# Mathematical Ideas, 14th edition

• Charles D. Miller,
• Vern E. Heeren,
• John Hornsby,
• Christopher Heeren

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## Overview

Ideal for students in liberal arts math and survey courses, Mathematical Ideas helps you develop a solid understanding of mathematical concepts while showing you how math plays an important role in your current and future life. It is a versatile text that has evolved to meet changing course and student needs, but maintains its primary objectives: comprehensive coverage, appropriate organization, clear language, many examples, and well-planned exercise sets with numerous applications. An even stronger emphasis on career applications in the 14th Edition includes additional “When Will I Ever Use This?” feature boxes, along with many new or modified exercises tied to career applications. Updated exercise sets include over 1000 new or modified exercises, with many emphasizing career applications.

ISBN-13: 9780136881292

Subject: Liberal Arts Math

Category: Liberal Arts Math

## Overview

1. The Art of Problem Solving
• 1.1 Solving Problems by Inductive Reasoning
• 1.2 An Application of Inductive Reasoning: Number Patterns
• 1.3 Strategies for Problem Solving
• 1.4 Numeracy in Today’s World
• CHAPTER 1 SUMMARY
• CHAPTER 1 TEST
2. The Basic Concepts of Set Theory
• 2.1 Symbols and Terminology
• 2.2 Venn Diagrams and Subsets
• 2.3 Set Operations
• 2.4 Surveys and Cardinal Numbers
• CHAPTER 2 SUMMARY
• CHAPTER 2 TEST
3. Introduction to Logic
• 3.1 Statements and Quantifiers
• 3.2 Truth Tables and Equivalent Statements
• 3.3 The Conditional and Circuits
• 3.4 The Conditional and Related Statements
• 3.5 Analyzing Arguments with Euler Diagrams
• 3.6 Analyzing Arguments with Truth Tables
• CHAPTER 3 SUMMARY
• CHAPTER 3 TEST
4. Numeration Systems
• 4.1 Historical Numeration Systems
• 4.2 More Historical Numeration Systems
• 4.3 Arithmetic in the Hindu-Arabic System
• 4.4 Conversion Between Number Bases
• CHAPTER 4 SUMMARY
• CHAPTER 4 TEST
5. Number Theory
• 5.1 Prime and Composite Numbers
• 5.2 Large Prime Numbers
• 5.3 Selected Topics from Number Theory
• 5.4 Greatest Common Factor and Least Common Multiple
• 5.5 The Fibonacci Sequence and the Golden Ratio
• 5.6 Magic Squares (online)*
• CHAPTER 5 SUMMARY
• CHAPTER 5 TEST
6. The Real Numbers and Their Representations
• 6.1 Real Numbers, Order, and Absolute Value
• 6.2 Operations, Properties, and Applications of Real Numbers
• 6.3 Rational Numbers and Decimal Representation
• 6.4 Irrational Numbers and Decimal Representation
• 6.5 Applications of Decimals and Percents
• CHAPTER 6 SUMMARY
• CHAPTER 6 TEST
7. The Basic Concepts of Algebra
• 7.1 Linear Equations
• 7.2 Applications of Linear Equations
• 7.3 Ratio, Proportion, and Variation
• 7.4 Linear Inequalities
• 7.5 Properties of Exponents and Scientific Notation
• 7.6 Polynomials and Factoring
• 7.7 Quadratic Equations and Applications
• CHAPTER 7 SUMMARY
• CHAPTER 7 TEST
8. Graphs, Functions, and Systems of Equations and Inequalities
• 8.1 The Rectangular Coordinate Systems and Circles
• 8.2 Lines, Slope, and Average Rate of Change
• 8.3 Equations of Lines
• 8.4 Linear Functions, Graphs, and Models
• 8.5 Quadratic Functions, Graphs, and Models
• 8.6 Exponential and Logarithmic Functions, Graphs, and Models
• 8.7 Systems of Linear Equations
• 8.8 Applications of Linear Systems
• 8.9 Linear Inequalities, Systems, and Linear Programming
• CHAPTER 8 SUMMARY
• CHAPTER 8 TEST
9. Geometry
• 9.1 Points, Lines, Planes, and Angles
• 9.2 Curves, Polygons, Circles, and Geometric Constructions
• 9.3 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
• 9.4 Perimeter, Area, and Circumference
• 9.5 Volume and Surface Area
• 9.6 Transformational Geometry
• 9.7 Non-Euclidian Geometry and Topology
• 9.8 Chaos and Fractal Geometry
• CHAPTER 9 SUMMARY
• CHAPTER 9 TEST
10. Counting Methods
• 10.1 Counting by Systematic Listing
• 10.2 Using the Fundamental Counting Principle
• 10.3 Using Permutations and Combinations
• 10.4 Using Pascal’s Triangle
• 10.5 Counting Problems Involving “Not” and “Or”
• CHAPTER 10 SUMMARY
• CHAPTER 10 TEST
11. Probability
• 11.1 Basic Concepts
• 11.2 Events Involving “Not” and “Or”
• 11.3 Conditional Probability and Events Involving “And”
• 11.4 Binomial Probability
• 11.5 Expected Value and Simulation
• CHAPTER 11 SUMMARY
• CHAPTER 11 TEST
12. Statistics
• 12.1 Visual Displays of Data
• 12.2 Measures of Central Tendency
• 12.3 Measures of Dispersion
• 12.4 Measures of Position
• 12.5 The Normal Distribution
• CHAPTER 12 SUMMARY
• CHAPTER 12 TEST
13. Personal Financial Management
• 13.1 The Time Value of Money
• 13.2 Consumer Credit
• 13.3 Truth in Lending
• 13.4 The Costs and Advantages of Home Ownership
• 13.5 Financial Investments
• CHAPTER 13 SUMMARY
14. Graph Theory
• 14.1 Basic Concepts
• 14.2 Euler Circuits and Route Planning
• 14.3 Hamilton Circuits and Algorithms
• 14.4 Trees and Minimum Spanning Trees
• CHAPTER 14 SUMMARY
• CHAPTER 14 TEST
15. Voting and Apportionment
• 15.1 The Possibilities of Voting
• 15.2 The Impossibilities of Voting
• 15.3 The Possibilities of Apportionment
• 15.4 The Impossibilities of Apportionment
• CHAPTER 15 SUMMARY
• CHAPTER 15 TEST

Answers to Selected Exercises (Annotated Instructor’s Edition only)

Answers to Selected Exercises (Student Edition Only)

Credits

Index of Applications

Index

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