A Survey of Mathematics

Description

1. Critical Thinking Skills 1.1 Inductive and Deductive 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 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 and Solving Equations 6.2 Formulas 6.3 Applications of Algebra 6.4 Variation 6.5 Linear Inequalities 6.6 Graphing Linear Equations 6.7 Solving Systems of Linear Equations 6.8 Linear Inequalities and Systems of Linear Inequalities 6.9 Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula 6.10 Functions and Their Graphs 7. The Metric System 7.1 Basic Terms and Conversions Within the Metric System 7.2 Length, Area, and Volume 7.3 Mass and Temperature 7.4 Dimensional Analysis and Conversions to and from the Metric System 8. Geometry 8.1 Points, Lines, Planes, and Angles 8.2 Polygons 8.3 Perimeter and Area 8.4 Volume and Surface Area 8.5 Transformational Geometry, Symmetry, and Tessellations 8.6 Topology 8.7 Non-Euclidean Geometry and Fractal Geometry 9. Mathematical Systems 9.1 Groups 9.2 Finite Mathematical Systems 9.3 Modular Arithmetic 9.4 Matrices 10. Consumer Mathematics 10.1 Percent 10.2 Personal Loans and Simple Interest 10.3 Compound Interest 10.4 Installment Buying 10.5 Buying a House with a Mortgage 10.6 Ordinary Annuities, Sinking Funds, and Retirement Investments 11. Probability 11.1 Empirical and Theoretical Probabilities 11.2 Odds 11.3 Expected Value (Expectation) 11.4 Tree Diagrams 11.5 OR and AND Problems 11.6 Conditional Probability 11.7 The Counting Principle and Permutations 11.8 Combinations 11.9 Solving Probability Problems by Using Combinations 11.10 Binomial Probability Formula 12. Statistics 12.1 Sampling Techniques and Misuses of Statistics 12.2 Frequency Distributions and Statistical Graphs 12.3 Measures of Central Tendency 12.4 Measures of Dispersion 12.5 The Normal Curve 12.6 Linear Correlation and Regression 13. Graph Theory 13.1 Graphs, Paths, and Circuits 13.2 Euler Paths and Euler Circuits 13.3 Hamilton Paths and Hamilton Circuits 13.4 Trees 14. Voting and Apportionment 14.1 Voting Methods 14.2 Flaws of the Voting Methods 14.3 Apportionment Methods 14.4 Flaws of the Apportionment Methods ANSWERS Credits Index of Applications Index