Elementary and Intermediate 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 and Equations of Lines

 

4. Polynomials

4.1 Exponents and Their Properties

4.2 Negative Exponents and Scientific Notation

4.3 Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials

4.6 Special Products

 

4.7 Polynomials in Several Variables

4.8 Division of Polynomials

 

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 Differences of Squares

5.5 Factoring Sums or Differences of Cubes

5.6 Factoring: A General Strategy

5.7 Solving Quadratic Equations by Factoring

5.8 Solving Applications

 

6. Rational Expression 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. Functions and Graphs

7.1 Introduction to Functions

7.2 Domain and Range

7.3 Graphs of Functions

7.4 The Algebra of Functions

7.5 Formulas, Applications, and Variation

 

8. Systems of Linear Equations and Problem Solving

8.1 Systems of Equations in Two Variables

8.2 Solving by Substitution or Elimination

8.3 Solving Applications: Systems of Two Equations

8.4 Systems of Equations in Three Variables

8.5 Solving Applications: Systems of Three Equations

8.6 Elimination Using Matrices

8.7 Determinants and Cramer’s Rule

8.8 Business and Economics Applications

9. Inequalities and Problem Solving

9.1 Inequalities and Applications

9.2 Intersections, Unions, and Compound Inequalities

9.3 Absolute-Value Equations and Inequalities

9.4 Inequalities in Two Variables

9.5 Applications Using Linear Programming

 

10. Exponents and Radicals

10.1 Radical Expressions and Functions

10.2 Rational Numbers as Exponents

10.3 Multiplying Radical Expressions

10.4 Dividing Radical Expressions

10.5 Expressions Containing Several Radical Terms

10.6 Solving Radical Equations

10.7 The Distance Formula, the Midpoint Formula, and Other Applications

10.8 The Complex Numbers

 

11. Quadratic Functions and Equations

11.1 Quadratic Equations

11.2 The Quadratic Formula

11.3 Studying Solutions of Quadratic Equations

11.4 Applications Involving Quadratic Equations

11.5 Equations Reducible to Quadratic

11.6 Quadratic Functions and Their Graphs

11.7 More About Graphing Quadratic Functions

11.8 Problem Solving and Quadratic Functions

11.9 Polynomial Inequalities and Rational Inequalities

 

12. Exponential Functions and Logarithmic Functions

12.1 Composite Functions and Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithmic Functions

12.5 Common Logarithms and Natural Logarithms

12.6 Solving Exponential Equations and Logarithmic Equations

12.7 Applications of Exponential Functions and Logarithmic Functions

 

13. Conic Sections

13.1 Conic Sections: Parabolas and Circles

13.2 Conic Sections: Ellipses

13.3 Conic Sections: Hyperbolas

13.4 Nonlinear Systems of Equations

 

14. Sequences, Series, and the Binomial Theorem

14.1 Sequences and Series

14.2 Arithmetic Sequences and Series

14.3 Geometric Sequences and Series

14.4 The Binomial Theorem

 

R. Elementary Algebra Review

R.1 Introduction to Algebraic Expressions

R.2 Equations, Inequalities, and Problem Solving

R.3 Introduction to Graphing

R.4 Polynomials

R.5 Polynomials and Factoring

R6. Rational Expressions and Equations

Appendix A. Mean, Median, and Mode

Appendix B. Sets

Appendix C. Synthetic Division and the Remainder Theorem