
Set Theory: Using Mathematics to Classify Objects 


1  (61) 


2  (14) 


16  (7) 


23  (7) 


30  (12) 


42  (20) 


51  (2) 


53  (2) 

Of Further Interest: Fuzzy Sets 


55  (7) 

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


62  (68) 

Statements, Connectives, and Quantifiers 


63  (12) 


75  (13) 

The Conditional and Biconditional 


88  (9) 


97  (11) 

Using Euler Diagrams to Verify Syllogisms 


108  (22) 


116  (3) 


119  (2) 

Of Further Interest: Fuzzy Logic 


121  (9) 

Graph Theory: The Mathematics of Relationships 


130  (72) 

Graphs, Puzzles, and Map Coloring 


131  (21) 

The Traveling Salesperson Problem 


152  (14) 


166  (11) 

Scheduling Projects Using PERT 


177  (25) 


189  (3) 


192  (4) 

Of Further Interest: Finite State Machines 


196  (6) 

Legislative Apportionment: How Do We Measure Fairness? 


202  (51) 

Understanding Apportionment 


203  (9) 


212  (4) 

The HuntingtonHill Apportionment Principle 


216  (8) 

Apportioning a Representative Board 


224  (8) 

Other Applications of Apportionment 


232  (21) 


239  (1) 


240  (2) 

Of Further Interest: Fair Division 


242  (11) 

Voting: Using Mathematics to Make Choices 


253  (53) 


254  (13) 

Defects in Voting Methods 


267  (16) 


283  (23) 


293  (2) 


295  (3) 

Of Further Interest: The ShapleyShubik Index 


298  (8) 

Consumer Mathematics: The Mathematics of Everyday Life 


306  (56) 


307  (14) 


321  (10) 


331  (9) 


340  (22) 


351  (2) 


353  (2) 

Of Further Interest: The Annual Percentage Rate 


355  (7) 

Data: How Do We Know What Is True? 


362  (407) 

Surveys and Survey Biases 


363  (10) 

Determining the Accuracy of Surveys 


373  (26) 


388  (1) 


389  (2) 

Of Further Interest: Experiments 


391  (8) 

Descriptive Statistics: What a Data Set Tells Us 



Organizing and Visualizing Data 


399  (13) 

Measures of Central Tendency 


412  (15) 


427  (14) 


441  (27) 


455  (2) 


457  (2) 

Of Further Interest: Linear Correlation 


459  (9) 

Counting: Just How Many Are There? 



Introduction to Counting Methods 


468  (9) 

The Fundamental Counting Principle 


477  (8) 

Permutations and Combinations 


485  (10) 


495  (15) 


502  (1) 


503  (1) 

Of Further Interest: Counting and Gambling 


504  (6) 

Probability: What Are the Chances? 



The Basics of Probability Theory 


510  (17) 

Complements and Unions of Events 


527  (8) 

Conditional Probability and Intersections of Events 


535  (12) 


547  (19) 


555  (1) 


556  (2) 

Of Further Interest: Binomial Experiments 


558  (8) 

Algebraic Models: How Do We Approximate Reality? 




566  (13) 

Modeling with Linear Equations 


579  (11) 

Modeling with Quadratic Equations 


590  (9) 

Exponential Equations and Growth 


599  (26) 


613  (1) 


614  (2) 

Of Further Interest: Dynamical Systems 


616  (9) 

Geometry: Ancient and Modern Mathematics Embrace 



Lines, Angles, and Circles 


625  (11) 


636  (12) 


648  (16) 


664  (11) 

Geometric Symmetry and Tessellations 


675  (37) 


694  (3) 


697  (4) 

Of Further Interest: Fractals 


701  (11) 

Matrices: Calculating with Tables of Numerical Information 



Matrix Terminology and Operations 


712  (10) 


722  (10) 

Transformational Geometry 


732  (12) 

More Transformations and Homogeneous Coordinates 


744  (25) 


755  (2) 


757  (2) 

Of Further Interest: Matrices and Directed Graphs 


759  (10) 
Answers to Quiz Yourself 

769  (10) 
Answers to Exercises 

779  
Index 

I1  