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Table of Contents

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Mathematics in Our World, Third Edition

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 The Nature of Sets

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 The Fundamentals of Algebra

6-2 Solving Linear Equations

6-3 Applications of Linear Equations

6-4 Ratio, Proportion, and Variation

6-5 Solving Linear Inequalities

6-6 Solving Quadratic Equations

Chapter 6 Summary

Chapter 7: Additional Topics in Algebra

7-1 The Rectangular Coordinate System and Linear Equations in Two Variables

7-2 Systems of Linear Equations

7-3 Linear Inequalities

7-4 Linear Programming

7-5 Functions

7-6 Quadratic, Exponential, and Logarithmic Functions

7-7 Available Online: Solving Systems of Linear Equations Using Matrices

Chapter 7 Summary

Chapter 8: Consumer Mathematics

8-1 Percents

8-2 Simple Interest

8-3 Compound Interest

8-4 Installment Buying

8-5 Student Loans and Home Buying

8-6 Investing in Stocks and Bonds

Chapter 8 Summary

Chapter 9: Measurement

9-1 Measures of Length: Converting Units and the Metric System

9-2 Measures of Area, Volume, and Capacity

9-3 Measures of Weight and Temperature

Chapter 9 Summary

Chapter 10: Geometry

10-1 Points, Lines, Planes and Angles

10-2 Triangles

10-3 Polygons and Perimeter

10-4 Areas of Polygons and Circles

10-5 Volume and Surface Area

10-6 Right Triangle Trigonometry

10-7 A Brief Survey of Non-Euclidean and

Transformational Geometries

Chapter 10 Summary

Chapter 11: Probability and Counting Techniques

11-1 The Fundamental Counting Rule and Permutations

11-2 Combinations

11-3 Basic Concepts of Probability

11-4 Tree Diagrams, Tables, and Sample Spaces

11-5 Probability Using Permutations and Combinations

11-6 Odds and Expectation

11-7 The Addition Rules for Probability

11-8 The Multiplication Rules and Conditional

Probability

11-9 The Binomial Distribution

Chapter 11 Summary

Chapter 12: Statistics

12-1 Gathering and Organizing Data

12-2 Picturing Data

12-3 Measures of Average

12-4 Measures of Variation

12-5 Measures of Position

12-6 The Normal Distribution

12-7 Applications of the Normal Distribution

12-8 Correlation and Regression Analysis

Supplement: Misuses of Statistics

Chapter 12 Summary

Chapter 13: Voting Methods

13-1 Preference Tables and the Plurality Method

13-2 The Borda Count Method and the Plurality-with-Elimination Method

13-3 The Pairwise Comparison Method and Approval Voting

13-4 Apportionment

13-5 Apportionment Flaws

Chapter 13 Summary

Chapter 14: Graph Theory

14-1 Basic Concepts of Graph Theory

14-2 Euler’s Theorem

14-3 Hamilton Paths and Circuits

14-4 Trees

Chapter 14 Summary

Chapter 15-Available online: Other Mathematical Systems

15-1 Mathematical Systems and Groups

15-2 Clock Arithmetic

15-3 Modular Systems

Chapter 15 Review

Appendix A: Area Under the Standard Normal Distribution

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

Selected Answers

Additional Exercise Sets

Answers to Additional Exercise Sets

Photo Credits

Index