Math in Our World ISE

Chapter 1: Problem Solving 

1-1 The Nature of Mathematical Reasoning 

1-2 Estimation and Interpreting Graphs 

1-3 Problem Solving Strategies 

Chapter 1 Summary 

Chapter 2: Sets 

2-1 Introduction to Set Theory

2-2 Subsets and Set Operations 

2-3 Using Venn Diagrams to Study Set Operations 

2-4 Using Sets to Solve Problems

2-5 Infinite Sets

Chapter 2 Summary 

Chapter 3: Logic 

3-1 Statements and Quantifiers 

3-2 Truth Tables 

3-3 Types of Statements

3-4 Logical Arguments 

3-5 Euler Circles 

Chapter 3 Summary 

Chapter 4: Numeration Systems 

4-1 Early and Modern Numeration Systems 

4-2 Tools and Algorithms in Arithmetic 

4-3 Base Number Systems 

4-4 Operations in Base Number Systems 

Chapter 4 Summary 

Chapter 5: The Real Number System 

5-1 The Natural Numbers 

5-2 The Integers 

5-3 The Rational Numbers 

5-4 The Irrational Numbers 

5-5 The Real Numbers 

5-6 Exponents and Scientific Notation 

5-7 Arithmetic and Geometric Sequences 

Chapter 5 Summary 

Chapter 6: Topics in Algebra 

6-1 Applications of Linear Equations 

6-2 Ratio, Proportion, and Variation 

6-3 The Rectangular Coordinate System and Linear Equations in Two Variables

6-4 Functions

6-5 Quadratic, Exponential, and Logarithmic Functions 

Chapter 6 Summary 

Chapter 7: Consumer Mathematics 

7-1 Percents 

7-2 Personal Budgeting

7-3 Simple Interest

7-4 Compound Interest 

7-5 Installment Buying 

7-6 Student Loans and Home Buying

7-7 Investing in Stocks and Bonds 

Chapter 7 Summary 

Chapter 8: Measurement 

8-1 Measures of Length: Converting Units and the Metric System 

8-2 Measures of Area, Volume, and Capacity 

8-3 Measures of Weight and Temperature 

Chapter 8 Summary 

Chapter 9: Geometry 

9-1 Points, Lines, Planes and Angles 

9-2 Triangles 

9-3 Polygons and Perimeter 

9-4 Areas of Polygons and Circles

9-5 Volume and Surface Area 

9-6 Right Triangle Trigonometry 

9-7 A Brief Survey of Non-Euclidean and Other Geometries

Chapter 9 Summary 

Chapter 10: Probability and Counting Techniques 

10-1 The Fundamental Counting Principle and Permutations 

10-2 Combinations 

10-3 Basic Concepts of Probability 

10-4 Tree Diagrams, Tables, and Sample Spaces 

10-5 Probability Using Permutations and Combinations 

10-6 Odds and Expectation 

10-7 The Addition Rules for Probability 

10-8 The Multiplication Rules and Conditional Probability 

10-9 The Binomial Distribution 

Chapter 10 Summary 

Chapter 11: Statistics 

11-1 Gathering and Organizing Data

11-2 Picturing Data 

11-3 Measures of Average 

11-4 Measures of Variation 

11-5 Measures of Position 

11-6 The Normal Distribution 

11-7 Applications of the Normal Distribution 

11-8 Correlation and Regression Analysis 

Supplement: Misuses of Statistics 

Chapter 11 Summary 

Chapter 12: Voting Methods 

12-1 Preference Tables and the Plurality Method 

12-2 The Borda Count Method and the Plurality-with-Elimination Method 

12-3 The Pairwise Comparison Method and Approval Voting 

12-4 Apportionment 

12-5 Apportionment Flaws 

Chapter 12 Summary 

Chapter 13: Graph Theory 

13-1 Basic Concepts of Graph Theory 

13-2 Euler’s Theorem 

13-3 Hamilton Paths and Circuits 

13-4 Trees 

Chapter 13 Summary 

Chapter 14-Available online: Other Mathematical Systems 

14-1 Mathematical Systems and Groups 

14-2 Clock Arithmetic 

14-3 Modular Systems 

Chapter 14 Summary 

Appendix A: Area Under the Standard Normal Distribution

Appendix B-Available Online: Using the TI-84 Plus Graphing Calculator

Selected Answers

Photo Credits

Index