Mathematics in Our World

Second Edition

Chapter 1: Problem Solving

1-1 The Nature of Mathematical Reasoning

1-2 Estimation and Interpreting Graphs

1-3 Problem Solving

Chapter 1 Review

Chapter 2: Sets

2-1 The Nature of Sets

2-2 Subsets and Set Operations

2-3 Venn Diagrams

2-4 Using Sets to Solve Problems

2-5 Infinite Sets

Chapter 2 Review

Chapter 3: Logic

3-1 Statements and Quantifiers

... MORE 3-2 Truth Tables

3-3 Types of Statements

3-4 Logical Arguments

3-5 Euler Circles

Chapter 3 Review

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 Review

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 Review

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 Review

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 Solving Systems of Linear Equations Using Matrices

7-4 Linear Inequalities

7-5 Linear Programming

7-6 Functions

7-7 Linear, Quadratic, and Exponential Functions

Supplement: An Application of Functions--Sound

Chapter 7 Review

Chapter 8: Consumer Mathematics

8-1 Percents

8-2 Simple Interest

8-3 Compound Interest

8-4 Installment Buying

8-5 Home Ownership

8-6 Stocks and Bonds

Chapter 8 Review

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 Review

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 Review

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 Review

Chapter 12: Statistics

12-1 The Nature of Statistics 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 Review

Chapter 13: Other Mathematical Systems

13-1 Mathematical Systems and Groups

13-2 Clock Arithmetic

13-3 Modular Systems

Chapter 13 Review

Chapter 14: Voting Methods

14-1 Preference Tables and the Plurality Method

14-2 The Borda Count Method and the Plurality-with-Elimination Method

14-3 The Pairwise Comparison Method and Approval Voting

14-4 Apportionment

14-5 Apportionment Flaws

Chapter 14 Review

Chapter 15: Graph Theory

15-1 Basic Concepts of Graph Theory

15-2 Euler’s Theorem

15-3 Hamilton Paths and Circuits

15-4 Trees

Chapter 15 Review