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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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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 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