Beginning Algebra with Applications & Visualization

Description

Gary Rockswold has been a professor and teacher of mathematics, computer science, astronomy, and physical science for over 35 years. He has taught not only at the undergraduate and graduate college levels, but he has also taught middle school, high school, vocational school, and adult education. He received his BA degree with majors in mathematics and physics from St. Olaf College and his Ph.D. in applied mathematics from Iowa State University. He has been a principal investigator at the Minnesota Supercomputer Institute, publishing research articles in numerical analysis and parallel processing and is currently an emeritus professor of mathematics at Minnesota State University, Mankato. He is an author for Pearson Education and has over 10 current textbooks at the developmental and precalculus levels. His developmental coauthor and friend is Terry Krieger. They have been working together for over a decade. Making mathematics meaningful for students and professing the power of mathematics are special passions for Gary. In his spare time he enjoys sailing, doing yoga, and spending time with his family.

 

Additional information about Gary Rockswold can be found at www.garyrockswold.net.

 

Terry Krieger has taught mathematics for 18 years at the middle school, high school, vocational, community college and university levels. His undergraduate degree in secondary education is from Bemidji State University in Minnesota, where he graduated summa cum laude. He received his MA in mathematics from Minnesota State University – Mankato. In addition to his teaching experience in the United States, Terry has taught mathematics in Tasmania, Australia, and in a rural school in Swaziland, Africa, where he served as a Peace Corps volunteer. Terry is currently teaching at Rochester Community and Technical College in Rochester, Minnesota. He has been involved with various aspects of mathematics textbook publication for more than 14 years and has joined his friend Gary Rockswold as coauthor of a developmental math series published by Pearson Education. In his free time, Terry enjoys spending time with his wife and two boys, physical fitness, wilderness camping, and trout fishing.

The Rockswold/Krieger algebra series fosters conceptual understanding by using relevant applications and visualization to show students why math matters. It answers the common question “When will I ever use this?” Rockswold teaches students the math in context, rather than including the applications at the end of the presentation. By seamlessly integrating meaningful applications that include real data and supporting visuals (graphs, tables, charts, colors, and diagrams), students are able to see how math impacts their lives as they learn the concepts. The authors believe this approach deepens conceptual understanding and better prepares students for future math courses and life.

1. Introduction to Algebra

1.1 Numbers, Variables, and Expressions

1.2 Fractions

1.3 Exponents and Order of Operations

1.4 Real Numbers and the Number Line

1.5 Addition and Subtraction of Real Numbers

1.6 Multiplication and Division of Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying and Writing Algebraic Expressions

 

2. Linear Equations and Inequalities

2.1 Introduction to Equations

2.2 Linear Equations

2.3 Introduction to Problem Solving

2.4 Formulas

2.5 Linear Inequalities

 

3. Graphing Equations

3.1 Introduction to Graphing

3.2 Linear Equations in Two Variables

3.3 More Graphing of Lines

3.4 Slope and Rates of Change

3.5 Slope-Intercept Form

3.6 Point-Slope Form

3.7 Introduction to Modeling

 

4. Systems of Linear Equations In Two Variables

4.1 Solving Systems of Linear Equations Graphically and Numerically

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Elimination

4.4 Systems of Linear Inequalities

 

5. Polynomials and Exponents

5.1 Rules for Exponents

5.2 Addition and Subtraction of Polynomials

5.3 Multiplication of Polynomials

5.4 Special Products

5.5 Integer Exponents and the Quotient Rule

5.6 Division of Polynomials

 

6. Factoring Polynomials and Solving Equations

6.1 Introduction to Factoring

6.2 Factoring Trinomials I (x + bx + c)

6.3 Factoring Trinomials II (ax² + bx + c)

6.4 Special Types of Factoring

6.5 Summary of Factoring

6.6 Solving Equations by Factoring I (Quadratics)

6.7 Solving Equations by Factoring II (Higher Degree)

 

7. Rational Expressions

7.1 Introduction to Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction with Like Denominators

7.4 Addition and Subtraction with Unlike Denominators

7.5 Complex Fractions

7.6 Rational Equations and Formulas

7.7 Proportions and Variation

 

