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Copyright, IV
To the Student, XI
Math We Use It Every Day!, XII
Supplements for Students, XVI
Supplements for Instructors, XVII
Acknowledgments, XVIII
Chapter 1. Critical Thinking Skills, 1
1.1. Inductive Reasoning, 2
1.2. Estimation, 9
1.3. Problem Solving, 20
Chapter 2. Sets, 44
2.1. Set Concepts, 45
2.2. Subsets, 54
2.3. Venn Diagrams and Set Operations, 60
2.4. Venn Diagrams with Three Sets and Verification of Equality of Sets, 72
2.5. Applications of Sets, 82
2.6. Infinite Sets, 89
Chapter 3. Logic, 100
3.1. Statements and Logical Connectives, 101
3.2. Truth Tables for Negation, Conjunction, and Disjunction, 113
3.3. Truth Tables for the Conditional and Biconditional, 126
3.4. Equivalent Statements, 136
3.5. Symbolic Arguments, 151
3.6. Euler Diagrams and Syllogistic Arguments, 162
3.7. Switching Circuits, 169
Chapter 4. Systems of Numeration, 181
4.1. Additive, Multiplicative, and Ciphered Systems of Numeration, 182
4.2. Place-Value or Positional-Value Numeration Systems, 190
4.3. Other Bases, 197
4.4. Computation in Other Bases, 204
4.5. Early Computational Methods, 214
Chapter 5. Number Theory and the Real Number System, 223
5.1. Number Theory, 224
5.2. The Integers, 235
5.3. The Rational Numbers, 245
5.4. The Irrational Numbers and the Real Number System, 261
5.5. Real Numbers and their Properties, 269
5.6. Rules of Exponents and Scientific Notation, 276
5.7. Arithmetic and Geometric Sequences, 289
5.8. Fibonacci Sequence, 298
Chapter 6. Algebra, Graphs, and Functions, 311
6.1. Order of Operations, 312
6.2. Linear Equations in One Variable, 317
6.3. Formulas, 330
6.4. Applications of Linear Equations in One Variable, 339
6.5. Variation, 346
6.6. Linear Inequalities, 355
6.7. Graphing Linear Equations, 362
6.8. Linear Inequalities in Two Variables, 376
6.9. Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula, 379
6.10. Functions and their Graphs, 390
Chapter 7. Systems of Linear Equations and Inequalities, 413
7.1. Systems of Linear Equations, 414
7.2. Solving Systems of Linear Equations by the Substitution and Addition Methods, 423
7.3. Matrices, 434
7.4. Solving Systems of Linear Equations by Using Matrices, 446
7.5. Systems of Linear Inequalities, 453
7.6. Linear Programming, 457
Chapter 8. The Metric System, 468
8.1. Basic Terms and Conversions within the Metric System, 469
8.2. Length, Area, and Volume, 478
8.3. Mass and Temperature, 490
8.4. Dimensional Analysis and Conversions to and From the Metric System, 498
Chapter 9. Geometry, 514
9.1. Points, Lines, Planes, and Angles, 515
9.2. Polygons, 527
9.3. Perimeter and Area, 538
9.4. Volume and Surface Area, 550
9.5. Transformational Geometry, Symmetry, and Tessellations, 566
9.6. Topology, 585
9.7. Non-Euclidean Geometry and Fractal Geometry, 594
Chapter 10. Mathematical Systems, 610
10.1. Groups, 611
10.2. Finite Mathematical Systems, 618
10.3. Modular Arithmetic, 631
Chapter 11. Consumer Mathematics, 645
11.1. Percent, 646
11.2. Personal Loans and Simple Interest, 657
11.3. Compound Interest, 668
11.4. Installment Buying, 678
11.5. Buying a House with a Mortgage, 693
11.6. Ordinary Annuities, Sinking Funds, and Retirement Investments, 706
Chapter 12. Probability, 723
12.1. The Nature of Probability, 724
12.2. Theoretical Probability, 733
12.3. Odds, 741
12.4. Expected Value (Expectation), 749
12.5. Tree Diagrams, 761
12.6. Or and And Problems, 771
12.7. Conditional Probability, 784
12.8. The Counting Principle and Permutations, 791
12.9. Combinations, 803
12.10. Solving Probability Problems by Using Combinations, 809
12.11. Binomial Probability Formula, 816
Chapter 13. Statistics, 832
13.1. Sampling Techniques, 833
13.2. The Misuses of Statistics, 839
13.3. Frequency Distributions, 843
13.4. Statistical Graphs, 849
13.5. Measures of Central Tendency, 860
13.6. Measures of Dispersion, 872
13.7. The Normal Curve, 881
13.8. Linear Correlation and Regression, 898
Appendix A. Using Microsoft Excel, AA-1
Appendix B. Graph Theory, AB-1
Answers, A-1
Credits, C-1
Index of Applications, I-1
Index, I-9

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