A survey of mathematics with applications

 Content: 1. Critical Thinking Skills  1.1 Inductive Reasoning  1.2 Estimation  1.3 Problem Solving  2. Sets  2.1 Set Concepts  2.2 Subsets  2.3 Venn Diagrams and Set Operations  2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets  2.5 Applications of Sets  2.6 Infinite Sets  3. Logic  3.1 Statements and Logical Connectives  3.2 Truth Tables for Negation, Conjunction, and Disjunction  3.3 Truth Tables for the Conditional and Biconditional  3.4 Equivalent Statements  3.5 Symbolic Arguments  3.6 Euler Diagrams and Syllogistic Arguments  3.7 Switching Circuits  4. Systems of Numeration  4.1 Additive, Multiplicative, and Ciphered Systems of Numeration  4.2 Place-Value or Positional-Value Numeration Systems  4.3 Other Bases  4.4 Computation In Other Bases  4.5 Early Computational Methods  5. Number Theory and the Real Number System  5.1 Number Theory  5.2 The Integers  5.3 The Rational Numbers  5.4 The Irrational Numbers and the Real Number System  5.5 Real Numbers and Their Properties  5.6 Rules of Exponents and Scientific Notation  5.7 Arithmetic and Geometric Sequences  5.8 Fibonacci Sequence  6. Algebra, Graphs, and Functions  6.1 Order of Operations  6.2 Linear Equations in One Variable  6.3 Formulas  6.4 Applications of Linear Equations In One Variable  6.5 Variation  6.6 Linear Inequalities  6.7 Graphing Linear Equations  6.8 Linear Inequalities In Two Variables  6.9 Solving Quadratic Equations By Using Factoring and By Using the Quadratic Formula  6.10 Functions and Their Graphs  7. Systems of Linear Equations and Inequalities  7.1 Systems of Linear Equations  7.2 Solving Systems of Linear Equations by the Substitution and Addition Methods  7.3 Matrices  7.4 Solving Systems of Linear Equations by Using Matrices  7.5 Systems of Linear Inequalities  7.6 Linear Programming  8. The Metric System  8.1 Basic Terms and Conversions Within the Metric System  8.2 Length, Area, and Volume  8.3 Mass and Temperature  8.4 Dimensional Analysis and Conversions To and From the Metric System  9. Geometry  9.1 Points, Lines, Planes, and Angles  9.2 Polygons  9.3 Perimeter and Area  9.4 Volume and Surface Area  9.5 Transformational Geometry, Symmetry, and Tessellations  9.6 Topology  9.7 Non-Euclidean Geometry and Fractal Geometry  10. Mathematical Systems  10.1 Groups  10.2 Finite Mathematical Systems  10.3 Modular Arithmetic  11. Consumer Mathematics  11.1 Percent  11.2 Personal Loans and Simple Interest  11.3 Compound Interest  11.4 Installment Buying  11.5 Buying A House With A Mortgage  11.6 Ordinary Annuities, Sinking Funds, and Retirement Investments  12. Probability  12.1 The Nature of Probability  12.2 Theoretical Probability  12.3 Odds  12.4 Expected Value (Expectation)  12.5 Tree Diagrams  12.6 OR and AND Problems  12.7 Conditional Probability  12.8 The Counting Principle and Permutations  12.9 Combinations  12.10 Solving Probability Problems By Using Combinations  12.11 Binomial Probability Formula  13. Statistics  13.1 Sampling Techniques  13.2 The Misuses of Statistics  13.3 Frequency Distributions and Statistical Graphs  13.4 Measures of Central Tendency  13.5 Measures of Dispersion  13.6 The Normal Curve  13.7 Linear Correlation and Regression  14. Graph Theory  14.1 Graphs, Paths, and Circuits  14.2 Euler Paths and Euler Circuits  14.3 Hamilton Paths and Hamilton Circuits  14.4 Trees  Answers  Credits  Index of Applications  Index