Preface 

ix  

The Art of Problem Solving 


1  (48) 

Solving Problems by Inductive Reasoning 


2  (8) 

An Application of Inductive Reasoning: Number Patterns 


10  (10) 

Strategies for Problem Solving 


20  (11) 

Calculating, Estimating, and Reading Graphs 


31  (18) 

Extension: Using Writing to Learn About Mathematics 


40  (6) 

Collaborative Investigation: Discovering Mathematics in Pascal's Triangle 


46  (1) 


47  (2) 

The Basic Concepts of Set Theory 


49  (45) 


50  (6) 

Venn Diagrams and Subsets 


56  (7) 

Set Operations and Cartesian Products 


63  (13) 

Cardinal Numbers and Surveys 


76  (7) 

Infinite Sets and Their Cardinalities 


83  (11) 

Collaborative Investigation: A Survey of Your Class 


90  (1) 


91  (3) 


94  (57) 

Statements and Quantifiers 


95  (7) 

Truth Tables and Equivalent Statements 


102  (11) 

The Conditional and Circuits 


113  (10) 


123  (6) 

Analyzing Arguments with Euler Diagrams 


129  (7) 


133  (3) 

Analyzing Arguments with Truth Tables 


136  (15) 

Collaborative Investigation: Logic Puzzles Revisited 


148  (1) 


149  (2) 

Numeration and Mathematical Systems 


151  (44) 

Historical Numeration Systems 


152  (8) 

Arithmetic in the HinduArabic System 


160  (9) 

Conversion Between Number Bases 


169  (10) 

Finite Mathematical Systems 


179  (7) 


186  (9) 

Collaborative Investigation: A Perpetual Calendar Algorithm 


193  (1) 


194  (1) 


195  (52) 

Prime and Composite Numbers 


196  (10) 

Selected Topics from Number Theory 


206  (6) 

Greatest Common Factor and Least Common Multiple 


212  (8) 

Clock Arithmetic and Modular Systems 


220  (12) 

The Fibonacci Sequence and the Golden Ratio 


232  (15) 


240  (4) 

Collaborative Investigation: Investigating an Interesting Property of Number Squares 


244  (1) 


245  (2) 

The Real Numbers and Their Representations 


247  (67) 

Real Numbers, Order, and Absolute Value 


248  (9) 

Operations, Properties, and Applications of Real Numbers 


257  (13) 

Rational Numbers and Decimal Representation 


270  (13) 

Irrational Numbers and Decimal Representation 


283  (10) 

Applications of Decimals and Percents 


293  (21) 

Extension: Complex Numbers 


306  (4) 

Collaborative Investigation: Budgeting to Buy a Car 


310  (1) 


311  (3) 

The Basic Concepts of Algebra 


314  (79) 


315  (10) 

Applications of Linear Equations 


325  (14) 

Ratio, Proportion, and Variation 


339  (13) 


352  (8) 

Properties of Exponents and Scientific Notation 


360  (12) 

Polynomials and Factoring 


372  (9) 

Quadratic Equations and Applications 


381  (12) 

Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Racewalkers? 


390  (1) 


391  (2) 

Graphs, Functions, and Systems of Equations and Inequalities 


393  (98) 

The Rectangular Coordinate System and Circles 


394  (8) 


402  (10) 

Equations of Lines and Linear Models 


412  (10) 

An Introduction to Functions: Linear Functions, Applications, and Models 


422  (12) 

Quadratic Functions, Applications, and Models 


434  (10) 

Exponential and Logarithmic Functions, Applications, and Models 


444  (12) 

Systems of Equations and Applications 


456  (25) 

Extension: Using Matrix Row Operations to Solve Systems 


476  (5) 

Linear Inequalities, Systems, and Linear Programming 


481  (10) 

Collaborative Investigation: Living with AIDS 


488  (1) 


489  (2) 


491  (85) 

Points, Lines, Planes, and Angles 


492  (10) 

Curves, Polygons, and Circles 


502  (10) 

Extension: Geometric Constructions 


509  (3) 

Perimeter, Area, and Circumference 


512  (11) 

The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem 


523  (13) 

Space Figures, Volume, and Surface Area 


536  (9) 

Transformational Geometry 


545  (11) 

NonEuclidean Geometry, Topology, and Networks 


556  (11) 

Chaos and Fractal Geometry 


567  (9) 

Collaborative Investigation: Generalizing the Angle Sum Concept 


573  (1) 


574  (2) 


576  (53) 

Angles and Their Measures 


577  (5) 

Trigonometric Functions of Angles 


582  (4) 


586  (5) 

Right Triangles and Function Values 


591  (9) 

Applications of Right Triangles 


600  (8) 

The Laws of Sines and Cosines; Area Formulas 


608  (12) 

The Unit Circle and Graphs 


620  (9) 

Collaborative Investigation: Making a Point About Trigonometric Function Values 


626  (1) 


627  (2) 


629  (44) 

Counting by Systematic Listing 


630  (7) 

Using the Fundamental Counting Principle 


637  (9) 

Using Permutations and Combinations 


646  (12) 

Using Pascal's Triangle and the Binomial Theorem 


658  (6) 

Counting Problems Involving ``Not'' and ``Or'' 


664  (9) 

Collaborative Investigation: Approximating Factorials Using Stirling's Formula 


671  (1) 


672  (1) 


673  (50) 


674  (10) 

Events Involving ``Not'' and ``Or'' 


684  (7) 


691  (10) 


701  (6) 


707  (9) 

Estimating Probabilities by Simulation 


716  (7) 

Collaborative Investigation: Finding Empirical Values of π 


720  (1) 


721  (2) 


723  (65) 

Frequency Distributions and Graphs 


725  (10) 

Measures of Central Tendency 


735  (13) 


748  (8) 


756  (7) 


763  (15) 

Extension: How to Lie with Statistics 


771  (7) 

Regression and Correlation 


778  (10) 

Collaborative Investigation: Combining Sets of Data 


784  (1) 


785  (3) 


788  (62) 


789  (17) 


802  (4) 


806  (7) 


813  (9) 


822  (10) 


832  (18) 

Collaborative Investigation: To Buy or to Rent? 


848  (1) 


849  (1) 

Graph Theory (available only in the expanded tenth edition) 


850  (61) 


851  (14) 


865  (15) 


880  (14) 

Trees and Minimum Spanning Trees 


894  (17) 

Collaborative Investigation: Finding the Number of Edges in a Complete Graph 


906  (2) 


908  (3) 

Voting and Apportionment (available only in the expanded tenth edition) 


911  (1) 

The Possibilities of Voting 


912  (18) 

The Impossibilities of Voting 


930  (17) 

The Possibilities of Apportionment 


947  (15) 

The Impossibilities of Apportionment 


962  (13) 

Collaborative Investigation: Class Favorites, an Election Exploration 


975  (2) 


977  
Appendix The Metric System 

1  (8) 
Answers to Selected Exercises 

9  (56) 
Credits 

65  
Index 

1  (18) 
Index of Applications 

19  