
Set Theory: Using Mathematics to Classify Objects 


1  (67) 


2  (14) 


16  (7) 


23  (7) 


30  (8) 


38  (12) 


50  (18) 


58  (3) 


61  (2) 

Of Further Interest: Infinite Sets 


63  (5) 

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


68  (72) 

Inductive and Deductive Reasoning 


69  (9) 

Statements, Connectives, and Quantifiers 


78  (10) 


88  (12) 

The Conditional and Biconditional 


100  (10) 


110  (9) 

Using Euler Diagrams to Verify Syllogisms 


119  (21) 


127  (2) 


129  (3) 

Of Further Interest: Fuzzy Logic 


132  (8) 

Graph Theory: The Mathematics of Relationships 


140  (54) 

Graphs, Puzzles, and Map Coloring 


141  (18) 

The Traveling Salesperson Problem 


159  (12) 


171  (23) 


180  (2) 


182  (2) 

Of Further Interest: Scheduling Projects Using PERT 


184  (10) 

Numeration Systems: Does It Matter How We Name Numbers? 


194  (50) 

The Evolution of Numeration Systems 


195  (11) 


206  (11) 

Calculating in Other Bases 


217  (27) 


230  (2) 


232  (1) 

Of Further Interest: Modular Systems 


233  (11) 

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


244  (75) 


245  (12) 


257  (9) 


266  (14) 


280  (12) 

Exponents and Scientific Notation 


292  (27) 


303  (3) 


306  (1) 

Of Further Interest: Sequences 


307  (12) 

Algebraic Models: How Do We Approximate Reality? 


319  (65) 


320  (13) 

Modeling with Linear Equations 


333  (9) 

Modeling with Quadratic Equations 


342  (9) 

Exponential Equations and Growth 


351  (12) 

Proportions and Variation 


363  (21) 


371  (3) 


374  (2) 

Of Further Interest: Dynamical Systems 


376  (8) 

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


384  (36) 

Systems of Linear Equations 


385  (14) 

Systems of Linear Inequalities 


399  (21) 


409  (1) 


410  (1) 

Of Further Interest: Linear Programming 


411  (9) 

Geometry: Ancient and Modern Mathematics Embrace 


420  (87) 

Lines, Angles, and Circles 


421  (10) 


431  (11) 


442  (13) 


455  (9) 

The Metric System and Dimensional Analysis 


464  (12) 

Geometric Symmetry and Tessellations 


476  (31) 


491  (4) 


495  (2) 

Of Further Interest: Fractals 


497  (10) 

Apportionment: How Do We Measure Fairness? 


507  (59) 

Understanding Apportionment 


508  (11) 

The HuntingtonHill Apportionment Principle 


519  (7) 

Applications of the Apportionment Principle 


526  (9) 

Other Paradoxes and Apportionment Methods 


535  (31) 


551  (3) 


554  (2) 

Of Further Interest: Fair Division 


556  (10) 

Voting: Using Mathematics to Make Choices 


566  (48) 


567  (12) 

Defects in Voting Methods 


579  (14) 


593  (21) 


602  (2) 


604  (2) 

Of Further Interest: The ShapleyShubik Index 


606  (8) 

Consumer Mathematics: The Mathematics of Everyday Life 


614  (63) 


615  (8) 


623  (14) 


637  (8) 


645  (9) 


654  (23) 


665  (3) 


668  (2) 

Of Further Interest: The Annual Percentage Rate 


670  (7) 

Counting: Just How Many Are There? 


677  (39) 

Introduction to Counting Methods 


678  (9) 

The Fundamental Counting Principle 


687  (8) 

Permutations and Combinations 


695  (21) 


709  (1) 


710  (1) 

Of Further Interest: Counting and Gambling 


711  (5) 

Probability: What Are the Chances? 


716  (59) 

The Basics of Probability Theory 


717  (18) 

Complements and Unions of Events 


735  (8) 

Conditional Probability and Intersections of Events 


743  (14) 


757  (18) 


765  (2) 


767  (1) 

Of Further Interest: Binomial Experiments 


768  (7) 

Descriptive Statistics: What a Data Set Tells Us 


775  (74) 

Organizing and Visualizing Data 


776  (15) 

Measures of Central Tendency 


791  (15) 


806  (13) 


819  (30) 


834  (2) 


836  (2) 

Of Further Interest: Linear Correlation 


838  (11) 
Answers to Quiz Yourself Problems 

849  (10) 
Answers to Exercises 

859  (46) 
Photo Credits 

905  
Index 

1  