Thinking Mathematically

<ul> <li>(NOTE: Each chapter concludes with a Chapter Summary, Review, and Test, and a comprehensive Chapter Test.) </li> </ul> <ol> <li>Problem Solving and Critical Thinking <ul> <li>1.1 Inductive and Deductive Reasoning</li> <li>1.2 Estimation, Graphs, and Mathematical Models</li> <li>1.3 Problem Solving</li> </ul></li> <li>Set Theory <ul> <li>2.1 Basic Set Concepts</li> <li>2.2 Subsets</li> <li>2.3 Venn Diagrams and Set Operations</li> <li>2.4 Set Operations and Venn Diagrams with Three Sets</li> <li>2.5 Survey Problems</li> </ul></li> <li>Logic <ul> <li>3.1 Statements, Negations, and Quantified Statements</li> <li>3.2 Compound Statements and Connectives</li> <li>3.3 Truth Tables for Negation, Conjunction, and Disjunction</li> <li>3.4 Truth Tables for the Conditional and the Biconditional</li> <li>3.5 Equivalent Statements and Variations of Conditional Statements</li> <li>3.6 Negations of Conditional Statements and De Morgan’s Laws</li> <li>3.7 Arguments and Truth Tables</li> <li>3.8 Arguments and Euler Diagrams</li> </ul></li> <li>Number Representation and Calculation <ul> <li>4.1 Our Hindu-Arabic System and Early Positional Systems</li> <li>4.2 Number Bases in Positional Systems</li> <li>4.3 Computation in Positional Systems</li> <li>4.4 Looking Back at Early Numeration Systems</li> </ul></li> <li>Number Theory and the Real Number System <ul> <li>5.1 Number Theory: Prime and Composite Numbers</li> <li>5.2 The Integers; Order of Operations</li> <li>5.3 The Rational Numbers</li> <li>5.4 The Irrational Numbers</li> <li>5.5 Real Numbers and Their Properties; Clock Addition</li> <li>5.6 Exponents and Scientific Notation</li> <li>5.7 Arithmetic and Geometric Sequences</li> </ul></li> <li>Algebra: Equations and Inequalities <ul> <li>6.1 Algebraic Expressions and Formulas</li> <li>6.2 Linear Equations in One Variable and Proportions</li> <li>6.3 Applications of Linear Equations</li> <li>6.4 Linear Inequalities in One Variable</li> <li>6.5 Quadratic Equations</li> </ul></li> <li>Algebra: Graphs, Functions, and Linear Systems <ul> <li>7.1 Graphing and Functions</li> <li>7.2 Linear Functions and Their Graphs</li> <li>7.3 Systems of Linear Equations in Two Variables</li> <li>7.4 Linear Inequalities in Two Variables</li> <li>7.5 Linear Programming</li> <li>7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions</li> </ul></li> <li>Personal Finance <ul> <li>8.1 Percent, Sales Tax, and Discounts</li> <li>8.2 Income Tax</li> <li>8.3 Simple Interest</li> <li>8.4 Compound Interest</li> <li>8.5 Annuities, Methods of Saving, and Investments</li> <li>8.6 Cars</li> <li>8.7 The Cost of Home Ownership</li> <li>8.8 Credit Cards</li> </ul></li> <li>Measurement <ul> <li>9.1 Measuring Length; The Metric System</li> <li>9.2 Measuring Area and Volume</li> <li>9.3 Measuring Weight and Temperature</li> </ul></li> <li>Geometry <ul> <li>10.1 Points, Lines, Planes, and Angles</li> <li>10.2 Triangles</li> <li>10.3 Polygons, Perimeter, and Tessellations</li> <li>10.4 Area and Circumference</li> <li>10.5 Volume and Surface Area</li> <li>10.6 Right Triangle Trigonometry</li> <li>10.7 Beyond Euclidean Geometry</li> </ul></li> <li>Counting Methods and Probability Theory <ul> <li>11.1 The Fundamental Counting Principle</li> <li>11.2 Permutations</li> <li>11.3 Combinations</li> <li>11.4 Fundamentals of Probability</li> <li>11.5 Probability with the Fundamental Counting Principle, Permutations, and Combinations</li> <li>11.6 Events Involving Not and Or; Odds</li> <li>11.7 Events Involving And; Conditional Probability</li> <li>11.8 Expected Value</li> </ul></li> <li>Statistics <ul> <li>12.1 Sampling, Frequency Distributions, and Graphs</li> <li>12.2 Measures of Central Tendency</li> <li>12.3 Measures of Dispersion</li> <li>12.4 The Normal Distribution</li> <li>12.5 Problem Solving with the Normal Distribution</li> <li>12.6 Scatter Plots, Correlation, and Regression Lines</li> </ul></li> <li>Voting and Apportionment <ul> <li>13.1 Voting Methods</li> <li>13.2 Flaws of Voting Methods</li> <li>13.3 Apportionment Methods</li> <li>13.4 Flaws of Apportionment Methods</li> </ul></li> <li>Graph Theory <ul> <li>14.1 Graphs, Paths, and Circuits</li> <li>14.2 Euler Paths and Euler Circuits</li> <li>14.3 Hamilton Paths and Hamilton Circuits</li> <li>14.4 Trees</li> </ul></li> </ol> <ul> <li>Answers to Selected Exercises</li> <li>Credits</li> <li>Subject Index</li> </ul>