Algebra for College Students / Edition 3

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Overview

An emphasis on the practical applications of algebra motivates readers and encourages them to see algebra as an important part of their daily lives. Strongly emphasizes good problem-solving skills, uses real-world applications. For anyone interested in Algebra.
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Product Details

  • ISBN-13: 9780321656605
  • Publisher: Pearson
  • Publication date: 7/26/2009
  • Edition number: 3
  • Product dimensions: 8.30 (w) x 10.80 (h) x 1.00 (d)

Meet the Author

Allen R. Angel received his AAS in Electrical Technology from New York City Community College. He then received his BS in Physics and his MS in Mathematics from SUNY at New Paltz, and he took additional graduate work at Rutgers University. He is Professor Emeritus at Monroe Community College in Rochester, New York where he served for many years as the chair of the Mathematics Department. He also served as the Assistant Director of the National Science Foundation Summer Institutes at Rutgers University from 1967—73. He served as the President of the New York State Mathematics Association of Two Year Colleges (NYSMATYC) and the Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). He is the recipient of many awards including a number of NISOD Excellence in Teaching Awards, NYSMATYC's Outstanding Contributions to Mathematics Education Award, and AMATYC's President Award. Allen enjoy tennis, worldwide travel, and visiting with his children and granddaughter.

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Read an Excerpt

PREFACE:

Preface

This book was written for college students who have successfully completed a first course in elementary algebra. My primary goal was to write a book that students can read, understand, and enjoy. To achieve this goal I have used short sentences, clear explanations, and many detailed worked-out examples. I have tried to make the book relevant to college students by using practical applications of algebra throughout the text.

Features of the Text

Four-Color Format: Color is used pedagogically in the following ways:

  • Important definitions and procedures are color screened.
  • Color screening or color type is used to make other important items stand out.
  • Artwork is enhanced and clarified with use of multiple colors.
  • The four-color format allows for easy identification of important features by students.
  • The four-color format makes the text more appealing and interesting to students.


Reability: One of the most important features of text is its readability. The book is very readable, even for those with weak reading skills. Short, clear senses are used and more easily recognized, and easy-to-understand language is used whenever possible.

Accuracy: Accuracy in a mathematics text is essential. To ensure accuracy in this book, mathematicians from around the country have read the pages carefully for typographical errors and have checked all the answers.

Connections: Many of our students do not thoroughly grasp new concepts the first time they are presented. In this text we encourage students to makeconnections. That is, we introduce a concept, then later in the text briefly reintroduce it and build upon it. Often an important concept is used in many sections of the text. Students are reminded where the material was seen before, or where it will be used again. This also serves to emphasize the importance of the concept. Important concepts are also reinforced throughout the text in the Cumulative Review Exercises and Cumulative Review Tests.

Chapter Opening Application: Each chapter begins with a real-life application related to the material covered in the chapter. By the time students complete the chapter, they should have the knowledge to work the problem.

Preview and Perspective: This feature at the beginning of each chapter explains to the students why they are studying the material and where this material will be used again in other chapters of the book. This material helps students see the connections between various topics in the book, and the connection to real-world situations.

Students Solution Manual, Videotape, and Software Icons: At the beginning of each section, Student's Solution Manual, videotape, and tutorial software icons are displayed. These icons tell the student where material in the section can be found in the Student's Solution Manual, on the videotapes, and in the tutorial software, saving your students time when they want to review this material. Small videotape icons are also placed next to exercises that are worked out on the videotapes.

Keyed Section Objectives: Each section opens with a list of skills that the student should learn in that section. The objectives are then keyed to the appropriate portions of the sections with symbols.

Problem Solving: Polya's five-step problem-solving procedure is discussed in Section 2.2. Throughout the book problem solving and Polya's problem-solving procedure are emphasized.

