Preface 

ix  

Set Theory: Using Mathematics to Classify Objects 


1  (73) 


2  (16) 


18  (8) 


26  (8) 


34  (8) 


42  (12) 


54  (20) 


64  (2) 


66  (2) 


68  (1) 

Of Further Interest: Infinite Sets 


69  (5) 

Logic: The Study of What's True or False or Somewhere in Between 


74  (71) 

Inductive and Deductive Reasoning 


75  (8) 

Statements, Connectives, and Quantifiers 


83  (10) 


93  (12) 

The Conditional and Biconditional 


105  (9) 


114  (9) 

Using Euler Diagrams to Verify Syllogisms 


123  (22) 


131  (3) 


134  (1) 


135  (2) 

Of Further Interest: Fuzzy Logic 


137  (8) 

Graph Theory (Networks): The Mathematics of Relationships 


145  (50) 

Graphs, Puzzles, and Map Coloring 


146  (15) 

The Traveling Salesperson Problem 


161  (11) 


172  (23) 


181  (2) 


183  (1) 


184  (2) 

Of Further Interest: Scheduling Projects Using PERT 


186  (9) 

Numeration Systems: Does It Matter How We Name Numbers? 


195  (47) 

The Evolution of Numeration Systems 


196  (9) 


205  (10) 

Calculating in Other Bases 


215  (27) 


229  (1) 


230  (1) 


231  (1) 

Of Further Interest: Modular Systems 


232  (10) 

Number Theory and the Real Number System: Understanding the Numbers All Around Us 


242  (72) 


243  (11) 


254  (8) 


262  (13) 


275  (12) 

Exponents and Scientific Notation 


287  (27) 


298  (2) 


300  (1) 


301  (2) 

Of Further Interest: Sequences 


303  (11) 

Algebraic Models: How Do We Approximate Reality? 


314  (78) 


315  (13) 

Modeling with Linear Equations 


328  (10) 

Modeling with Quadratic Equations 


338  (9) 

Exponential Equations and Growth 


347  (12) 

Proportions and Variation 


359  (8) 


367  (25) 


378  (2) 


380  (2) 


382  (2) 

Of Further Interest: Dynamical System 


384  (8) 

Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It? 


392  (34) 

Systems of Linear Equations 


393  (13) 

Systems of Linear Inequalities 


406  (20) 


416  (1) 


417  (1) 


417  (1) 

Of Further Interest: Linear Programming 


418  (8) 

Geometry. Ancient and Modern Mathematics Embrace 


426  (87) 

Lines, Angles, and Circles 


427  (10) 


437  (11) 


448  (13) 


461  (9) 

The Metric System and Dimensional Analysis 


470  (12) 

Geometric Symmetry and Tessellations 


482  (31) 


497  (3) 


500  (2) 


502  (2) 

Of Further Interest: Fractals 


504  (9) 

Apportionment: How Do We Measure Fairness? 


513  (57) 

Understanding Apportionment 


514  (11) 

The HuntingtonHill Apportionment Principle 


525  (7) 

Applications of the Apportionment Principle 


532  (8) 

Other Paradoxes and Apportionment Methods 


540  (30) 


556  (2) 


558  (1) 


559  (2) 

Of Further Interest: Fair Division 


561  (9) 

Voting: Using Mathematics to Make Choices 


570  (48) 


571  (11) 

Defects in Voting Methods 


582  (13) 


595  (23) 


605  (1) 


606  (2) 


608  (2) 

Of Further Interest: The ShapleyShubik Index 


610  (8) 

Consumer Mathematics: The Mathematics of Everyday Life 


618  (62) 


619  (8) 


627  (13) 


640  (9) 


649  (8) 


657  (23) 


668  (3) 


671  (1) 


671  (2) 

Of Further Interest: The Annual Percentage Rate 


673  (7) 

Counting: Just How Many Are There? 


680  (40) 

Introduction to Counting Methods 


681  (9) 

The Fundamental Counting Principle 


690  (8) 

Permutations and Combinations 


698  (22) 


712  (1) 


713  (1) 


713  (2) 

Of Further Interest: Counting and Gambling 


715  (5) 

Probability: What Are the Chances? 


720  (60) 

The Basics of Probability Theory 


721  (16) 

Complements and Unions of Events 


737  (8) 

Conditional Probability and Intersections of Events 


745  (16) 


761  (19) 


770  (1) 


771  (1) 


772  (1) 

Of Further Interest: Binomial Experiments 


773  (7) 

Descriptive Statistics: What a Data Set Tells Us 


780  (67) 

Organizing and Visualizing Data 


781  (13) 

Measures of Central Tendency 


794  (13) 


807  (12) 


819  (28) 


834  (2) 


836  (1) 


837  (1) 

Of Further Interest: Linear Correlation 


838  (9) 
Appendix A 

847  (4) 
Answers to Quiz Yourself Problems 

851  (8) 
Answers to Exercises 

859  
Photo Credits 

1  (1) 
Index 

1  