Charles Miller

Vern Heeren grew up in the Sacramento Valley of California. After earning a Bachelor of Arts degree in mathematics, with a minor in physics, at Occidental College, and completing his Master of Arts degree in mathematics at the University of California, Davis, he began a 38-year teaching career at American River College, teaching math and a little physics. He coauthored Mathematical Ideas in 1968 with office mate Charles Miller, and he has enjoyed researching and revising it over the years. It has been a joy for him to complete the thirteenth edition, along with long time coauthor John Hornsby, and now also with son Christopher. These days, besides pursuing his mathematical interests, Vern enjoys spending time with his wife Carole and their family, exploring the wonders of nature near their home in central Oregon.

John Hornsby joined the author team of Margaret Lial, Charles Miller, and Vern Heeren in 1988. In 1990, the sixth edition of Mathematical Ideas became the first of nearly 150 titles he has coauthored for Scott Foresman, HarperCollins, Addison-Wesley, and Pearson in the years that have followed. His books cover the areas of developmental and college algebra, precalculus, trigonometry, and mathematics for the liberal arts. He is a native and resident of New Roads, Louisiana.

Christopher Heeren is a native of Sacramento, California. While studying engineering in college, he had an opportunity to teach a math class at a local high school, and this sparked both a passion for teaching and a change of major. He received a Bachelor of Arts degree and a Master of Arts degree, both in mathematics, from California State University¿—Sacramento. Chris has taught mathematics at the middle school, high school, and college levels, and he currently teaches at American River College in Sacramento. He has a continuing interest in using technology to bring mathematics to life. When not writing, teaching, or preparing to teach, Chris enjoys spending time with his lovely wife Heather and their three children (and two dogs and a guinea pig).

1.      The Art of Problem Solving

Skill Review Topics

1.R.1 Evaluate algebraic expressions, given values of variables.

1.R.2 Use the order of operations.

1.R.3 Translate word phrases to algebraic expressions.

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

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

3.      Introduction to Logic

Skill Review Topics

3.R.1 Graph intervals on a number line.

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

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

5.      Number Theory

Skill Review Topics

5.R.1 Use exponents.

5.R.2 Use the power rules for exponents.

5.R.3 Know the meaning of relational operators.

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

6.      The Real Numbers and Their Representations

Skill Review Topics

6.R.1 Use the multiplication property of equality.

6.R.2 Find principal square roots.

6.R.3 Translate from words to mathematical expressions.

6.1    Real Numbers, Order, and Absolute Value

6.2    Operations, Properties, and Applications of Real Numbers

6.3    Rational Numbers and Decimal Representations

6.4    Irrational Number and Decimal Representations

6.5    Applications of Decimals and Percents

7.      The Basic Concepts of Algebra

Skill Review Topics

7.R.1 Identify solutions to equations.

7.R.2 Solve problems involving sums of quantities.

7.R.3 Divide real numbers.

7.R.4 Identify like terms.

7.R.5 Solve linear equations by using the addition and multiplication properties of equality.

7.R.6 Find all square roots of a number.

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

8.      Graphs, Functions, and Systems of Equations and Inequalities

Skill Review Topics

8.R.1 Complete and factor perfect square trinomials.

8.R.2 Write solutions as ordered pairs.

8.R.3 Decide whether an equation defines a function.

8.R.4 Write an equation of a line by using its slope and any point on the line.

8.R.5 Use function notation.

8.R.6 Use the distributive property.

8.R.7 Graph inverse functions.

8.R.8 Decide whether given ordered pairs are solutions of a system.

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

9.      Geometry

Skill Review Topics

9.R.1 Solve proportions.

9.R.2 Evaluate algebraic expressions for given values of variables.

9.R.3 Divide rational expressions.

9.R.4 Identify like terms.

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

10.    Counting Methods

Skill Review Topics

10.R.1 Write fractions in lowest terms.

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”

11.    Probability

Skill Review Topics

11.R.1 Add and subtract fractions.

11.R.2 Multiply and divide fractions.

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

12.    Statistics

Skill Review Topics

12.R.1 Plot ordered pairs.

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

13.    Personal Financial Management

Skill Review Topics

13.R.1 Solve exponential equations.

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

14.    Graph Theory

14.1  Basic Concepts

14.2  Euler Circuits and Algorithms

14.3  Hamilton Circuits and Algorithms

14.4  Trees and Minimum Spanning Trees

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

Answers to Selected Exercises

Credits

Index of Applications

Index

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

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