Survey of Mathematics with Applications, A, 10th edition

Published by Pearson (January 3, 2016) © 2017

  • Allen R. Angel Monroe Community College
  • Christine D. Abbott Monroe Community College
  • Dennis Runde State College of Florida
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About the Book
  • Seeing the relevance of the material motivates students to learn.
    • The authors emphasize Why This Is Important when presenting math concepts to help students make the connection between their lives and the mathematics they are learning. “Why This Is Important” notes appear in all chapter and section opener applications, as well as the “Mathematics Today” features.
    • Recreational Math boxes show how math is can be entertaining. In addition, Recreational Mathematics exercises are available the exercise sets so that they can be assigned as homework.
    • Mathematics Today boxes discuss current, real-life uses of the mathematical concept in the chapter. Each box ends with Why This Is Important.
    • Chapter and section openers incorporate applications as a way to motivate students. For example, the opener for Chapter 3 (Logic) demonstrates how logic has become important in electronic devices such as cell phones and digital cameras.
      • NEW! Many chapter and section openers contain new, interesting, and motivational information and applications that illustrate the real-world nature of the material.
    • Did You Know? are thoughtful boxes that highlight the connections of mathematics to a broad variety of disciplines including history, the arts, science, and technology.
    • Profiles in Mathematics present the stories of people who have advanced the discipline of mathematics in brief historical sketches and vignettes.
  • Support for problem solving and exam preparation helps students achieve success in the course.
    • Problem solving begins in Chapter 1, where students are introduced to problem-solving techniques and critical thinking. Problem solving exercises help develop these skills throughout the text.
    • Critical thinking skills are developed throughout the book, including the sections on inductive reasoning, estimation, and dimensional analysis. Challenge Problems also appear in the exercise sets to test a student’s ability to think critically.
    • Timely Tips are easy-to-identify boxes that help students with concept comprehension or relate the material to other sections of the book.
    • Chapter Summaries, organized in a chart format, provide an intuitive study and review experience. For each concept, definition, or idea presented, students are directed to the exact place in the text where the item is discussed.
    • Procedures are boxed and set apart from the text for easy identification and future reference.
  • Extensive opportunities to practice and apply the concepts help students learn by doing. In the Tenth Edition, approximately 30% of the examples and exercises are new or updated to reflect current data and topics of interest to today’s students.
    • Exercise sets begin with fill-in-the-blank Warm Up Exercises. Exercises also include Practice the Skills, Problem Solving, Challenge Problems/Group Activities, Recreational Mathematics, and Research Activities.
      • NEW! Data-driven improvements: the authors have analyzed usage and performance data from the previous edition's MyMathLab course to improve the quality and quantity of exercises that matter most to instructors and students.
    • Group Projects, available in MyMathLab, provide an opportunity for student collaboration.
    • Review Exercises are organized by section, helping students see where they are proficient and where they need additional study. In the Tenth Edition, Chapter Tests each contain 20 questions to provide consistency in exam preparation.
    • MyMathLab, available for course management and online homework, has increased exercise coverage, course options that minimize set-up time, and additional functionality to make it easier to teach the course.
  • Technology Tips explain how students can use calculators or Microsoft Excel® to work certain types of application problems.

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and engage with media resources to help them absorb course material and understand difficult concepts. NEW!  This edition’s MyMathLab course provides additional tools to help with understanding and preparedness.

