Mathematical Ideas

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: Service Math

Category: Liberal Arts Math

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 IA-1 (Annotated Instructor’s Edition only)
ANSWERS TO SELECTED EXERCISES A-1 (Student Edition Only)
CREDITS C-1
INDEX OF APPLICATIONS I-1
INDEX

*The online section on Magic Squares as well as a Trigonometry chapter, a Metrics chapter, and Extension topics can all at www.pearsonhighered.com/mathstatsresources

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