A Survey of Mathematics with Applications

In a Liberal Arts Math course, a common question students ask is, "Why do I have to know this?" A Survey of Mathematics with Applications continues to be a best-seller because it shows students how we use mathematics in our daily lives and why this is important. The Ninth Edition further emphasizes this with the addition of new "Why This Is Important" sections throughout the text. Real-life and up-to-date examples motivate the topics throughout, and a wide range of exercises help students to develop their problem-solving and critical thinking skills. Angel, Abbott, and Runde present the material in a way that is clear and accessible to non-math majors. The text includes a wide variety of math topics, with contents that are flexible for use in any one- or two-semester Liberal Arts Math course.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 15. Voting and Apportionment 15.1 Voting Methods 15.2 Flaws of Voting 15.3 Apportionment Methods 15.4 Flaws of the Apportionment Methods Answers Credits Index of Applications Index