Practical Applications: Practical applications of algebra are stressed throughout the text. Students need to learn how to translate application problems into algebraic symbols. The problem-solving approach used throughout this text gives students ample practice in setting up and solving application problems. The use of practical applications motivates students.

Detailed Worked-Out Examples: A wealth of examples have been worked out in a step-by-step, detailed manner. Important steps are highlighted in color, and no steps are omitted until after the student has seen a sufficient number of similar examples.

Now Try Exercise: In each section, students are asked to work exercises that parallel the examples given in the text. These Now Try Exercises make the students active, rather than passive, learners and they reinforce the concepts as students work the exercises.

Study Skills Section: Many students taking this course have poor study skills in mathematics. Section 1.1, the first section of this text, discusses the study skills needed to be successful in mathematics. This section should be very beneficial for your students and should help them to achieve success in mathematics.

Helpful Hints: The helpful hint boxes offer useful suggestions for problem solving and other varied topics. They are set off in a special manner so that students will be sure to read them.

Avoiding Common Errors: Errors that students often make are illustrated. The reasons why certain procedures are wrong are explained, and the correct procedure for working the problem is illustrated. These Avoiding Common Errors boxes will help prevent your students from making those errors we see so often.

Using Your Calculator: The Using Your Calculator boxes, placed at appropriate intervals in the text, are written to reinforce the algebraic topics presented in the section and to give the student pertinent information on using the calculator to solve algebraic problems.

Using Your Graphing Calculator: Using Your Graphing Calculator boxes are placed at appropriate locations throughout the text. They reinforce the algebraic topics taught and sometimes offer alternate methods of working problems. This book is designed to give the instructor the option of using or not using a graphing calculator in their course. Many Using Your Graphing Calculator boxes contain graphing calculator exercises, whose answers appear in the answer section of the book. The illustrations shown in the Using Your Graphing Calculator boxes are from a Texas Instrument 83 calculator. The Using Your Graphing Calculator boxes are written assuming that the student has no prior graphing calculator experience.

Exercise Sets

The exercise sets are broken into three main categories: Concept/Writing Exercises, Practice the Skills, and Problem Solving. Many exercise sets also contain Challenge Problems and/or Group Activities. Each exercise set is graded in difficulty. The early problems help develop the student's confidence, and then students are eased gradually into the more difficult problems. A sufficient number and variety of examples are given in each section for the student to successfully complete even the more difficult exercises. The number of exercises in each section is more than ample for student assignments and practice. Many exercise sets contain graphing calculator exercises for instructors who wish to assign them.

Concept/Writing Exercises: Most exercise sets include exercises that require students to write out the answers in words. These exercises improve students' understanding and comprehension of the material. Many of these exercises involve problem solving, and conceptualization, and help develop better reasoning and critical thinking skills. Writing exercises are indicated by a symbol.

Challenge Problems: These exercises, which are part of many exercise sets, provide a variety of problems. Many were written to stimulate student thinking. Others provide additional applications of algebra or present material from future sections of the book so that students can see and learn the material on their own before it is covered in class. Others are more challenging than those in the regular exercise set.

Problem Solving Exercises: These exercises have been added to help students become better thinkers and problem solvers. Many of these exercises are applied in nature.

Cumulative Review Exercises: All exercise sets (after the first two) contain questions from previous sections in the chapter and from previous chapters. These cumulative review exercises will reinforce topics that were previously covered and help students retain the earlier material, while they are learning new material. For the students' benefit the Cumulative Review Exercises are keyed to the section where the material is covered.

Group Activities: Many exercise sets have group activity exercises that lead to interesting group discussions. Many students learn well in a cooperative learning atmosphere, and these exercises will get students talking mathematics to one another.

Chapter Summary: At the end of each chapter is a chapter summary which includes a glossary and important chapter facts.

Review Exercises: At the end of each chapter are review exercises that cover all types of exercises presented the chapter. The review exercises are keyed to the sections where the material was first introduced.