  • NEW! A new video program walks students through the concepts from every section of the text in a fresh, modern presentation format.
  • NEW! Interactive Concept Videos require students’ input and interaction as they walk through a concept. Incorrect answers are followed by a video explanation of the solution, addressing the misconception that may have led to that particular mistake.
    • Corresponding assignable exercises allow instructors to check student understanding.
  • NEW! Video assessment questions check students’ understanding of the video lectures, allowing the videos to be truly assignable.
  • NEW! Learning Catalytics uses students’ devices in the classroom to create an engagement, assessment, and classroom intelligence system that gives instructors real-time feedback on student learning. Learning Catalytics is available through MyMathLab
    • Premade quantitative literacy questions are available for assignment.
    • In the Annotated Instructor’s Edition, special Learning Catalytics annotations suggest which LC questions to use for that portion of the lesson, with a corresponding tag to search for that question.
  • NEW! An Integrated Review MyMathLab course option provides a complete liberal arts course with embedded review of select developmental topics at the chapter level.
    • Assignments on prerequisite topics are pre-assigned in this course—students begin with a Skills Check quiz on prerequisite topics needed for that chapter.
    • Students who prove mastery can move on to the Survey of Mathematics content, while students who need additional review can remediate using resources like the developmental videos and Integrated Review Worksheets.
    • This course solution can be used in a co-requisite course model, or simply to help underprepared students master prerequisite skills and concepts.
  • NEW! Skills for Success Modules are integrated into the MyMathLab course to help students succeed in college courses and prepare for their future professions.
  • NEW! Flashcards are available in a modern, mobile-ready format, so students can study and reinforce vocabulary on the go.
  • NEW! Group Projects have been moved from the text to the MyMathLab course and provide opportunities for students to collaborate.
New and updated features
  • Topics such as geometry, consumer mathematics, and voting have been rewritten for greater clarity.
  • NEW! Workbook including Integrated Review Worksheets provides additional study support with objective summaries, note taking, worked-out problems and additional problems for practice. Integrated Review Worksheets in the Workbook support the Integrated Review version of the MyMathLab course, covering prerequisite developmental-level topics necessary to move on to each chapter. This Workbook is available for download in MyMathLab, or is available as a printed, unbound, three-hole-punched workbook that can be used as the foundation for a course notebook.
  • In the Annotated Instructor’s Edition, new Learning Catalytics icons indicate which Learning Catalytics questions are ideal to use in that portion of the lesson. Tags indicate how to search for each question in Learning Catalytics, and suggestions from the authors on how to use them is available in the instructor’s section in MyMathLab. Learning Catalytics is a bring-your-own-device engagement tool that is available through MyMathLab.
  • Many chapter and section openers have been updated to contain new, interesting, and motivational information and applications that illustrate the real-world nature of the material. For example, Section 2.3 introduces Venn diagrams and set operations with the experience of purchasing a laptop computer.
  • New Did You Know?, Mathematics Today, and Profile in Mathematics boxes have been added, while others have been updated.
  • Data-driven improvements: the authors have analyzed usage and performance data from the previous edition's MyMathLab course to improve the quality and quantity of exercises that matter most to instructors and students.

Content Updates

  • Chapter 1 “Critical Thinking Skills,” includes exciting and current examples and exercises.
  • Chapter 2 “Sets,” includes many new applications of sets pertaining to a greater variety of relevant topics, including Facebook and other social media sites.
  • Chapter 3 “Logic,” contains many new examples and exercises. The authors updated several of the puzzles, including Sudoku, Kakuro, and KenKen.
  • Chapter 4 “Systems of Numeration,” contains many new examples and exercises that relate to the digital language used by modern devices, including smartphones, computers, and smart televisions.
  • Chapter 5 “Number Theory and the Real Number System,” has updated information regarding the largest prime number found and the most calculated digits of pi. The authors updated the examples and exercise sets to reflect current economic numbers such as the national debt, the gross domestic product, population growth, and so on.
  • Chapter 6 In “Algebra, Graphs, and Functions,” the authors combined the order of operations and solving linear equations into one section to emphasize the relationship between the two topics. They also moved material on solving systems of linear equations and systems of linear inequalities into Chapter 6, and removed Chapter 7. The material on matrices from Chapter 7 was incorporated into Chapter 9, “Mathematical Systems.”
  • Chapter 7 “The Metric System,” has many new up-to-date examples, exercises, and photographs of real-life metric use throughout the world.
  • Chapter 8 “Geometry,” includes many updated examples and exercises, and the authors rewrote several topics for greater clarity.
  • Chapter 9 “Mathematical Systems,” has many new examples and exercises. The authors included a section on matrices and how they can form a group under matrix addition.
  • Chapter 10 “Consumer Mathematics

1. Critical Thinking Skills

1.1 Inductive and Deductive Reasoning

1.2 Estimation

1.3 Problem Solving

 

2. Sets

2.1 Set Concepts

2.2 Subsets

2.3 Venn Diagrams and Set Operations

2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets

2.5 Applications of Sets

2.6 Infinite Sets

 

3. Logic

3.1 Statements and Logical Connectives

3.2 Truth Tables for Negation, Conjunction, and Disjunction

3.3 Truth Tables for the Conditional and Biconditional

3.4 Equivalent Statements

3.5 Symbolic Arguments

3.6 Euler Diagrams and Syllogistic Arguments

3.7 Switching Circuits

 

