Preface 

xi  

The Art of Problem Solving 


1  (51) 

Solving Problems by Inductive Reasoning 


2  (9) 

An Application of Inductive Reasoning: Number Patterns 


11  (10) 

Strategies for Problem Solving 


21  (12) 

Calculating, Estimating, and Reading Graphs 


33  (19) 

Extension: Using Writing to Learn About Mathematics 


42  (7) 

Collaborative Investigation: Discovering Mathematics in Pascal's Triangle 


49  (1) 


50  (2) 

The Basic Concepts of Set Theory 


52  (48) 


53  (7) 

Venn Diagrams and Subsets 


60  (8) 

Set Operations and Cartesian Products 


68  (14) 

Cardinal Numbers and Surveys 


82  (7) 

Infinite Sets and Their Cardinalities 


89  (11) 

Collaborative Investigation: A Survey of Your Class 


96  (1) 


97  (3) 


100  (59) 

Statements and Quantifiers 


101  (7) 

Truth Tables and Equivalent Statements 


108  (12) 

The Conditional and Circuits 


120  (10) 


130  (6) 

Analyzing Arguments with Euler Diagrams 


136  (10) 


141  (5) 

Analyzing Arguments with Truth Tables 


146  (13) 

Collaborative Investigation: Logic Puzzles Revisited 


157  (1) 


158  (1) 

Numeration and Mathematical Systems 


159  (49) 

Historical Numeration Systems 


160  (10) 

Arithmetic in the HinduArabic System 


170  (9) 

Conversion Between Number Bases 


179  (11) 

Finite Mathematical Systems 


190  (8) 


198  (10) 

Collaborative Investigation: A Perpetual Calendar Algorithm 


205  (1) 


206  (2) 


208  (51) 

Prime and Composite Numbers 


209  (11) 

Selected Topics from Number Theory 


220  (7) 

Greatest Common Factor and Least Common Multiple 


227  (7) 


234  (10) 

The Fibonacci Sequence and the Golden Ratio 


244  (15) 


252  (5) 

Collaborative Investigation: Investigating an Interesting Property of Number Squares 


257  (1) 


258  (1) 

The Real Numbers and Their Representations 


259  (72) 

Real Numbers, Order, and Absolute Value 


260  (10) 

Operations, Properties, and Applications of Real Numbers 


270  (13) 

Rational Numbers and Decimal Representation 


283  (16) 

Irrational Numbers and Decimal Representation 


299  (10) 

Applications of Decimals and Percents 


309  (22) 

Extension: Complex Numbers 


322  (4) 

Collaborative Investigation: Budgeting to Buy a Car 


326  (1) 


327  (4) 

The Basic Concepts of Algebra 


331  (84) 


332  (10) 

Applications of Linear Equations 


342  (14) 

Ratio, Proportion, and Variation 


356  (14) 


370  (9) 

Properties of Exponents and Scientific Notation 


379  (14) 

Polynomials and Factoring 


393  (9) 

Quadratic Equations and Applications 


402  (13) 

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


412  (1) 


413  (2) 

Graphs, Functions, and Systems of Equations and Inequalities 


415  (105) 

The Rectangular Coordinate System and Circles 


416  (10) 


426  (11) 

Equations of Lines and Linear Models 


437  (10) 

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


447  (14) 

Quadratic Functions, Applications, and Models 


461  (10) 

Exponential and Logarithmic Functions, Applications, and Models 


471  (12) 

Systems of Equations and Applications 


483  (26) 

Extension: Using Matrix Row Operations to Solve Systems 


504  (5) 

Linear Inequalities, Systems, and Linear Programming 


509  (11) 

Collaborative Investigation: Olympic Track and Field Results 


517  (1) 


518  (2) 


520  (88) 

Points, Lines, Planes, and Angles 


522  (10) 

Curves, Polygons, and Circles 


532  (10) 

Perimeter, Area, and Circumference 


542  (14) 

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


556  (19) 

Extension: Right Triangle Trigonometry 


570  (5) 

Space Figures, Volume, and Surface Area 


575  (10) 

NonEuclidean Geometry, Topology, and Networks 


585  (12) 

Chaos and Fractal Geometry 


597  (11) 

Collaborative Investigation: Generalizing the Angle Sum Concept 


604  (1) 


604  (4) 


608  (49) 

Counting by Systematic Listing 


609  (10) 

Using the Fundamental Counting Principle 


619  (9) 

Using Permutations and Combinations 


628  (12) 

Using Pascal's Triangle and the Binomial Theorem 


640  (8) 

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


648  (9) 

Collaborative Investigation: Approximating Factorials Using Stirling's Formula 


655  (1) 


656  (1) 


657  (53) 


658  (11) 

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


669  (8) 


677  (11) 


688  (6) 


694  (9) 

Estimating Probabilities by Simulation 


703  (7) 

Collaborative Investigation: Finding Empirical Values of π 


707  (1) 


708  (2) 


710  (76) 

Frequency Distributions and Graphs 


712  (12) 

Measures of Central Tendency 


724  (15) 


739  (9) 


748  (8) 


756  (17) 

Extension: How to Lie with Statistics 


766  (7) 

Regression and Correlation 


773  (13) 

Collaborative Investigation: Combining Sets of Data 


782  (1) 


783  (3) 


786  (60) 


787  (18) 


801  (4) 


805  (8) 


813  (9) 


822  (12) 

Investing in the Stock Market 


834  (12) 

Collaborative Investigation: To Buy or to Rent? 


844  (1) 


845  (1) 


846  (71) 


847  (16) 


863  (18) 


881  (16) 

Trees and Minimum Spanning Trees 


897  (20) 

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


911  (1) 


912  (5) 


917  

The Possibilities of Voting 


918  (21) 

The Impossibilities of Voting 


939  (21) 

The Possibilities of Apportionment 


960  (17) 

The Impossibilities of Apportionment 


977  

Collaborative Investigation: Class Favorites, An Election Exploration 


990  (2) 


992  
Appendix The Metric System 

A1  
Answers to Selected Exercises 

A9  
Credits 

A59  
Index 

I1  
Index of Applications 

I18  