Practice Tests: The comprehensive end-of-chapter practice test will enable the students to see how well they are prepared for the actual class test. The Test Item File includes several forms of each chapter test that are similar to the student's practice test. Multiple choice tests are also included in the Test Item File.

Cumulative Review Test: These tests, which appear at the end of each chapter, test the students' knowledge of material from the beginning of the book to the end of that chapter. Students can use these tests for review, as well as for preparation for the final exam. These exams, like the cumulative review exercises, will serve to reinforce topics taught earlier.

Answers: The odd answers are provided for the exercise sets. All answers are provided for the Using Your Graphing Calculator Exercises, Cumulative Review Exercises, the Review Exercises, Practice Tests, and the Cumulative Practice Test. Answers are not provided for the Group Activity exercises since we want students to reach agreement by themselves on the answers to these exercises.

National Standards

Recommendations of the Curriculum and Evaluation Standards for School Mathematics, prepared by the National Council of Teachers of Mathematics, (NCTM) and Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus, prepared by the American Mathematical Association of Two Year Colleges (AMATYC) are incorporated into this edition.

Prerequisite

The prerequisite for this course is a working knowledge of elementary algebra. Although some elementary algebra topics are briefly reviewed in the text, students should have a basic understanding of elementary algebra before taking this course.

Modes of Instruction

The format and readability of this book lends itself to many different modes of instruction. The constant reinforcement of concepts will result in greater understanding and retention of the material by your students.

The features of the text and the large variety of supplements available make this text suitable for many types of instructional modes including:

  • lecture
  • self-paced instruction
  • modified lecture
  • cooperative or group study
  • learning laboratory


Contents

This book covers both intermediate algebra material and material from college algebra. The material from some of the later chapters, especially Chapters 10 through 12, is often covered in college algebra.

Here are some content features of this book.

  • Real-life chapter-opening applications are used.
  • Using Your Graphing Calculator boxes are placed throughout the text. They are used to provide information on using a graphing calculator. The text is designed so that instructors have the opportunity of using, or not using, a graphing calculator with this book.
  • The table of contents has been organized to reduce the overlap between the material covered in an elementary algebra course and this book.
  • Functions are integrated throughout the text to help better prepare your students for additional mathematics courses.
  • The exercise sets start with Concept/Writing Exercises, followed by Practice the Skills Exercises, followed by Problem Solving Exercises.
  • Problem Solving and George Polya's problem-solving procedure are stressed throughout the book. Problem-solving examples are worked using the following steps: Understand, Translate, Carry out, Check, and Answer.
  • Cumulative Review Tests are at the end of every chapter.
  • Many exercise sets contain Challenge Problem and/or Group Activity exercises.
  • The exercise sets have a great variety of exercises, and many challenging exercises have been included for those instructors who wish to assign them. The exercise sets are graded in level of difficulty.
  • Many problem solving, and thought provoking, exercises are included in the exercise sets throughout the book.
  • Although functions are presented early, certain function topics such as inverse and composite functions are introduced later. This gives students the opportunity to learn and understand functions before being introduced to these more complex topics.
  • In the graphing chapters, emphasis is placed on understanding the meaning of graphs.
  • Many graphing calculator exercises are included in the exercise sets for those who wish to assign them.
  • The Using Your Calculator and Using Your Graphing Calculator boxes are colored differently for easy identification.
  • The exercise sets contain many real-life applications.
  • A colorful and appealing design results in distinct features being more recognizable. The exciting design also results in students being more willing to read the text.
  • Graphing AIE answers appear in an appendix in the back of the text. This results in the students' text not having large blocks of empty space in their text.
  • Definitions are given in Definition Boxes and Procedures are given in Procedure Boxes.
  • In the AIE, Teaching Tips are included to provide ideas for exploration.
  • All Chapter Tests have 25 problems, and all Cumulative Review Tests have 20 problems.
  • Now Try Exercises are included in each section after many examples. Students are asked to work specific exercises after they read specific examples. Working these exercises reinforces what the student has just learned, and also serves to make students active, rather than passive, learners. The Now Try Exercises are marked in green in the Exercise Sets for easy identification by the student.
  • Exercises that are worked on the videotapes are indicated by an icon next to the exercises.
  • There are many writing exercises, that is, exercises that require a written answer. Writing exercises are indicated with a pencil icon.
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Table of Contents

