, Planes, and Angles
	9.2: Curves, Polygons, Circles, and Geometric Constructions
	9.3: The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
	9.4: Perimeter, Area, and Circumference
	9.5: Volume and Surface Area
	9.6: Transformational Geometry
	9.7: Non-Euclidean Geometry and Topology
	9.8: Chaos and Fractal Geometry
	Chapter 9 Summary
	Chapter 9 Test
Chapter 10: Counting Methods
	Chapter Opener
	10.1: Counting by Systematic Listing
	10.2: Using the Fundamental Counting Principle
	10.3: Using Permutations and Combinations
	10.4: Using Pascal's Triangle
	10.5: Counting Problems Involving "Not" and "Or"
	Chapter 10 Summary
	Chapter 10 Test
Chapter 11: Probability
	Chapter Opener
	11.1: Basic Concepts
	11.2: Events Involving "Not" and "Or"
	11.3: Conditional Probability and Events Involving "And"
	11.4: Binomial Probability
	11.5: Expected Value and Simulation
	Chapter 11 Summary
	Chapter 11 Test
Chapter 12: Statistics
	Chapter Opener
	12.1: Visual Displays of Data
	12.2: Measures of Central Tendency
	12.3: Measures of Dispersion
	12.4: Measures of Position
	12.5: The Normal Distribution
	Chapter 12 Summary
	Chapter 12 Test
	Extension: Regression and Correlation (Online)
Chapter 13: Personal Financial Management
	Chapter Opener
	13.1: The Time Value of Money
	13.2: Consumer Credit
	13.3: Truth in Lending
	13.4: The Costs and Advantages of Home Ownership
	13.5: Financial Investments
	13.6: Income Tax Liability
	Chapter 13 Summary
	Chapter 13 Test
	Extension: Ponzi Schemes and Other Investment Frauds (Online)
Chapter 14: Graph Theory
	Chapter Opener
	14.1: Basic Concepts
	14.2: Euler Circuits and Route Planning
	14.3: Hamilton Circuits and Algorithms
	14.4: Trees and Minimum Spanning Trees
	Chapter 14 Summary
	Chapter 14 Test
	Extension: Route Planning (Online)
Chapter 15: Voting and Apportionment
	Chapter Opener
	15.1: The Possibilities of Voting
	15.2: The Impossibilities of Voting
	15.3: The Possibilities of Apportionment
	15.4: The Impossibilities of Apportionment
	Chapter 15 Summary
	Chapter 15 Test
Chapter T: Trigonometry (Online)
	Chapter Opener
	T.1: Angles and Their Measures
	T.2: Trigonometric Functions of Angles
	T.3: Trigonometric Identities
	T.4: Right Triangles and Function Values
	T.5: Applications of Right Triangles
	T.6: The Laws of Sines and Cosines
	Extension: Area Formulas for Triangles
	Chapter T Test
Appendix: The Metric System (Online)
Answers to Selected Exercises
Answers to Selected Online Exercises
Selected Answers to Extension Exercises
Index of Applications
Index