Synopses & Reviews
Helping students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples - both numerical and algebraic-helps students compare and contrast related ideas and understand the sometimes subtle distinctions among a variety of situations. This author team carefully prepares students to succeed in higher level mathematics.
About the Author
Lewis Hirsch (Ph.D., Pennsylvania State University) currently teaches in the mathematics department at Rutgers University. Dr. Hirsch teaches both developmental mathematics and higher level courses such as college algebra and pre-calculus. His experiences in the classroom make him committed to properly preparing students in lower-level courses so they can succeed in for credit courses, and this is reflected in the way he writes his textbooks.Dr. Arthur Goodman (Ph.D., Yeshiva University) currently teaches in the mathematics department at Queens College of the City University of New York. Dr. Goodman takes great pride in the mathematical accuracy and in depth explanation in all of his textbooks.
Table of Contents
1. THE FUNDAMENTAL CONCEPTS. Basic Definitions: The Real Numbers and the Real Number Line. Operations with Real Numbers. Algebraic Expressions. Translating Phrases and Sentences into Algebraic Form. First-Degree Equations and Inequalities. Chapter Summary, Review Exercises, and Practice Test. 2. EQUATIONS AND INEQUALITITES. Equations as Mathematical Models. First-Degree Equations and Applications. First-Degree Inequalities and Applications. Absolute-Value Equations and Inequalities. Chapter Summary, Review Exercises, and Practice Test. 3. GRAPHING STRAIGHT LINES AND FUNCTIONS. The Rectangular Coordinate System and Graphing Straight Lines. Graphs and Equations. Relations and Functions: Basic Concepts. Function Notation. Interpreting Graphs. Chapter Summary, Review Exercises, and Practice Test. Cumulative Review and Practice Test: Chapters 1-3. 4. EQUATIONS OF A LINE AND LINEAR SYSTEMS IN TWO VARIABLES. Straight Lines and Slope. Equations of a Line and Linear Functions as Mathematical Models. Linear Systems in Two Variables. Graphing Linear Inequalities in Two Variables. Chapter Summary, Review Exercises, and Practice Test. 5. POLYNOMIAL EXPRESSIONS AND FUNCTIONS. Polynomial Functions as Mathematical Models. Polynomials: Sums, Differences, and Products. General Forms and Special Products. Factoring out the Greatest Common Factor. Factoring Trinomials. Solving Polynomial Equations by Factoring. Polynomial Division. Chapter Summary, Review Exercises, and Practice Test. 6. RATIONAL EXPRESSIONS AND FUNCTIONS. Rational Functions. Equivalent Fractions. Multiplication and Division of Rational Expressions. Sums and Differences of Rational Expressions. Mixed Operations and Complex Fractions. Fractional Equations and Inequalities. Literal Equations. Applications: Rational Functions and Equations as Mathematical Models. Chapter Summary, Review Exercises, and Practice Test. Cumulative Review and Practice Test: Chapters 4-6. 7. EXPONENTS AND RADICALS. Natural Number and Integer Exponents. Scientific Notation. Rational Exponents and Radical Notation. Simplifying Radical Expressions. Adding and Subtracting Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Functions and Equations. Complex Numbers. Chapter Summary, Review Exercises, and Practice Test. 8. QUADRATIC FUNCTIONS AND EQUATIONS. Quadratic Functions as Mathematical Models. Solving Quadratic Equations: The Factoring and Square Root Methods. Solving Quadratic Equations: Completing the Square. Solving Quadratic Equations: The Quadratic Formula. Equations Reducible to Quadratic Form (and More Radical Equations). Graphing Quadratic Functions. Quadratic and Rational Inequalities. The Distance Formula: Circles. Chapter Summary, Review Exercises, and Practice Test. 9. MORE ON FUNCTIONS. More on Function Notation: Split Functions. Composition and the Algebra of Functions. Types of Functions. Inverse Functions. Variation. Chapter Summary, Review Exercises, and Practice Test. Cumulative Review And Practice Test: Chapters 7-9. 10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithms and Logarithmic Functions. Properties of Logarithms. Common Logarithms, Natural Logarithms, and Change of Base. Exponential and Logarithmic Equations. Applications: Exponential and Logarithmic Functions as Mathematical Models. Chapter Summary, Review Exercises, and Practice Test. 11. MORE SYSTEMS OF EQUATIONS AND SYSTEMS OF INEQUALITITIES. 3x3 Linear Systems. Solving Linear Systems Using Augmented Matrices. The Algebra of Matrices. Solving Linear Systems Using Matrix Inverses. Determinants and Cramers Rule. Systems of Linear Inequalities. Nonlinear Systems of Equations. Chapter Summary, Review Exercises, and Practice Test. Cumulative Review And Practice Test: Chapters 10-11. Appendix A: Sets. Appendix B: The Conic Sections. Answers to Selected Exercises and Chapter Tests. Index.