Mathematical Ideas, 14th edition

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

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Overview

Mathematical Ideas helps students in liberal arts and survey courses develop a solid understanding of mathematical concepts and shows you how math will play an important role in your future career.

Pearson eText is an easy-to-use digital textbook that you can read online or offline. Make it your own by adding highlights and notes, and learn on the go with the mobile app. At the end of your subscription, you can opt to renew access to your eText and personalized notes.

Published by Pearson (July 15th 2020) - Copyright © 2020

ISBN-13: 9780136881292

Subject: Liberal Arts Math

Category: Liberal Arts Math

Table of contents

Table of Contents

  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

*The online section on Magic Squares as well as a Trigonometry chapter, a Metrics chapter, and Extension topics can all be found in the MyLab™ Math course or at www.pearsonhighered.com/mathstatsresources

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