Introductory and Intermediate Algebra for College Students

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to his Developmental Algebra Series, Bob has written textbooks covering college algebra, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson Education. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.  

1. Variables, Real Numbers, and Mathematical Models

1.1 Introduction to Algebra: Variables and Mathematical Models

1.2 Fractions in Algebra

1.3 The Real Numbers

1.4 Basic Rules of Algebra

            Mid-Chapter Check Point

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponents and Order of Operations

 

2. Linear Equations and Inequalities in One Variable

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 Solving Linear Equations

2.4 Formulas and Percents

            Mid-Chapter Check Point

2.5 An Introduction to Problem Solving

2.6 Problem Solving in Geometry

2.7 Solving Linear Inequalities

 

3. Linear Equations in Two Variables

3.1 Graphing Linear Equations in Two Variables

3.2 Graphing Linear Equations Using Intercepts

3.3 Slope

3.4 The Slope-Intercept Form of the Equation of a Line

            Mid-Chapter Check Point

3.5 The Point-Slope Form of the Equation of a Line

 

4. Systems of Linear Equations

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by the Substitution Method

4.3 Solving Systems of Linear Equations by the Addition Method

            Mid-Chapter Check Point

4.4 Problem Solving Using Systems of Equations

4.5 Systems of Linear Equations in Three Variables

 

5. Exponents and Polynomials

5.1 Adding and Subtracting Polynomials

5.2 Multiplying Polynomials

5.3 Special Products

5.4 Polynomials in Several Variables

            Mid-Chapter Check Point

5.5 Dividing Polynomials

5.6 Long Division of Polynomials; Synthetic Division

5.7 Negative Exponents and Scientific Notation

 

6. Factoring Polynomials

6.1 The Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials Whose Leading Coefficient is 1

6.3 Factoring Trinomials Whose Leading Coefficient is Not 1

            Mid-Chapter Check Point

6.4 Factoring Special Forms

6.5 A General Factoring Strategy

6.6 Solving Quadratic Equations by Factoring

 

7. Rational Expressions

7.1 Rational Expressions and Their Simplification

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

            Mid-Chapter Check Point

7.5 Complex Rational Expressions

7.6 Solving Rational Equations

7.7 Applications Using Rational Equations and Proportions

7.8 Modeling Using Variation

 

8. Basics of Functions

8.1 Introduction to Functions

8.2 Graphs of Functions

8.3 The Algebra of Functions

            Mid-Chapter Check Point

8.4 Composite and Inverse Functions

 

9. Inequalities and Problem Solving

9.1 Reviewing Linear Inequalities and Using Inequalities in Business Applications

9.2 Compound Inequalities

9.3 Equations and Inequalities Involving Absolute Value

            Mid-Chapter Check Point

9.4 Linear Inequalities in Two Variables

 

10. Radicals, Radical Functions, and Rational Exponents

10.1 Radical Expressions and Functions

10.2 Rational Exponents

10.3 Multiplying and Simplifying Radical Expressions

10.4 Adding, Subtracting, and Dividing Radical Expressions

            Mid-Chapter Check Point

10.5 Multiplying with More Than One Term and Rationalizing Denominators

10.6 Radical Equations

10.7 Complex Numbers

 

11. Quadratic Equations and Functions

11.1 The Square Root Property and Completing the Square; Distance and Midpoint Formula

11.2 The Quadratic Formula

11.3 Quadratic Functions and Their Graphs

            Mid-Chapter Check Point

11.4 Equations Quadratic in Form

11.5 Polynomial and Rational Inequalities

 

12. Exponential and Logarithmic Functions

12.1 Exponential Functions

12.2 Logarithmic Functions

12.3 Properties of Logarithms

            Mid-Chapter Check Point

12.4 Exponential and Logarithmic Equations

12.5 Exponential Growth and Decay; Modeling Data

 

13. Conic Sections and Systems of Nonlinear Equations

13.1 The Circle

13.2 The Ellipse

13.3 The Hyperbola

            Mid-Chapter Check Point

13.4 The Parabola; Identifying Conic Sections

13.5 Systems of Nonlinear Equations in Two Variables

 

14. Sequences, Series, and the Binomial Theorem

14.1 Sequences and Summation Notation

14.2 Arithmetic Sequences

14.3 Geometric Sequences

            Mid-Chapter Check Point

14.4 The Binomial Theorem