PrologueWhy Math? A Historical Overview 

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1 THE NATURE OF PROBLEM SOLVING 

1  (52) 


2  (14) 

1.2 Inductive and Deductive Reasoning 


16  (8) 

1.3 Scientific Notation and Estimation 


24  (15) 


39  (8) 


47  (6) 
2 THE NATURE OF LOGIC 

53  (48) 


54  (7) 

2.2 Truth Tables and the Conditional 


61  (8) 

2.3 Operators and Laws of Logic 


69  (6) 


75  (9) 

2.5 Problem Solving Using Logic 


84  (6) 


90  (4) 


94  (7) 
3 THE NATURE OF NUMERATION SYSTEMS 

101  (40) 

3.1 Early Numeration Systems 


102  (8) 

3.2 HinduArabic Numeration System 


110  (4) 

3.3 Different Numeration Systems 


114  (5) 

3.4 Binary Numeration System 


119  (5) 

3.5 History of Calculating Devices 


124  (12) 


136  (5) 
4 THE NATURE OF NUMBERS 

141  (74) 


142  (7) 


149  (11) 


160  (8) 


168  (7) 


175  (9) 

4.6 Groups, Fields, and Real Numbers 


184  (10) 


194  (9) 


203  (5) 


208  (7) 
5 THE NATURE OF ALGEBRA 

215  (80) 


216  (7) 


223  (5) 

5.3 Evaluation, Applications, and Spreadsheets 


228  (11) 


239  (8) 


247  (4) 

5.6 Algebra in Problem Solving 


251  (11) 

5.7 Ratios, Proportions, and Problem Solving 


262  (10) 


272  (9) 

5.9 Modeling Uncategorized Problems 


281  (9) 


290  (5) 
6 THE NATURE OF GEOMETRY 

295  (56) 


296  (9) 


305  (8) 


313  (6) 


319  (7) 

6.5 RightTriangle Trigonometry 


326  (8) 


334  (6) 

6.7 Projective and NonEuclidean Geometries 


340  (6) 


346  (5) 
7 THE NATURE OF MAEASUREMENT 

351  (46) 


352  (8) 


360  (10) 

7.3 Surface Area, Volume, and Capacity 


370  (11) 

7.4 Miscellaneous Measurements 


381  (11) 


392  (5) 
8 THE NATURE OF GROWTH 

397  (30) 

8.1 Exponential Equations 


398  (8) 

8.2 Logarithmic Equations 


406  (7) 

8.3 Applications of Growth and Decay 


413  (10) 


423  (4) 
9 THE NAUTRE OF FINANCIAL MANAGEMENT 

427  (70) 


428  (13) 


441  (9) 


450  (10) 


460  (10) 


470  (7) 


477  (8) 

9.7 Summary of Financial Formulas 


485  (4) 


489  (8) 
10 THE NATURE OF SET THEORY AND COUNTING 

497  (54) 

10.1 Sets, Subsets, and Venn Diagrams 


498  (7) 

10.2 Combined Operations with Sets 


505  (8) 


513  (8) 


521  (5) 

10.5 Counting without Counting 


526  (10) 


536  (5) 

10.7 Rubik's Cube and Instant Insanity 


541  (3) 


544  (7) 
11 THE NATURE OF PROBABILITY 

551  (56) 

11.1 Introduction to Probability 


552  (11) 

11.2 Mathematical Expectation 


563  (9) 


572  (11) 

11.4 Calculated Probabilities 


583  (11) 

GUEST ESSAY: "Extrasensory Perception" 


591  (3) 

11.5 The Binomial Distribution 


594  (7) 


601  (6) 
12 THE NATURE OF STATISTICS 

607  (58) 

12.1 Frequency Distributions and Graphs 


608  (14) 

12.2 Descriptive Statistics 


622  (11) 


633  (10) 

12.4 Correlation and Regression 


643  (8) 


651  (7) 


658  (7) 
13 THE NATURE OF GRAPHS AND FUNCTIONS 

665  (44) 

13.1 Cartesian Coordinates and Graphing Lines 


666  (9) 

13.2 Graphing HalfPlanes 


675  (2) 


677  (5) 


682  (13) 


695  (8) 


703  (6) 
14 THE NATURE OF MATHEMATICAL SYSTEMS 

709  (52) 

14.1 Systems of Linear Equations 


710  (4) 

14.2 Problem Solving with Systems 


714  (10) 

14.3 Matrix Solution of a System of Equations 


724  (10) 


734  (14) 

14.5 Systems of Inequalities 


748  (1) 

14.6 Modeling with Linear Programming 


749  (8) 


757  (4) 
15 THE NATURE OF NETWORKS AND GRAPH THEORY 

761  (40) 

15.1 Euler Circuit and Hamiltonian Cycles 


762  (12) 

15.2 Trees and Minimum Spanning Trees 


774  (11) 

15.3 Topology and Fractals 


785  (11) 

GUEST ESSAY: "What Good Are Fractals?" 


790  (5) 


795  (1) 


796  (5) 
16 THE NATURE OF VOTING AND APPORTIONMENT 

801  (60) 


802  (11) 


813  (18) 


831  (18) 

16.4 Apportionment Paradoxes 


849  (8) 


857  (4) 
17 THE NATURE OF CALCULUS 

861  


862  (10) 


872  (5) 


877  (11) 


888  (8) 


896  
EpilogueWhy Not Math? Mathematics in the Natural Sciences Social Sciences, and Humanities 

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A Glossary 

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B Selected Answer 

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C Credit 

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D Index 

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