1. Basic Concepts.
2. Equations and Inequalities.
3. Graphs and Functions.
4. Systems of Equations and Inequalities.
5. Polynomials and Polynomial Functions.
6. Rational Expressions, Equations, and Functions.
7. Roots, Radicals and Complex Numbers.
8. Quadratic Functions.
9. Exponential and Logarithmic Functions.
10. Conic Sections.
11. Polynomial, Rational and Additional Functions.
12. Sequences, Series, and Probability.
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Preface

Preface

This book was written for college students who have successfully completed a first course in elementary algebra. My primary goal was to write a book that students can read, understand, and enjoy. To achieve this goal I have used short sentences, clear explanations, and many detailed worked-out examples. I have tried to make the book relevant to college students by using practical applications of algebra throughout the text.

Features of the Text

Four-Color Format: Color is used pedagogically in the following ways:

  • Important definitions and procedures are color screened.
  • Color screening or color type is used to make other important items stand out.
  • Artwork is enhanced and clarified with use of multiple colors.
  • The four-color format allows for easy identification of important features by students.
  • The four-color format makes the text more appealing and interesting to students.


Reability: One of the most important features of text is its readability. The book is very readable, even for those with weak reading skills. Short, clear senses are used and more easily recognized, and easy-to-understand language is used whenever possible.

Accuracy: Accuracy in a mathematics text is essential. To ensure accuracy in this book, mathematicians from around the country have read the pages carefully for typographical errors and have checked all the answers.

Connections: Many of our students do not thoroughly grasp new concepts the first time they are presented. In this text we encourage students to makeconnections. That is, we introduce a concept, then later in the text briefly reintroduce it and build upon it. Often an important concept is used in many sections of the text. Students are reminded where the material was seen before, or where it will be used again. This also serves to emphasize the importance of the concept. Important concepts are also reinforced throughout the text in the Cumulative Review Exercises and Cumulative Review Tests.

Chapter Opening Application: Each chapter begins with a real-life application related to the material covered in the chapter. By the time students complete the chapter, they should have the knowledge to work the problem.

Preview and Perspective: This feature at the beginning of each chapter explains to the students why they are studying the material and where this material will be used again in other chapters of the book. This material helps students see the connections between various topics in the book, and the connection to real-world situations.

Students Solution Manual, Videotape, and Software Icons: At the beginning of each section, Student's Solution Manual, videotape, and tutorial software icons are displayed. These icons tell the student where material in the section can be found in the Student's Solution Manual, on the videotapes, and in the tutorial software, saving your students time when they want to review this material. Small videotape icons are also placed next to exercises that are worked out on the videotapes.

Keyed Section Objectives: Each section opens with a list of skills that the student should learn in that section. The objectives are then keyed to the appropriate portions of the sections with symbols.

Problem Solving: Polya's five-step problem-solving procedure is discussed in Section 2.2. Throughout the book problem solving and Polya's problem-solving procedure are emphasized.

Practical Applications: Practical applications of algebra are stressed throughout the text. Students need to learn how to translate application problems into algebraic symbols. The problem-solving approach used throughout this text gives students ample practice in setting up and solving application problems. The use of practical applications motivates students.

Detailed Worked-Out Examples: A wealth of examples have been worked out in a step-by-step, detailed manner. Important steps are highlighted in color, and no steps are omitted until after the student has seen a sufficient number of similar examples.

