Elementary Algebra

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana, with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.   David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts–Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.   Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in math from Clemson University. She has taught high school and college math for 25 years, and enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she recently earned a black belt in karate.

1. Introduction to Algebraic Expressions

1.1 Introduction to Algebra

1.2 The Commutative, Associative, and Distributive Laws

1.3 Fraction Notation

1.4 Positive and Negative Real Numbers

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponential Notation and Order of Operations

 

2. Equations, Inequalities, and Problem Solving

2.1 Solving Equations

2.2 Using the Principles Together

2.3 Formulas

2.4 Applications with Percent

2.5 Problem Solving

2.6 Solving Inequalities

2.7 Solving Applications with Inequalities

 

3. Introduction to Graphing

3.1 Reading Graphs, Plotting Points, and Scaling Graphs

3.2 Graphing Linear Equations

3.3 Graphing and Intercepts

3.4 Rates

3.5 Slope

3.6 Slope-Intercept Form

3.7 Point-Slope Form

 

4. Polynomials

4.1 Exponents and Their Properties

4.2 Polynomials

4.3 Addition and Subtraction of Polynomials

4.4 Multiplication of Polynomials

4.5 Special Products

4.6 Polynomials in Several Variables

4.7 Division of Polynomials

4.8 Negative Exponents and Scientific Notation

 

5. Polynomials and Factoring

5.1 Introduction to Factoring

5.2 Factoring Trinomials of the Type x2 + bx + c

5.3 Factoring Trinomials of the Type ax2 + bx + c

5.4 Factoring Perfect-Square Trinomials and Difference of Squares

5.5 Factoring: A General Strategy

5.6 Solving Quadratic Equations by Factoring

5.7 Solving Applications

 

6. Rational Expressions and Equations

6.1 Rational Expressions

6.2 Multiplication and Division

6.3 Addition, Subtraction, and Least Common Denominators

6.4 Addition and Subtraction with Unlike Denominators

6.5 Complex Rational Expressions

6.6 Rational Equations

6.7 Applications Using Rational Equations and Proportions

 

7. Systems and More Graphing

7.1 Systems of Equations and Graphing

7.2 Systems of Equations and Substitution

7.3 Systems of Equations and Elimination

7.4 More Applications Using Systems

7.5 Linear Inequalities in Two Variables

7.6 Systems of Linear Inequalities

7.7 Direct Variation and Inverse Variation

 

8. Radical Expressions and Equations

8.1 Introduction to Square Roots and Radical Expressions

8.2 Multiplying and Simplifying Radical Expressions

8.3 Quotients Involving Square Roots

8.4 Radical Expressions with Several Terms

8.5 Radical Equations

8.6 Applications Using Right Triangles

8.7 Higher Roots and Rational Exponents

 

9. Quadratic Equations

9.1 Solving Quadratic Equations: The Principle of Square Roots

9.2 Solving Quadratic Equations: Completing the Square

9.3 The Quadratic Formula and Applications

9.4 Formulas

9.5 Complex Numbers as Solutions of Quadratic Equations

9.6 Graphs of Quadratic Functions

9.7 Functions

Appendix A. Factoring Sums or Differences of Cubes

Appendix B. Mean, Median, and Mode

Appendix C. Sets