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1. The Art of Problem Solving 1.1 Solving Problems by Inductive Reasoning 1.2 An Application of Inductive Reasoning: Number Patterns 1.3 Strategies for Problem Solving 1.4 Calculating, Estimating, and Reading Graphs Extension: Using Writing to Learn about Mathematics Collaborative Investigation: Discovering Patterns in Pascal's Triangle Chapter 1 Test 2. The Basic Concepts of Set Theory 2.1 Symbols and Terminology 2.2 Venn Diagrams and Subsets 2.3 Set Operations and Cartesian Products 2.4 Surveys and Cardinal Numbers Extension: Infinite Sets and Their Cardinalities Collaborative Investigation: Surveying the Members of Your Class Chapter 2 Test 3. Introduction to Logic 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 Extension: Logic Problems and Sudoku 3.6 Analyzing Arguments with Truth Tables Collaborative Investigation: Logic Problems and Sudoku Revisited Chapter 3 Test 4. Numeration Systems 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 Extension: Modular Systems Collaborative Investigation: A Perpetual Calendar Algorithm Chapter 4 Test 5. Number Theory 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 Extension: Modern Cryptography 5.5 The Fibonacci Sequence and the Golden Ratio Collaborative Investigation: Investigating an Interesting Property of Number Squares Chapter 5 Test 6. The Real Numbers and Their Representations 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 Extension: Complex Numbers Collaborative Investigation: Budgeting to Buy a Car Chapter 6 Test 7. The Basic Concepts of Algebra 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 Extension: Complex Solutions of Quadratic Equations Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Race-walkers? Chapter 7 Test 8. Graphs, Functions, and Systems of Equations and Inequalities 8.1 The Rectangular Coordinate System and Circles 8.2 Lines, Slope, and Average Rate of Change 8.3 Equations of Lines and Linear Models 8.4 An Introduction to Functions: Linear Functions, Applications, and Models 8.5 Quadratic Functions, Graphs, and Models 8.6 Exponential and Logarithmic Functions, Applications, and Models 8.7 Systems of Equations 8.8 Applications of Systems Extension: Using Matrix Row Operations to Solve Systems 8.9 Linear Inequalities, Systems, and Linear Programming Collaborative Investigation: Tracking an Epidemic Chapter 8 Test 9. Geometry 9.1 Points, Lines, Planes, and Angles 9.2 Curves, Polygons, and Circles Extension: 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, Topology, and Networks 9.8 Chaos and Fractal Geometry Collaborative Investigation: Generalizing the Angle Sum Concept Chapter 9 Test 10. Counting Methods (formerly Chapter 11) 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 Extension: Magic Squares 10.5 Counting Problems Involving "Not" and "Or" Collaborative Investigation: Solving a Traveling Salesman Problem Chapter 10 Test 11. Probability (formerly Chapter 12) 11.1 Basic Concepts 11.2 Events Involving "Not" and "Or" 11.3 Conditional Probability; Events Involving "And" 11.4 Binomial Probability 11.5 Expected Value Extension: Estimating Probabilities by Simulation Collaborative Investigation: Finding Empirical Values of Chapter 11 Test 12. Statistics (formerly Chapter 13) 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 Extension: Regression and Correlation Collaborative Investigation: Combining Sets of Data Chapter 12 Test 13. Personal Financial Management (formerly Chapter 14) 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 Extension: Ponzi Schemes and Other Investment Frauds Collaborative Investigation: To Buy or to Rent? Chapter 13 Test 14. Trigonometry (formerly Ch. 10) 14.1 Angles and Their Measures 14.2 Trigonometric Functions of Angles 14.3 Trigonometric Identities 14.4 Right Triangles and Function Values 14.5 Applications of Right Triangles 14.6 The Laws of Sines and Cosines Extension: Area Formulas for Triangles Collaborative Investigation: Making a Point about Trigonometric Function Values Chapter 14 Test 15. Graph Theory 15.1 Basic Concepts 15.2 Euler Circuits 15.3 Hamilton Circuits and Algorithms 15.4 Minimum Spanning Trees Extension: Route Planning Collaborative Investigation: Finding the Number of Edges in a Complete Graph Chapter 15 Test 16. Voting and Apportionment 16.1 The Possibilities of Voting 16.2 The Impossibilities of Voting 16.3 The Possibilities of Apportionment Extension: Two Additional Apportionment Methods 16.4 The Impossibilities of Apportionment Collaborative Investigation: Favorites, An Election Exploration Chapter 16 Test Table of Contents
Get Mathematical Ideas, 12th Edition by Charles D. Miller, American River College Vern E. Heeren, American River College John Hornsby, University of New Orleans
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