Higher Education

Understanding Intermediate Algebra: A Course for College Students, 6th Edition

  • includes CD-ROM and iLrn™ Tutorial
  • Lewis R. Hirsch Rutgers University
  • Arthur Goodman Queens College of the City University of New York
  • ISBN-10: 0534417957  |  ISBN-13: 9780534417956
  • 880 Pages
  • Previous Editions: 2002, 1998, 1994
  • © 2006 | Published
  • College Bookstore Wholesale Price = $167.50

About

Overview

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 situations. Through this learning this author team carefully prepares students to succeed in higher-level mathematics.

Additional Product Information

Features and Benefits

  • CAREFULLY EXPLAINED EXAMPLES. The authors have constructed examples to cast students as active thinkers, rather than passive readers. Many steps appear with notations, highlighted in color, to explain to students how and why a solution is proceeding in a certain way with related ideas that are compared and contrasted, helping students to understand the sometimes subtle distinctions.
  • DIFFERENT PERSPECTIVES boxes highlight the connection between algebraic and geometric aspects of the same concepts, encouraging students to think about mathematical ideas from more than one point of view.
  • MARGIN COMMENTS, located throughout each section, involve students in active learning emphasizing a point made in the text presentation or asking a question requiring the student to focus attention on a particularly crucial aspect of the discussion.
  • STUDY SKILLS. Found at the end of each section throughout the first four chapters, these vignettes provide a brief paragraph that discusses an aspect of studying algebra, doing homework, or preparing or taking exams; thereby providing helpful material to aid students in their study needs.
  • EXERCISE SETS. Each exercise set contains odd/even-matched exercises, with successive odd-numbered problems that compare and contrast subtle differences in applying the concept covered in the section.
  • QUESTIONS FOR THOUGHT. Found in many of the exercise sets, these problems require students to think about various algebraic ideas. For example, students are asked to compare and contrast related ideas or examine an incorrect solution and explain why the solution is wrong.
  • MINI-REVIEW. Located throughout numerous exercise sets are problems that review important topics covered and prepare students for material yet to be covered.
  • CHAPTER SUMMARY. A review and summary of the basic concepts in the chapter accompanied by an example illustrating the concept or procedure.

Table of Contents

1. 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.
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 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.
Appendix A: Sets.
Appendix B: The Conic Sections.
Answers to Selected Exercises and Chapter Tests.
Index.

What's New

  • THINKING OUT LOUD features have been added to more examples to support stronger active learning for the students. These features, located throughout the margins, present solutions to certain examples in a question and answer format, so that students can see examples of the thought processes involved in approaching and solving new or unfamiliar problems.
  • Based on reviewer feedback, Interval Notation has been added to this edition. It is introduced in Section 2.3, First Degree Inequalities.
  • UPDATED APPLICATIONS THAT INTRODUCE NEW CONCEPTS. A real-world application is presented at the start of many sections to illuminate the topic to be discussed. The authors then return to the application later in the chapter for students to solve the problem. These applications have been updated for this edition.
  • UPDATED EXERCISES AND APPLICATIONS. The text's more then 6000 exercises have been updated with real-world material. Each exercise set contains odd/even-numbered exercises, with successive odd-numbered problems that compare and contrast subtle differences in applying concepts.
  • ADDITIONAL EXERCISES have been added to the text to allow for a more gradual progression of difficulty as the student moves through the exercise sets.
  • 40 HOURS/WEEK OF ONLINE TUTORING are available to your students with the purchase of a new textbook. Students can access vMentor� tutoring service through iLrn� Tutorial, which is packaged with their text.

Learning Resource Bundles

Choose the textbook packaged with the resources that best meet your course and student needs. Contact your Learning Consultant for more information.

Bundle: Text + iLrn™ Student Resource Kit

ISBN-10: 0495144932 | ISBN-13: 9780495144939

List Price = $119.95  | College Bookstore Wholesale Price = $89.00

This Bundle Includes:

  • Understanding Intermediate Algebra: A Course for College Students
    List Price = $222.95  | CengageBrain Price = $222.95  | College Bookstore Wholesale Price = $167.50


Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Student Supplements

Bundle: Text + Student Solutions Manual  (ISBN-10: 0534611540 | ISBN-13: 9780534611545)

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 situations. Through this learning this author team carefully prepares students to succeed in higher-level mathematics.

List Price = $351.95  | CengageBrain Price = $351.95  | College Bookstore Wholesale Price = $264.75

Meet the Author

Author Bio

Lewis R. Hirsch

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.

Arthur Goodman

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.