Developmental Mathematics with Applications and Visualization Prealgebra, Beginning Algebra, and Intermediate Algebra

Gary Rockswold has been a professor and teacher of mathematics, computer science, astronomy, and physical science for over 35 years. He has taught not only at the undergraduate and graduate college levels, but he has also taught middle school, high school, vocational school, and adult education. He received his BA degree with majors in mathematics and physics from St. Olaf College and his Ph.D. in applied mathematics from Iowa State University. He has been a principal investigator at the Minnesota Supercomputer Institute, publishing research articles in numerical analysis and parallel processing and is currently an emeritus professor of mathematics at Minnesota State University, Mankato. He is an author for Pearson Education and has over 10 current textbooks at the developmental and precalculus levels. His developmental coauthor and friend is Terry Krieger. They have been working together for over a decade. Making mathematics meaningful for students and professing the power of mathematics are special passions for Gary. In his spare time he enjoys sailing, doing yoga, and spending time with his family.

Additional information about Gary Rockswold can be found at www.garyrockswold.net.

1. Whole Numbers

1.1 Introduction to Whole Numbers

1.2 Adding and Subtracting Whole Numbers; Perimeter

1.3 Multiplying and Dividing Whole Numbers; Area

1.4 Exponents, Variables, and Algebraic Expressions

1.5 Rounding and Estimating; Square Roots

1.6 Order of Operations

1.7 More with Equations and Problem Solving

2. Integers

2.1 Integers and the Number Line

2.2 Adding Integers

2.3 Subtracting Integers

2.4 Multiplying and Dividing Integers

2.5 Order of Operations; Averages

2.6 Solving Equations with Integer Solutions

3. Algebraic Expressions and Linear Equations

3.1 Simplifying Algebraic Expressions

3.2 Translating Words to Equations

3.3 Properties of Equality

3.4 Solving Linear Equations

3.5 Applications and Problem Solving

4. Fractions

4.1 Introduction to Fractions and Mixed Numbers

4.2 Prime Factorization and Lowest Terms

4.3 Multiplying and Dividing Fractions

4.4 Adding and Subtracting Fractions-Like Denominators

4.5 Adding and Subtracting Fractions-Unlike Denominators

4.6 Operations on Mixed Numbers

4.7 Complex Fractions and Order of Operations

4.8 Solving Equations Involving Fractions

5. Decimals

5.1 Introduction to Decimals

5.2 Adding and Subtracting Decimals

5.3 Multiplying and Dividing Decimals

5.4 Real Numbers, Square Roots, and Order of Operations

5.5 Solving Equations Involving Decimals

5.6 Applications from Geometry and Statistics

6. Ratios, Proportions, and Measurement

6.1 Ratios and Rates

6.2 Proportions and Similar Figures

6.3 The American System of Measurement

6.4 The Metric System of Measurement

6.5 American-Metric Conversions; Temperature

6.6 Time and Speed

7. Percents

7.1 Introduction to Percents; Circle Graphs

7.2 Using Equations to Solve Percent Problems

7.3 Using Proportions to Solve Percent Problems

7.4 Applications:  Sales Tax, Discounts, and Net Pay

7.5 Applications:  Simple and Compound Interest

7.6 Probability and Percent Chance

8. Geometry

8.1 Plane Geometry:  Points, Lines, and Angles

8.2 Triangles

8.3 Polygons and Circles

8.4 Perimeter and Circumference

8.5 Area, Volume, and Surface Area

9. Linear Equations and Inequalities

9.1 Review of Linear Equations

9.2 Further Problem Solving

9.3 Linear Inequalities

10. Graphing Equations

10.1 Introduction to Graphing

10.2 Linear Equations in Two Variables

10.3 More Graphing of Lines

10.4 Slope and Rates of Change

10.5 Slope-Intercept Form

10.6 Point-Slope Form

10.7 Introduction to Modeling

11. Systems of Linear Equations in Two Variables

11.1 Solving Systems of Linear Equations Graphically and Numerically

11.2 Solving Systems of Linear Equations by Substitution

11.3 Solving Systems of Linear Equations by Elimination

11.4 Systems of Linear Inequalities

12. Polynomials and Exponents

12.1 Rules for Exponents

12.2 Addition and Subtraction of Polynomials

12.3 Multiplication of Polynomials

12.4 Special Products

12.5 Integer Exponents and the Quotient Rule

12.6 Division of Polynomials

13. Factoring Polynomials and Solving Equations

13.1 Introduction to Factoring

13.2 Factoring Trinomials I (x ² + bx + c)

13.3 Factoring Trinomials II (ax ² + bx + c)

13.4 Special Types of Factoring

13.5 Summary of Factoring

13.6 Solving Equations by Factoring I (Quadratics)

13.7 Solving Equations by Factoring II (Higher Degree)

14. Rational Expressions

14.1 Introduction to Rational Expressions

14.2 Multiplication and Division of Rational Expressions

14.3 Addition and Subtraction with Like Denominators

14.4 Addition and Subtraction with Unlike Denominators

14.5 Complex Fractions

14.6 Rational Equations and Formulas

14.7 Proportions and Variation

15. Introduction to Functions

15.1 Functions and Their Representations

15.2 Linear Functions

15.3 Compound Inequalities

15.4 Other Functions and Their Properties

15.5 Absolute Value Equations and Inequalities

16. Systems of Linear Equations

16.1 Systems of Linear Equations in Three Variables

16.2 Matrix Solutions of Linear Systems

16.3 Determinants

17. Radical Expressions and Functions

17.1 Radical Expressions and Functions

17.2 Rational Exponents

17.3 Simplifying Radical Expressions

17.4 Operations on Radical Expressions

17.5 More Radical Functions

17.6 Equations Involving Radical Expressions

17.7 Complex Numbers

18. Quadratic Functions and Equations

18.1 Quadratic Functions and Their Graphs

18.2 Parabolas and Modeling

18.3 Quadratic Equations

18.4 The Quadratic Formula

18.5 Quadratic Inequalities

18.6 Equations in Quadratic Form

19. Exponential and Logarithmic Functions

19.1 Composite and Inverse Functions

19.2 Exponential Functions

19.3 Logarithmic Functions

19.4 Properties of Logarithms

19.5 Exponential and Logarithmic Equations

20. Conic Sections

20.1 Parabolas and Circles

20.2 Ellipses and Hyperbolas

20.3 Nonlinear Systems of Equations and Inequalities

21. Sequences and Series

21.1 Sequences

21.2 Arithmetic and Geometric Sequences

21.3 Series

21.4 The Binomial Theorem

Appendix A: Using the Graphing Calculator

Appendix B: Sets

Appendix C: Linear Programming

Appendix D: Synthetic Division

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