4. Systems of Numeration

4.1 Additive, Multiplicative, and Ciphered Systems of Numeration

4.2 Place-Value or Positional-Value Numeration Systems

4.3 Other Bases

4.4 Computation in Other Bases

4.5 Early Computational Methods

 

5. Number Theory and the Real Number System

5.1 Number Theory

5.2 The Integers

5.3 The Rational Numbers

5.4 The Irrational Numbers

5.5 Real Numbers and Their Properties

5.6 Rules of Exponents and Scientific Notation

5.7 Arithmetic and Geometric Sequences

5.8 Fibonacci Sequence

 

6. Algebra, Graphs, and Functions

6.1 Order of Operations and Solving Equations

6.2 Formulas

6.3 Applications of Algebra

6.4 Variation

6.5 Linear Inequalities

6.6 Graphing Linear Equations

6.7 Solving Systems of Linear Equations

6.8 Linear Inequalities and Systems of Linear Inequalities

6.9 Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula

6.10 Functions and Their Graphs

 

7. The Metric System

7.1 Basic Terms and Conversions Within the Metric System

7.2 Length, Area, and Volume

7.3 Mass and Temperature

7.4 Dimensional Analysis and Conversions to and from the Metric System

 

8. Geometry

8.1 Points, Lines, Planes, and Angles

8.2 Polygons

8.3 Perimeter and Area

8.4 Volume and Surface Area

8.5 Transformational Geometry, Symmetry, and Tessellations

8.6 Topology

8.7 Non-Euclidean Geometry and Fractal Geometry

 

9. Mathematical Systems

9.1 Groups

9.2 Finite Mathematical Systems

9.3 Modular Arithmetic

9.4 Matrices

10. Consumer Mathematics

10.1 Percent

10.2 Personal Loans and Simple Interest

10.3 Compound Interest

10.4 Installment Buying

10.5 Buying a House with a Mortgage

10.6 Ordinary Annuities, Sinking Funds, and Retirement Investments

 

11. Probability

11.1 Empirical and Theoretical Probabilities

11.2 Odds

11.3 Expected Value (Expectation)

11.4 Tree Diagrams

11.5 OR and AND Problems

11.6 Conditional Probability

11.7 The Counting Principle and Permutations

11.8 Combinations

11.9 Solving Probability Problems by Using Combinations

11.10 Binomial Probability Formula

 

12. Statistics

12.1 Sampling Techniques and Misuses of Statistics

12.2 Frequency Distributions and Statistical Graphs

12.3 Measures of Central Tendency

12.4 Measures of Dispersion

12.5 The Normal Curve

12.6 Linear Correlation and Regression

 

13. Graph Theory

13.1 Graphs, Paths, and Circuits

13.2 Euler Paths and Euler Circuits

13.3 Hamilton Paths and Hamilton Circuits

13.4 Trees

 

14. Voting and Apportionment

14.1 Voting Methods

14.2 Flaws of the Voting Methods

14.3 Apportionment Methods

14.4 Flaws of the Apportionment Methods

 

ANSWERS

Credits

Index of Applications

Index



Allen Angel received his BS and MS in mathematics from SUNY at New Paltz. He completed additional graduate work at Rutgers University. He taught at Sullivan County Community College and Monroe Community College, where he served as chairperson of the Mathematics Department. He served as Assistant Director of the National Science Foundation at Rutgers University for the summers of 1967 - 1970. He was President of The New York State Mathematics Association of Two Year Colleges (NYSMATYC). He also served as Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). Allen lives in Palm Harbor, Florida but spends his summers in Penfield, New York. He enjoys playing tennis and watching sports. He also enjoys traveling with his wife Kathy.

Christine Abbott received her undergraduate degree in mathematics from SUNY Brockport and her graduate degree in mathematics education from Syracuse University. Since then she has taught mathematics at Monroe Community College and has recently chaired the department. In her spare time she enjoys watching sporting events, particularly baseball, college basketball, college football, and the NFL. She also enjoys spending time with her family, traveling, and reading

Dennis Runde has a BS degree and an MS degree in Mathematics from the University of Wisconsin—Platteville and Milwaukee, respectively. He has a PhD in Mathematics Education from the University of South Florida. He has been teaching for more than twenty-five years at State College of Florida—Manatee-Sarasota. His interests include reading, history, fishing, canoeing, and cooking. He and his wife Kristin stay busy keeping up with their three sons–Alex, Nick, and Max.

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