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Mathematical Ideas, 13th edition

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

Published by Pearson (December 24th 2014) - Copyright © 2016

13th edition

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Mathematical Ideas captures the interest of non-majors who take the Liberal Arts Math course by showing how mathematics plays an important role in everyday life. With a fresh, new focus on math in the workplace, this program shows students how math will play an important role in their future, while encouraging them to understand and embrace the mathematical concepts.


0321978269 / 9780321978264 Mathematical Ideas plus MyMathLab -- Access Card Package

Package consists of:

0321431308 / 9780321431301 MyMathLab -- Glue-in Access Card

0321654064 / 9780321654069 MyMathLab Inside Star Sticker

0321977076 / 9780321977076 Mathematical Ideas

Table of contents



About the Authors


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 System 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-Euclidean 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

            Chapter 13 Test 


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


Index of Applications



NOTE: Trigonometry module and Metrics module available in MyMathLab or online at www.pearsonhighered.com/mathstatsresources.

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