Now Try Exercise: In each section, students are asked to work exercises that parallel the examples given in the text. These Now Try Exercises make the students active, rather than passive, learners and they reinforce the concepts as students work the exercises.

Study Skills Section: Many students taking this course have poor study skills in mathematics. Section 1.1, the first section of this text, discusses the study skills needed to be successful in mathematics. This section should be very beneficial for your students and should help them to achieve success in mathematics.

Helpful Hints: The helpful hint boxes offer useful suggestions for problem solving and other varied topics. They are set off in a special manner so that students will be sure to read them.

Avoiding Common Errors: Errors that students often make are illustrated. The reasons why certain procedures are wrong are explained, and the correct procedure for working the problem is illustrated. These Avoiding Common Errors boxes will help prevent your students from making those errors we see so often.

Using Your Calculator: The Using Your Calculator boxes, placed at appropriate intervals in the text, are written to reinforce the algebraic topics presented in the section and to give the student pertinent information on using the calculator to solve algebraic problems.

Using Your Graphing Calculator: Using Your Graphing Calculator boxes are placed at appropriate locations throughout the text. They reinforce the algebraic topics taught and sometimes offer alternate methods of working problems. This book is designed to give the instructor the option of using or not using a graphing calculator in their course. Many Using Your Graphing Calculator boxes contain graphing calculator exercises, whose answers appear in the answer section of the book. The illustrations shown in the Using Your Graphing Calculator boxes are from a Texas Instrument 83 calculator. The Using Your Graphing Calculator boxes are written assuming that the student has no prior graphing calculator experience.

Exercise Sets

The exercise sets are broken into three main categories: Concept/Writing Exercises, Practice the Skills, and Problem Solving. Many exercise sets also contain Challenge Problems and/or Group Activities. Each exercise set is graded in difficulty. The early problems help develop the student's confidence, and then students are eased gradually into the more difficult problems. A sufficient number and variety of examples are given in each section for the student to successfully complete even the more difficult exercises. The number of exercises in each section is more than ample for student assignments and practice. Many exercise sets contain graphing calculator exercises for instructors who wish to assign them.

Concept/Writing Exercises: Most exercise sets include exercises that require students to write out the answers in words. These exercises improve students' understanding and comprehension of the material. Many of these exercises involve problem solving, and conceptualization, and help develop better reasoning and critical thinking skills. Writing exercises are indicated by a symbol.

Challenge Problems: These exercises, which are part of many exercise sets, provide a variety of problems. Many were written to stimulate student thinking. Others provide additional applications of algebra or present material from future sections of the book so that students can see and learn the material on their own before it is covered in class. Others are more challenging than those in the regular exercise set.

Problem Solving Exercises: These exercises have been added to help students become better thinkers and problem solvers. Many of these exercises are applied in nature.

Cumulative Review Exercises: All exercise sets (after the first two) contain questions from previous sections in the chapter and from previous chapters. These cumulative review exercises will reinforce topics that were previously covered and help students retain the earlier material, while they are learning new material. For the students' benefit the Cumulative Review Exercises are keyed to the section where the material is covered.

Group Activities: Many exercise sets have group activity exercises that lead to interesting group discussions. Many students learn well in a cooperative learning atmosphere, and these exercises will get students talking mathematics to one another.

Chapter Summary: At the end of each chapter is a chapter summary which includes a glossary and important chapter facts.

Review Exercises: At the end of each chapter are review exercises that cover all types of exercises presented the chapter. The review exercises are keyed to the sections where the material was first introduced.

Practice Tests: The comprehensive end-of-chapter practice test will enable the students to see how well they are prepared for the actual class test. The Test Item File includes several forms of each chapter test that are similar to the student's practice test. Multiple choice tests are also included in the Test Item File.

Cumulative Review Test: These tests, which appear at the end of each chapter, test the students' knowledge of material from the beginning of the book to the end of that chapter. Students can use these tests for review, as well as for preparation for the final exam. These exams, like the cumulative review exercises, will serve to reinforce topics taught earlier.

