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Lewis Hirsch and Arthur Goodman strongly believe that students can understand what they are learning in algebra and why. The authors meticulously explain why things are done in a certain way, illustrate how and why concepts are related and demonstrate how 'new' topics are actually new applications of concepts already learned. 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… More situations. Through this learning this author team carefully prepares students to succeed in higher-level mathematics.Less

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List price: $245.95 Edition: 6th Copyright year: 2006 Publisher: Brooks/Cole Publication date: 9/14/2005 Binding: Hardcover Pages: 880 Size: 8.75" wide x 10.75" long x 1.50" tall Weight: 4.620 Language: English

AuthorTable of Contents

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.

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.

The Fundamental Concepts

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

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

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

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

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

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

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

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

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

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

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 Cramer's Rule

Systems of Linear Inequalities

Nonlinear Systems of Equations

Chapter Summary

Review Exercises and Practice Test

Cumulative Review And Practice Test: Chapters 10-11

Sets

The Conic Sections

Answers to Selected Exercises and Chapter Tests

Index

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