8. Radical Expressions

8.1 Introduction to Radical Expressions

8.2 Multiplication and Division of Radical Expressions

8.3 Addition and Subtraction of Radical Expressions

8.4 Simplifying Radical Expressions

8.5 Equations Involving Radical Expressions

8.6 Higher Roots and Rational Exponents

 

9. Quadratic Equations

9.1 Parabolas

9.2 Introduction to Quadratic Equations

9.3 Solving by Completing the Square

9.4 The Quadratic Formula

9.5 Complex Solutions

9.6 Introduction to Functions

Appendix A: Using the Graphing Calculator

Appendix B: Sets

Answers to Selected Exercises

Glossary

Bibliography

Photo Credits

Index

The Rockswold/Krieger algebra series fosters conceptual understanding by using relevant applications and visualization to show students why math matters. It answers the common question “When will I ever use this?” Rockswold teaches students the math in context, rather than including the applications at the end of the presentation. By seamlessly integrating meaningful applications that include real data and supporting visuals (graphs, tables, charts, colors, and diagrams), students are able to see how math impacts their lives as they learn the concepts. The authors believe this approach deepens conceptual understanding and better prepares students for future math courses and life.

New and Updated Features

• Updated data in hundreds of exercises and examples keep the applications relevant and fresh.
• Increased visualization: whenever appropriate, the mathematics have been made more visual by using more graphs, tables, charts, color, and diagrams to explain important concepts with fewer words. Titles and comments have been added to the graphs. Green equation labels have been added to calculator graphs that are written in standard notation.
• New Vocabulary is listed at the start of every section, highlighting the math concepts that are introduced in that section. This gives students a glimpse of the big picture of the section and helps with test preparation.
• Reading Check questions appear alongside important concepts, ensuring that students understand the material they have just read. These are located throughout every section.
• Study Tips appear throughout the text to give not only general study advice but also specific pointers that relate to learning specific mathematical concepts.
• Application Topics: students are more engaged when mathematics is tied to current and relevant topics. Several new examples have been added that discuss the mathematics of the Internet, social networking, tablet computers, and other contemporary topics.
• Online Exploration Exercises throughout the text invite students to use the Internet to explore real-world mathematics.

 

New Instructor and Student Resources

• Objective-based Worksheetsprovide extra practice for every text section. Designed to be lab- and classroom-friendly, they offer:

• Vocabulary review and practice problems.
• A structured learning process to promote student success.
• Extra practice exercises with ample space for students to show their work.
• Opportunities to explore and compare multiple problem-solving methods through Understanding Concepts through Multiple Approaches.

• Teaching Examples: in the Annotated Instructor’s Edition, every example in the text is now paired with a teaching example that instructors can use in class to promote further understanding.

 

New to MyMathLab^®

New! Two MyMathLab course options are now available: a standard course and a Ready to Go course.

• Standard MyMathLab courses allow instructors to build their course their way, offering maximum flexibility and complete control over all aspects of assignment creation. 
• The new Ready to Go courses provide students with all the same great MyMathLab features, but make it easier for instructors to get started. Each course includes pre-assigned homework and quizzes to make creating a course even easier.

Both course options feature the following items:

• Increased exercise coverage provides an assignable MyMathLab problem for almost every problem type from the text
• Pre-made (and pre-assigned in the Ready to Go course) section-level homework assignments.
• Pre-made chapter review quizzes that are pre-assigned in the Ready to Go course and generate personalized homework assignments based on students’ quiz results.
• A Pre-made(and pre-assigned in the Ready to Go Course) pre- and post- test for every chapter.
• Two new types of exercises are now assignable:
• Concept and Vocabulary exercises provide true/false and fill-in-the blank exercises that assess students’ understanding of the definitions and concepts presented in each section.
• Guided Solutions exercises walk students through the steps as they interact with the problem, helping them understand the reasoning behind it. Some of these exercises require students to use multiple methods—(algebraic, numerical, graphical, etc.)—to deepen understanding.
• All Lecture Series Videos for every section of the text and Chapter Test Prep Videos are available within MyMathLab.
• Video lectures are correlated directly to the content in each section of the text.
• Material is presented in a format that stresses student interaction, often using examples from the text.
• Video lectures include English captions.
• The Chapter Test Prep Videos let students watch instructors work through step-by-step solutions to all the Chapter Test exercises from the textbook.  Chapter Test Prep videos are also available on YouTube™ (search using author name and book title).

