Elementary Algebra Concepts and Applications

For courses in Beginning Algebra.

Understanding and Applying Mathematical Concepts

The goal of the Bittinger Concepts and Applications Series is to help today’s student learn and retain mathematical concepts. This proven program prepares students for the transition from skills-oriented elementary algebra courses to more concept-oriented college-level mathematics courses. This requires the development of critical-thinking skills: to reason mathematically, to communicate mathematically, and to identify and solve mathematical problems. The new editions support students with a tightly integrated MyLab™ Math course; a strong focus on problem-solving, applications, and concepts, and the robust MyMathGuide workbook and objective-based video program. In addition, new material – developed as a result of the authors’ experience in the classroom, as well as from insights from faculty and students – includes more systematic review and preparation for practice, as well as stronger focus on real-world applications.

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Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in mathematics from Clemson University, and she is currently pursuing a PhD in Educational Studies at Ball state University. She has taught high school and college math for 30 years, and she 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 is also a student of karate.

Marvin Bittinger has taught math at the university level for more than thirty-eight years, and he is now professor emeritus of mathematics education at Indiana University-Purdue University. Professor Bittinger has authored numerous textbooks 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. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." 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.

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 x ² + bx + c

5.3 Factoring Trinomials of the Type ax ² + 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

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