College Algebra A Narrative Approach

Stephen Majewicz received his PhD in mathematics at the CUNY Graduate Center and is currently an associate professor of mathematics at Kingsborough Community College in Brooklyn, New York. He began teaching mathematics in 1990 at the age of 19 as a teaching assistant at SUNY Stonybrook, and has been teaching math ever since. In addition to College Algebra: A Narrative Approach, Professor Majewicz is  also the author of Precalculus: A Narrative Approach, College Trigonometry: A Narrative Approach, and Algebra for Mat R3.

Section 1.1. The Classification of Numbers

1.2. Arithmetic of Real Numbers

1.3. Approximation of a Decimal

1.4. The Order of Operations

1.5. Properties of the Real Numbers

1.6. The Real Number Line and Inequalities

1.7. Absolute Value

1.8. Introduction to Algebra

Section 2.1. Definition and Properties of Integer Exponents

2.2. Negative Integer Exponents Revisited

2.3. Scientific Notation

Section 3.1. Definitions and Examples of Polynomials

3.2. Addition and Subtraction of Polynomials

3.3. Multiplication of Polynomials

3.4. Division of Polynomials

3.5. Factoring Polynomials

(1) Greatest Common Factors

(2) Difference of 2 Squares

(3) Sum / Difference of 2 Cubes

(4) Quadratic Trinomials

(5) Polynomials with Four Terms

(6) Putting It All Together

Section 4.1. Definitions and Simplifying Rational Expressions

4.2. Multiplication and Division of Rational Expressions

4.3. Addition and Subtraction of Rational Expressions

4.4. Mixed Quotients (Complex Fractions)

Section 5.1. Square Roots

(1) Introduction to Square Roots

(2) Simplifying Square Roots

(3) Multiplying and Dividing Square Roots

(4) Combining (Adding and Subtracting) Square Roots

(5) Multiplying Square Roots (Revisited)

(6) Rationalizing the Numerator or Denominator

5.2. Cube Roots

5.3. Radicals

Section 6.1. Definition and Examples of Rational Exponents

6.2. Radical Problems Made Easy

Section 7.1. Preliminary Definitions

7.2. Linear Equations in One Variable

7.3. Literal Equations

7.4. Quadratic Equations

(1) The Factoring Method

(2) Special Cases of ax2 + bx + c = 0, a _= 0

(3) Completing the Square

(4) The Quadratic Formula

7.5. Complex Numbers and Quadratic Equations

with Negative Discriminant

Section 8.1. The Pythagorean Theorem

8.2. Formulas for Plane Figures

8.3. Formulas for Solid Figures

Section 9.1. Basic Set Theory

9.2. Notations Used with Inequalities and Their Interpretations

9.3. Properties of Inequalities

9.4. Solving Linear Inequalities

Section 10.1. The Cartesian Plane and Analytic Geometry

10.2. Linear Equations in Two Variables and Their Graphs

10.3. Parallel Lines and Perpendicular Lines

10.4. Equations of Circles

Section 11.1. Definition of a Function and Notations

11.2. Functional Equations and Evaluating Functions

11.3. Finding the Domain of a Function

Section 12.1. Definition of a System of Linear Equations

12.2. The Graphing Technique

12.3. The Substitution Method

12.4. The Elimination Method

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