 

Content Updates:

• Chapter 1: New step diagrams were added to provide students with an organized, visual process for finding the greatest common factor and the least common denominator.
• Chapter 2: New tables summarizing words and phrases associated with mathematical symbols are now included to give students at-a-glance references to aid in setting up and solving application problems.
• Chapter 3: At the request of reviewers, exercises that require students to complete tables of values for linear equations in two variables are now given in both vertical and horizontal format. Also, additional exercises asking students to interpret the meaning of the slope and the intercepts in applications modeled by linear equations in two variables are now included.
• Chapter 4: The discussion and visual representations of the types of systems of equations have been moved to the first section of Chapter 4 to give students immediate exposure to the types of systems that they will encounter throughout the chapter.
• Chapter 5: New tables summarizing rules for exponents are now included to give students immediate access to these important concepts.
• Chapter 7: A new visual method for finding the least common denominator for rational expressions has been added to make this important concept more accessible for students. Also, joint variation is a new optional topic for those who wish to cover it in this chapter.

 

Showing why math matters, with applications, visualization, and continuous reinforcement of concepts

• Chapter Openers begin each chapter with an application that motivates students by offering insight into the relevance of that chapter’s mathematical concept.
• NEW! New Vocabulary is listed at the start of every section, highlighting the math concepts that are introduced in that section. This gives students a glimpse of the big picture of the section and helps with test preparation.
• A Look Into Math introduces each section with a practical application of the math topic students are about to learn.
• Throughout the text, the authors present math from multiple perspectives—verbal, graphical, numerical, and symbolic—to support multiple learning styles and problem-solving methods.
• Making Connections occur throughout the text and help students see how previous concepts are related to new concepts.
• Real-World Connection notes expand on specific math topics and their connections to the everyday world.
• A modeling data approach thoughout the text provides students with opportunities to model real and relevant data with their own functions.
• NEW! Online Exploration exercises invite students to find data on the Internet and then use mathematics to analyze the data.
• Putting It All Together boxes at the end of each section summarize techniques and reinforce the mathematical concepts presented in the section.

 

Exercise sets and end-of-chapter highlights

• Multiple types of exercises throughout the text support the authors’ application-based and conceptual approach. These exercises are designed to reinforce the skills students need to move on to the next concept.
• Now Try exercises follow every example for immediate reinforcement of the skills and concepts.
• NEW! Reading Check questions appear alongside important concepts, ensuring that students understand the material they have just read. These are located throughout every section.
• Checking Basic Concepts exercises appear after every other section and can be used for individual or group review. These exercises require 10–20 minutes to complete and are also appropriate for in-class work.
• Thinking Generally exercises appear in most exercise sets and offer open-ended conceptual questions that encourage students to synthesize what they have just learned.
• Critical Thinking exercises are included in most sections. They pose questions that can be used for classroom discussion or homework assignments.
• Writing about Mathematics exercises appear at the end of most sections. Students are asked to explain the concepts behind the mathematical procedures they just learned in their own words, encouraging true understanding instead of simple rote memorization.
• Group Activities: Working with Real Data appear once or twice per chapter and provide an opportunity for students to work collaboratively on a problem that involves real-world data. Most activities can be completed with limited use of class time.
• Extended and Discovery exercises are capstone projects at the end of every chapter, challenging students to synthesize what they’ve learned and apply it in other college courses.
• Comprehensive end-of-chapter material serves as an excellent resource for extra practice and test preparation. Each chapter concludes with a Chapter Summary, including a recap of the chapter’s Important Terms, Chapter Review Exercises, a Chapter Test, and Cumulative Review Exercises.

 

Study skills

• NEW! Study Tips offer just-in-time suggestions to help students stay organized and focused on the material at hand.

 

Additional information

Dimensions	1.30 × 8.50 × 10.80 in
Imprint	Pearson
Format	gen
ISBN-13	09780321773302
ISBN-10	0321773306
Author	Gary K. Rockswold, Terry A. Krieger
Subjects	mathematics, higher education, Developmental Math, Elementary Algebra