Answers: The odd answers are provided for the exercise sets. All answers are provided for the Using Your Graphing Calculator Exercises, Cumulative Review Exercises, the Review Exercises, Practice Tests, and the Cumulative Practice Test. Answers are not provided for the Group Activity exercises since we want students to reach agreement by themselves on the answers to these exercises.

National Standards

Recommendations of the Curriculum and Evaluation Standards for School Mathematics, prepared by the National Council of Teachers of Mathematics, (NCTM) and Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus, prepared by the American Mathematical Association of Two Year Colleges (AMATYC) are incorporated into this edition.

Prerequisite

The prerequisite for this course is a working knowledge of elementary algebra. Although some elementary algebra topics are briefly reviewed in the text, students should have a basic understanding of elementary algebra before taking this course.

Modes of Instruction

The format and readability of this book lends itself to many different modes of instruction. The constant reinforcement of concepts will result in greater understanding and retention of the material by your students.

The features of the text and the large variety of supplements available make this text suitable for many types of instructional modes including:

  • lecture
  • self-paced instruction
  • modified lecture
  • cooperative or group study
  • learning laboratory


Contents

This book covers both intermediate algebra material and material from college algebra. The material from some of the later chapters, especially Chapters 10 through 12, is often covered in college algebra.

Here are some content features of this book.

  • Real-life chapter-opening applications are used.
  • Using Your Graphing Calculator boxes are placed throughout the text. They are used to provide information on using a graphing calculator. The text is designed so that instructors have the opportunity of using, or not using, a graphing calculator with this book.
  • The table of contents has been organized to reduce the overlap between the material covered in an elementary algebra course and this book.
  • Functions are integrated throughout the text to help better prepare your students for additional mathematics courses.
  • The exercise sets start with Concept/Writing Exercises, followed by Practice the Skills Exercises, followed by Problem Solving Exercises.
  • Problem Solving and George Polya's problem-solving procedure are stressed throughout the book. Problem-solving examples are worked using the following steps: Understand, Translate, Carry out, Check, and Answer.
  • Cumulative Review Tests are at the end of every chapter.
  • Many exercise sets contain Challenge Problem and/or Group Activity exercises.
  • The exercise sets have a great variety of exercises, and many challenging exercises have been included for those instructors who wish to assign them. The exercise sets are graded in level of difficulty.
  • Many problem solving, and thought provoking, exercises are included in the exercise sets throughout the book.
  • Although functions are presented early, certain function topics such as inverse and composite functions are introduced later. This gives students the opportunity to learn and understand functions before being introduced to these more complex topics.
  • In the graphing chapters, emphasis is placed on understanding the meaning of graphs.
  • Many graphing calculator exercises are included in the exercise sets for those who wish to assign them.
  • The Using Your Calculator and Using Your Graphing Calculator boxes are colored differently for easy identification.
  • The exercise sets contain many real-life applications.
  • A colorful and appealing design results in distinct features being more recognizable. The exciting design also results in students being more willing to read the text.
  • Graphing AIE answers appear in an appendix in the back of the text. This results in the students' text not having large blocks of empty space in their text.
  • Definitions are given in Definition Boxes and Procedures are given in Procedure Boxes.
  • In the AIE, Teaching Tips are included to provide ideas for exploration.
  • All Chapter Tests have 25 problems, and all Cumulative Review Tests have 20 problems.
  • Now Try Exercises are included in each section after many examples. Students are asked to work specific exercises after they read specific examples. Working these exercises reinforces what the student has just learned, and also serves to make students active, rather than passive, learners. The Now Try Exercises are marked in green in the Exercise Sets for easy identification by the student.
  • Exercises that are worked on the videotapes are indicated by an icon next to the exercises.
  • There are many writing exercises, that is, exercises that require a written answer. Writing exercises are indicated with a pencil icon.
Read More Show Less

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