Thinking Mathematically

For a one- or two-term course in Liberal Arts Mathematics, Survey of Mathematics, Finite Mathematics, and Mathematics for education majors. This general survey of mathematical topics helps diverse students, with different backgrounds and career plans, to succeed in mathematics. Blitzer provides the applications and technology students need to gain an appreciation of mathematics through their college careers and beyond. His goal is to demonstrate how mathematics can be applied to students' lives in interesting, enjoyable, and meaningful ways.

Chapter 1. Problem Solving and Critical Thinking 1.1 Inductive and Deductive Reasoning 1.2 Estimation, Graphs, and Mathematical Models 1.3 Problem Solving Chapter 2. Set Theory 2.1 Basic Set Concepts 2.2 Subsets 2.3 Venn Diagrams and Set Operations 2.4 Set Operations and Venn Diagrams with Three Sets 2.5 Survey Problems Chapter 3. Logic 3.1 Statements, Negations, and Quantified Statements 3.2 Compound Statements and Connectives 3.3 Truth Tables for Negation, Conjunction, and Disjunction 3.4 Truth Tables for the Conditional and the Biconditional 3.5 Equivalent Statements, Variations of Conditional Statements, and DeMorgan's Laws 3.6 Arguments and Truth Tables 3.7 Arguments and Euler Diagrams Chapter 4. Number Representation and Calculation 4.1 Our Hindu-Arabic System and Early Positional Systems 4.2 Number Bases in Positional Systems 4.3 Computation in Positional Systems 4.4 Looking Back at Early Numeration Systems Chapter 5. Number Theory and the Real Number System 5.1 Number Theory: Prime and Composite Numbers 5.2 The Integers; Order of Operations 5.3 The Rational Numbers 5.4 The Irrational Numbers 5.5 Real Numbers and Their Properties 5.6 Exponents and Scientific Notation 5.7 Arithmetic and Geometric Sequences Chapter 6. Algebra: Equations and Inequalities 6.1 Algebraic Expressions and Formulas 6.2 Linear Equations in One Variable 6.3 Applications of Linear Equations 6.4 Ratio, Proportion, and Variation 6.5 Linear Inequalities in One Variable 6.6 Quadratic Equations Chapter 7. Algebra: Graphs, Functions, and Linear Systems 7.1 Graphing and Functions 7.2 Linear Functions and Their Graphs 7.3 Systems of Linear Equations in Two Variables 7.4 Linear Inequalities in Two Variables 7.5 Linear Programming 7.6 Approximating Reality with Nonlinear Models Chapter 8. Consumer Mathematics and Financial Management 8.1 Percent, Sales Tax, and Income Tax 8.2 Simple Interest 8.3 Compound Interest 8.4 Annuities, Stocks, and Bonds 8.5 Installment Buying 8.6 Amortization and the Cost of Home Ownership Chapter 9. Measurement 9.1 Measuring Length; The Metric System 9.2 Measuring Area and Volume 9.3 Measuring Weight and Temperature Chapter 10. Geometry 10.1 Points, Lines, Planes, and Angles 10.2 Triangles 10.3 Polygons, Perimeter, and Tessellations 10.4 Area and Circumstances 10.5 Volume 10.6 Right Triangle Trigonometry 10.7 Beyond Euclidean Geometry Chapter 11. Counting Methods and Probability Theory 11.1 The Fundamental Counting Principle 11.2 Permutations 11.3 Combinations 11.4 Fundamentals of Probability 11.5 Probability with the Fundamental Counting Principle, Permutations, and Combinations 11.6 Events Involving Not and Or; Odds 11.7 Events Involving And; Conditional Probability 11.8 Expected Value Chapter 12. Statistics 12.1 Sampling, Frequency Distributions, and Graphs 12.2 Measures of Central Tendency 12.3 Measure of Dispersion 12.4 The Normal Distribution 12.5 Scatter Plots, Correlation, and Regression Lines Chapter 13. Mathematical Systems 13.1 Mathematical Systems 13.2 Rotational Symmetry, Groups, and Clock Arithmetic Chapter 14. Voting and Apportionment 14.1 Voting Methods 14.2 Flaws of Voting Methods 14.3 Apportionment Methods 14.4 Flaws of Apportionment Methods Chapter 15. Graph Theory 15.1 Graphs, Paths, and Circuits 15.2 Euler Paths and Euler Circuits 15.3 Hamilton Paths and Hamilton Circuits 15.4 Trees

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