Math in Our World

Title 1 Contents 20 1 Problem Solving 30 1-1 The Nature of Mathematical Reasoning 32 1-2 Estimation and Interpreting Graphs 44 1-3 Problem Solving 54 Chapter 1 Summary 63 2 Sets 68 2-21 The Nature of Sets 70 22-2 Subsets and Set Operations 82 2-23 Using Venn Diagrams to Study Set Operations 93 2-24 Using Sets to Solve Problems 102 2 2-5 Infi nite Sets 110 Chapter 2 Summary 114 3 Logic 118 3-31 Statements and Quantifi ers 120 33-2 Truth Tables 128 33-3 Types of Statements 143 3-34 Logical Arguments 151 3-3 5 Euler Circles 162 Chapter 3 Summary 169 4 Numeration Systems 174 4-1 Early and Modern Numeration Systems 176 4-2 Tools and Algorithms in Arithmetic 191 4-3 Base Number Systems 198 4-4 Operations in Base Number Systems 211 Chapter 4 Summary 221 5 The Real Number System 224 5-1 The Natural Numbers 226 5-2 The Integers 238 5-3 The Rational Numbers 249 5-4 The Irrational Numbers 263 5-5 The Real Numbers 272 5-6 Exponents and Scientifi c Notation 279 5-7 Arithmetic and Geometric Sequences 289 Chapter 5 Summary 299 6 Topics in Algebra 304 6-1 The Fundamentals of Algebra 306 6-2 Solving Linear Equations 316 6-3 Applications of Linear Equations 329 6-4 Ratio, Proportion, and Variation 336 6-5 Solving Linear Inequalities 347 6-6 Solving Quadratic Equations 356 Chapter 6 Summary 369 7 Additional Topics in Algebra 374 7-1 The Rectangular Coordinate System and Linear Equations in Two Variables 376 7-2 Systems of Linear Equations 387 7-3 Solving Systems of Linear Equations Using Matrices 402 7- 4 Linear Inequalities 410 7-5 Linear Programming 417 7-6 Functions 422 7-7 Linear, Quadratic, and Exponential Functions 429 Chapter 7 Summary 441 Available Online at www.mhhe.com/sobecki: Chapter 7 Supplement: An Application of Functions—Sound CHAPTER 36 8 Consumer Mathematics 446 8-1 Percents 448 8-2 Simple Interest 457 8-3 Compound Interest 465 8-4 Installment Buying 474 8-5 Home Ownership 485 8-6 Stocks and Bonds 493 Chapter 8 Summary 502 9 Measurement 508 9-1 Measures of Length: Converting Units and the Metric System 510 9-2 Measures of Area, Volume, and Capacity 518 9-3 Measures of Weight and Temperature 527 Chapter 9 Summary 534 10 Geometry 538 10-1 Points, Lines, Planes, and Angles 540 10-2 Triangles 549 10-3 Polygons and Perimeter 559 10-4 Areas of Polygons and Circles 564 10-5 Volume and Surface Area 572 10-6 Right Triangle Trigonometry 580 10-7 A Brief Survey of Non-Euclidean and Transformational Geometries 587 Chapter 10 Summary 592 11 Probability and Counting Techniques 600 11-1 The Fundamental Counting Principle and Permutations 602 11-2 Combinations 610 11-3 Basic Concepts of Probability 615 11-4 Tree Diagrams, Tables, and Sample Spaces 625 11-5 Probability Using Permutations and Combinations 632 11-6 Odds and Expectation 637 11-7 The Addition Rules for Probability 644 11-8 The Multiplication Rules and Conditional Probability 651 11-9 The Binomial Distribution 660 Chapter 11 Summary 667 12 Statistics 674 12-1 Gathering and Organizing Data 676 12-2 Picturing Data 685 12-3 Measures of Average 693 12-4 Measures of Variation 703 12-5 Measures of Position 709 12-6 The Normal Distribution 713 12-7 Applications of the Normal Distribution 721 12-8 Correlation and Regression Analysis 727 Chapter 12 Summary 738 Available Online at www.mhhe.com/sobecki: Chapter 12 Supplement: Misuses of Statistics CHAPTER 41 13 Other Mathematical Systems 744 13-1 Mathematical Systems and Groups 746 13-2 Clock Arithmetic 753 13-3 Modular Systems 760 Chapter 13 Summary 766 14 Voting Methods 770 14-1 Preference Tables and the Plurality Method 772 14-2 The Borda Count Method and the Plurality-with-Elimination Method 779 14-3 The Pairwise Comparison Method and Approval Voting 787 14-4 Apportionment 795 14-5 Apportionment Flaws 806 Chapter 14 Summary 812 15 Graph Theory 818 15-1 Basic Concepts of Graph Theory 820 15-2 Euler’s Theorem 828 15-3 Hamilton Paths and Circuits 834 15-4 Trees 842 Chapter 15 Summary 850 Appendix A Area Under the Standard Normal Distribution 856 Photo Credits 882 Index 885 'Mathematics in Our World' conveys the basic concepts which are fundamental to a liberal arts math curriculum for even the most hesitant student