Survey of Mathematics with Applications, A

Allen R. Angel / Christine D. Abbott / Dennis Runde
Oktober 2007
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Understanding mathematics means understanding how a great deal of the world works. A Survey of Mathematics with Applications, Eighth Edition, introduces students to the practical, interesting, accessible, and powerful world of mathematics today.


  • Chapter Openers and Section Openers introduce each chapter and section with interesting and motivational applications, illustrating the real-world nature of the
    chapter topics.

  • Problem Solving begins in Chapter 1 where students are introduced to problem solving and critical thinking. The problem-solving theme is then continued throughout the text, and special problem-solving exercises are presented in the exercise sets.

  • Critical Thinking Skills are featured in sections on inductive reasoning and the important skills of estimation and dimensional analysis.

  • Profiles in Mathematics present the stories of people who have advanced the discipline of mathematics in brief historical sketches and vignettes.

  • Mathematics Today relates mathematics to everyday life, helping students to recognize the need for math and gain an appreciation for math in their lives.

  • Did You Know? features highlights the connections between mathematics and a variety of other disciplines, including history, the arts and sciences, and technology in colorful and engaging boxed features.

  • Timely Tips, added to assist students, help with concept comprehension or relate the material to other sections of the book.

  • Technology Tips appear as notes that have been added in selected sections to explain how a graphing calculator and/or Microsoft Excel may be used to work certain problems.

  • Exercise Sets include diverse and numerous exercise types such as Concept/Writing, Practice the Skills, Problem Solving, Challenge Problem/Group Activity, Recreational Mathematics, and Internet/Research Activities.

  • Chapter Summaries, Review Exercises, and Chapter Tests comprise end-of-chapter sections that help students review material and prepare for tests.

  • Group Projects appear at the end of each chapter and are suggested projects that can be used to have students work together. These projects can also be assigned to individual students if desired.

New to this Edition

In this edition, certain topics have been revised or expanded in order to introduce new material and increase understanding:


  • Chapter 1: Critical Thinking Skills was updated with exciting and current examples and exercises.
  • Chapter 2: Sets includes more information on countable sets and infinite sets. New material on difference of sets and Cartesian products has been included.
  • Chapter 3: Logic has more exercises and a greater variety of exercises, such as in Section 3.1. Certain material has been rewritten for greater clarity. A new Section 3.7 on switching circuits has been added.
  • Chapter 4: Systems of Numeration includes increased use of the bases 2, 8, and 16, which have applications to modern computers and electronics.
  • Chapter 5: Number Theory and the Real Number System has the most current number theory information (largest prime number, most accurate value of pi, etc.). Updated examples and exercises include the most current economic numbers such as federal debt and gross domestic product.
  • Chapter 6: Algebra, Graphs and Functions has more and a greater variety of examples and exercises dealing with real-life situations. Additional exercises involving exponential equations have been included.
  • Chapter 7: Systems of Linear Equations and Inequalities now includes more detailed explanations of certain topics.
  • Chapter 8: The Metric System now includes many examples and interesting photographs of real-life (metric) situations taken from around the world.
  • Chapter 9: Geometry now includes information on finding surface area. Some information on non-Euclidean geometry has been rewritten.
  • Chapter 10: Mathematical Systems has additional exercises and examples. We have integrated this material more with real-life situations.
  • Chapter 11: Consumer Mathematics includes current interest rates and ­updated information on items that may be of interest to students, including material on sources of credit and mutual funds. There is also additional information on stocks, bonds, and mutual funds. Section 11.6, “Ordinary Annuities, Sinking Funds, and Retirement Investments,” has been added.
  • Chapter 12: Probability has a greater variety of examples and exercises; more examples and exercises have been added that deal with real-life situations. Some material has been rewritten for greater clarity. Calculator keystrokes for solving permutation and combination exercises are included.
  • Chapter 13: Statistics now includes calculator keystrokes and commands for using Microsoft Excel to determine several statistical measures.  Material related to z-scores has been revised.
 In addition, several important improvements have been made to the presentation of the material:
  • Section Openers provide interesting and motivational applications that introduce each section and illustrate the real-world nature of the material in the section.
  • Technology Tips are notes that have been added in selected sections to explain how a graphing calculator and/or Microsoft Excel may be used to work certain problems
  • The number of examples has been increased throughout the text to promote student understanding.
  • Real Data Sources have been added; up-to-date tables, graphs, and charts make the material more relevant and encourage students to read graphs and analyze data.
  • The number and variety of exercises have been various exercise sets. Approximately 40% of the exercises have been revised or updated to reflect current data, new material in the text, and the needs and interests of today's students.These exercise types include Concept/Writing Exercises, Practice the Skills Exercises, Problem Solving Exercises, Challenge Problem/Group Activity exercises, Recreational Mathematics, and Internet/Research Activities.


Table of Contents

Chapter 1 Critical Thinking Skills

1.1 Inductive Reasoning

1.2 Estimation

1.3 Problem Solving


Chapter 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 Application of Sets

2.6 Infinite Sets


Chapter 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


Chapter 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


Chapter 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 and the Real Number System

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


Chapter 6 Algebra, Graphs, and Functions

6.1 Order of Operations

6.2 Linear Equations In One Variable

6.3 Formulas

6.4 Applications of Linear Equations In One Variable

6.5 Variation

6.6 Linear Inequalities

6.7 Graphing Linear Equations

6.8 Linear Inequalities In Two Variables

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

6.10 Functions and Their Graphs


Chapter 7 Systems of Linear Equations and Inequalities

7.1 Systems of Linear Equations

7.2 Solving Systems of Linear Equations By the Substitution and Addition Methods

7.3 Matrices

7.4 Solving Systems of Linear Equations by Using Matrices

7.5 Systems of Linear Inequalities

7.6 Linear Programming


Chapter 8 The Metric System

8.1 Basic Terms and Conversions Within The Metric System

8.2 Length, Area, and Volume

8.3 Mass and Temperature

8.4 Dimensional Analysis and Conversions To and From the Metric System


Chapter 9 Geometry

9.1 Points, Lines, Planes, and Angles

9.2 Polygons

9.3 Perimeter and Area

9.4 Volume and Surface Area

9.5 Transformational Geometry, Symmetry, and Tessellations

9.6 Topology

9.7 Non-Euclidean Geometry and Fractal Geometry


Chapter 10 Mathematical Systems

10.1 Groups

10.2 Finite Mathematical Systems

10.3 Modular Arithmetic


Chapter 11 Consumer Mathematics

11.1 Percent

11.2 Personal Loans and Simple Interest

11.3 Compound Interest

11.4 Installment Buying

11.5 Buying a House with a Mortgage

11.6 Ordinary Annuities, Sinking Funds, and Retirement Investments


Chapter 12 Probability

12.1 The Nature of Probability

12.2 Theoretical Probability

12.3 Odds

12.4 Expected Value (Expectation)

12.5 Tree Diagrams

12.6 Or and And Problems

12.7 Conditional Probability

12.8 The Counting Principle and Permutations

12.9 Combinations

12.10 Solving Probability Problems By Using Combinations

12.11 Binomial Probability


Chapter 13 Statistics

13.1 Sampling Techniques

13.2 The Misuses of Statistics

13.3 Frequency Distributions

13.4 Statistical Graphs

13.5 Measures of Central Tendency

13.6 Measures of Dispersion

13.7 The Normal Curve

13.8 Linear Correlation and Regression





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 over fifteen years at Manatee Community College in Florida and for almost ten at Saint Stephen's Episcopal School. Besides coaching little league baseball, his other interests include history, politics, 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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