Thinking Mathematically

<p>1. Problem Solving and Critical Thinking</p> <p>1.1 Inductive and Deductive Reasoning</p> <p>1.2 Estimation, Graphs, and Mathematical Models</p> <p>1.3 Problem Solving</p> <p>&nbsp;</p> <p>2. Set Theory</p> <p>2.1 Basic Set Concepts</p> <p>2.2 Subsets</p> <p>2.3 Venn Diagrams and Set Operations</p> <p>2.4 Set Operations and Venn Diagrams with Three Sets</p> <p>2.5 Survey Problems</p> <p>&nbsp;</p> <p>3. Logic</p> <p>3.1 Statements, Negations, and Quantified Statements</p> <p>3.2 Compound Statements and Connectives</p> <p>3.3 Truth Tables for Negations, Conjunction, and Disjunction</p> <p>3.4 Truth Tables for the Conditional and the Biconditional</p> <p>3.5 Equivalent Statements and Variations of Conditional Statements</p> <p>3.6 Negations of Conditional Statements and De Morgan's Laws</p> <p>3.7 Arguments and Truth Tables</p> <p>3.8 Arguments and Euler Diagrams</p> <p>&nbsp;</p> <p>4. Number Representation and Calculation</p> <p>4.1 Our Hindu-Arabic System and Early Positional Systems</p> <p>4.2 Number Bases in Positional Systems</p> <p>4.3 Computation in Positional Systems</p> <p>4.4 Looking Back at Early Numeration Systems</p> <p>&nbsp;</p> <p>5. Number Theory and the Real Number System</p> <p>5.1 Number Theory, Prime and Composite Numbers</p> <p>5.2 The Integers; Order of Operations</p> <p>5.3 The Rational Numbers</p> <p>5.4 The Irrational Numbers</p> <p>5.5 Real Numbers and Their Properties</p> <p>5.6 Exponents and Scientific Notation</p> <p>5.7 Arithmetic and Geometric Sequences</p> <p>&nbsp;</p> <p>6. Algebra: Equations and Inequalities</p> <p>6.1 Algebraic Expressions and Formulas</p> <p>6.2 Linear Equations in One Variable and Proportions</p> <p>6.3 Applications of Linear Equations</p> <p>6.4 Linear Inequalities in One Variable</p> <p>6.5 Quadratic Equations</p> <p>&nbsp;</p> <p>7. Algebra: Graphs, Functions, and Linear Systems</p> <p>7.1 Graphing and Functions</p> <p>7.2 Linear Functions and Their Graphs</p> <p>7.3 Systems of Linear Equations in Two Variables</p> <p>7.4 Linear Inequalities in Two Variables</p> <p>7.5 Linear Programming</p> <p>7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions</p> <p>&nbsp;</p> <p>8. Consumer Mathematics and Financial Management</p> <p>8.1 Percent, Sales Tax, and Income Tax</p> <p>8.2 Simple Interest</p> <p>8.3 Compound Interest</p> <p>8.4 Annuities, Stocks, and Bonds</p> <p>8.5 Installment Loans, Amortization, and Credit Cards</p> <p>&nbsp;</p> <p>9. Measurement</p> <p>9.1 Measuring Length; The Metric System</p> <p>9.2 Measuring Area and Volume</p> <p>9.3 Measuring Weight and Temperature</p> <p>&nbsp;</p> <p>10. Geometry</p> <p>10.1 Points, Lines, Planes, and Angles</p> <p>10.2 Triangles</p> <p>10.3 Polygons, Perimeter, and Tessellations</p> <p>10.4 Area and Circumference</p> <p>10.5 Volume</p> <p>10.6 Right Triangle Trigonometry</p> <p>10.7 Beyond Euclidean Geometry</p> <p>&nbsp;</p> <p>11. Counting Methods and Probability Theory</p> <p>11.1 The Fundamental Counting Principle</p> <p>11.2 Permutations</p> <p>11.3 Combinations</p> <p>11.4 Fundamentals of Probability</p> <p>11.5 Probability with the Fundamental Counting principle, Permutations, and Combinations</p> <p>11.6 Events Involving Not and Or; Odds</p> <p>11.7 Events Involving And; Conditional Probability</p> <p>11.8 Expected Value</p> <p>&nbsp;</p> <p>12. Statistics</p> <p>12.1 Sampling, Frequency Distributions, and Graphs</p> <p>12.2 Measures of Central Tendency</p> <p>12.3 Measures of Dispersion</p> <p>12.4 The Normal Distribution</p> <p>12.5 Problem Solving with the Normal Distribution</p> <p>12.6 Scatter Plots, Correlation, and Regression Lines</p> <p>&nbsp;</p> <p>13. Mathematical Systems</p> <p>13.1 Mathematical Systems</p> <p>13.2 Rotational Symmetry, Groups, and Clock Arithmetic</p> <p>&nbsp;</p> <p>14. Voting and Apportionment</p> <p>14.1 Voting Methods</p> <p>14.2 Flaws of Voting Methods</p> <p>14.3 Apportionment Methods</p> <p>14.4 Flaws of Apportionment Methods</p>