## Overview

Written for the Math for Liberal Arts course, Topics in Contemporary Mathematics helps students see math at work in the world by presenting problem solving in purposeful and meaningful contexts. Many of the problems in the text demonstrate how math relates to subjects--such as sociology, psychology, business, and technology--that generally interest students.

## Table of Contents

Each chapter concludes with a Summary, Research Questions, a Practice Test, and Answers.

1. Problem Solving

1.1 Inductive Reasoning

1.2 Estimation: A Problem Solving Tool

1.3 Graph Interpretation: A Problem-Solving Tool

2. Sets

2.1 Sets: A Problem-Solving Tool

2.2 Set Operations

2.3 Venn Diagrams

2.4 The Number of Elements in a Set: A Problem-Solving Tool

2.5 Infinite Sets

3. Logic

3.1 Statements

3.2 Truth Tables: A Problem-Solving Tool

3.3 The Conditional and the Biconditional

3.4 Variations of the Conditional and Implications

3.5 Euler Diagrams: A Problem-Solving Tool

3.6 Truth Tables and Validity Arguments

Online Only: 3.7 Switching Networks: A Problem-Solving Tool

4. Numeration Systems

4.1 Egyptian, Babylonian, and Roman Numeration Systems

4.2 The Hindu-Arabic (Decimal) System

4.3 Number Systems with Bases Other Than 10

4.4 Binary Arithmetic

4.5 Octal and Hexadecimal Arithmetic

5. Number Theory and the Real Numbers

5.1 Number Theory: Primes and Composites

5.2 Whole Numbers, Integers, and Order of Operations

5.3 The Rational Numbers

5.4 Decimals, Scientific Notation, and Significant Digits

5.5 Rationals as Decimals: Percents

5.6 Real Numbers, Square Roots, and Decimal Representation

5.7 Radicals

5.8 Number Sequences

6. Equations, Inequalities, and Problem Solving

6.1 Solutions of First-Degree Sentences

6.2 Graphs of Algebraic Sentences

6.3 Sentences Involving Absolute Values

6.4 Quadratic Equations

6.5 Modeling and Problem Solving

6.6 Ratio, Proportion, and Variation

7. Functions and Graphs

7.1 Graphing Relations and Functions

7.2 Linear Functions, Relations, and Applications

7.3 Slopes and Equations of a Line

7.4 Quadratic Functions and Their Graphs

7.5 Exponential and Logarithmic Functions

7.6 Two Linear Equations in Two Variables

7.7 Linear Inequalities

Online Only: 7.8 Linear Programming

8. Geometry

8.1 Points, Lines, Planes, and Angles

8.2 Triangles and Other Polygons

8.3 Perimeter and Circumfrence

8.4 Area Measure and the Pythagorean Theorem

8.5 Volume and Surface Area

8.6 Networks, Non-Euclidean Geometry, and Topology

Online Only: 8.7 Right Triangle Trigonometry

Online Only: 8.8 Chaos and Fractals

9. Mathematical Systems and Matrices

9.1 Matrix Operations

9.2 Solving Systems of Linear Equations with Matrices

9.3 Clock and Modular Arithmetic

9.4 Abstract Mathematical Systems: Groups and Fields

9.4 Game Theory

10. Counting Techniques

10.1 The Sequential Counting Principle (SCP): A Problem-Solving Tool

10.2 Permutations

10.3 Combinations

10.4 Miscellaneous Counting Methods

11. Probability

11.1 Sample Spaces and Probability

11.2 Counting Techniques and Probability

11.3 Computation of Probability

11.4 Conditional Probability

11.5 Independent Events

11.6 Odds and Mathematical Expectation

12. Statictics

12.1 Sampling and Frequency Distribution

12.2 Measures of Central Tendency: The Mean, Median, and Mode

12.3 Measures of Depression: The Range and Standard Deviation

12.4 The Normal Dsitribution: A Problem Solving Tool

12.5 Statistical Graphs: A Problem-Solving Tool

12.6 Making Predictions: Linear Regression

12.7 Scattergrams and Correlation

13. Your Money and Your Math

13.1 Interest, Taxes, and Discounts

13.2 Credit Cards and Consumer Credit

13.3 Annual Percentage Rate (APR) and the Rules of 78

13.4 Buying a House

13.5 Investing in Stocks, Bonds, and Mutual Funds

Online Only: 14. Voting and Apportionment

14.1 Voting Systems

14.2 Voting Objections

14.3 Apportionment Methods

14.4 Apportionment Objections

Online Only: 15. Graph Theory

15.1 Introduction to Graph Theory

15.2 Euler Paths and Euler Circuits

15.3 Hamilton Paths and Hamilton Circuits

15.4 Trees

Online Only: Appendix. The Metric System

A.1 Metric Units of Measurement

A.2 Convert If You Must