Fundamentals of Mathematics / Edition 10

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Overview

Demystifying mathematics like no other, this book presents the basics in a straightforward, easy-to-understand way. The authors emphasize the development of skills and confidence in mathematics for readers with a wide range of abilities. Presents material in a thorough, patient manner with a wealth of worked examples and systematic step-by-step solutions. Revises design and layout for a more engaging, accessible presentation. Includes more real-world problems throughout. Includes more applications with real sourced data. Provides online Web exercises in each chapter, noted by a special icon for easy identification. A useful reference for anyone who needs to brush up on their mathematics skills.
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Editorial Reviews

Booknews
New edition of a standard text first published in 1976, for liberal arts students in math courses at community colleges. A working knowledge of arithmetic is prerequisite. Coverage includes the fundamentals of problem solving, sets, logic, probability, statistics, mathematical systems, systems of numeration, and introductions to algebra, geometry, and the metric system. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780131139411
  • Publisher: Pearson
  • Publication date: 3/25/2004
  • Edition description: REV
  • Edition number: 10
  • Pages: 848
  • Product dimensions: 8.60 (w) x 10.40 (h) x 1.40 (d)

Table of Contents

Each chapter concludes with Summary, Key Terms and Concepts, Review Exercises, and Chapter Quiz.

1. Fundamentals of Problem Solving

1.1 Introduction

1.2 Problem-Solving Traits and Methods

1.3 Estimation

1.4 Pattern Recognition and Inductive Reasoning

1.5 Inductive Reasoning and Sequences and Series (optional)

1.6 Polya's General Problem-Solving Framework



2. Sets

2.1 Introduction

2.2 Notation and Description

2.3 Subsets

2.4 Set Operations

2.5 Pictures of Sets (Venn Diagrams)

2.6 An Application of Sets and Venn Diagrams

2.7 Cartesian Products



3. Logic

3.1 Introduction

3.2 Statements and Symbols

3.3 Dominance of Connectives

3.4 Truth Tables for Negation, Conjunction, and Disjunction

3.5 Truth Tables for Conditional and Biconditional

3.6 DeMorgan's Law and Equivalent Statements

3.7 The Conditional (Optional)

3.8 Valid Arguments

3.9 Picturing Statements with Venn Diagrams (Optional)

3.10 Valid Arguments and Venn Diagrams

3.11 Switching Networks (Optional)



4. Probability

4.1 Introduction

4.2 Definition of Probability

4.3 Sample Spaces

4.4 Tree Diagrams

4.5 Odds and Expectation

4.6 Compound Probability

4.7 Counting, Ordered Arrangements, and Permutations (Optional)

4.8 Combinations (Optional)

4.9 More Probability (Optional)



5. Statistics

5.1 Introduction

5.2 Measures of Central Tendency

5.3 Measures of Dispersion

5.4 Measures of Position (Percentiles)

5.5 Pictures of Data

5.6 The Normal Curve

5.7 Uses and Misuses of Statistics



6. Mathematical Systems

6.1 Introduction

6.2 Clock Arithmetic

6.3 More New Systems

6.4 Modular Systems

6.5 Mathematical Systems Without Numbers

6.6 Axiomatic Systems



7.Systems of Numeration

7.1 Introduction

7.2 Early Counting and Calculation Systems

7.3 Grouping Systems

7.4 Place-Value Systems

7.5 Numeration in Bases Other than 10

7.6 Base 5 Arithmetic

7.7 The Language of Computers: Binary and Hexadecimal Bases



8.Sets of Numbers and Their Structure

8.1 Introduction

8.2 Natural Numbers—Primes and Composites

8.3 Greatest Common Divisor and Least Common Multiple

8.4 Integers

8.5 Rational Numbers

8.6 Rational Numbers and Decimals

8.7 Irrational Numbers and the Set of Real Numbers

8.8 Scientific Notation (Optional)



9.An Introduction to Algebra

9.1 Introduction

9.2 Basic Concepts of Algebra

9.3 Open Sentences and Their Graphs

9.4 More Open Sentences - Solving Linear Equations

9.5 Applications of Linear Equations (Problem Solving)

9.6 Linear Equations in Two Variables

9.7 Graphing Equations

9.8 Inequalities in Two Variables



10.Selected Topics in Algebra

10.1 Introduction

10.2 The Slope of a Line

10.3 The Equation of a Line

10.4 Linear Programming

10.5 Solving Quadratic Equations

10.6 Graphing y = ax2 + bx + c



11.An Introduction to Geometry

11.1 Introduction

11.2 Points, Lines, and Angles

11.3 Planes

11.4 Angles

11.5 Polygons

11.6 Perimeter and Area

11.7 Solids

11.8 Congruent and Similar Triangles

11.9 Networks



12.Consumer Mathematics

12.1 Introduction

12.2 Ratio and Proportion

12.3 Percents, Decimals, and Fractions

12.4 Markups and Markdowns

12.5 Simple Interest

12.6 Compound Interest

12.7 Effective Rate of Interest

12.8 Life Insurance

12.9 Installment Buying

12.10 Mortgages



13. An Introduction to the Metric System

13.1 Introduction

13.2 History of Systems of Measurement

13.3 Length and Area

13.4 Volume

13.5 Mass (Weight)

13.6 Temperature



Appendix:

Table 1: Factorials

Table 2: Squares, Square Roots, and Prime Factors for 1 - 100

Glossary

Answers to Odd-Numbered Exercises, All Review Exercises, and All Chapter Quizzes

Photo Credits

Index

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Preface

To the Instructor

The success and longevity of Fundamentals can be summed up in two words: It Works! Throughout its history, Fundamentals of Mathematics has established itself as a leader in its field. What distinguishes this textbook from its competitors is its straight forward approach that succeeds in doing what others claim to do, namely, it demystifies mathematics. The text motivates students to master the material because of its patient and friendly style. The topics and concepts discussed in the book are explained fully and simply in an uncomplicated manner, thus making them accessible to nearly all levels of readers.

The approach is intuitive. This text contains an abundance of completely worked-out examples with systematic step-by-step solutions; there are no gaps or "magic" solutions. We have found that this type of experience provides the student with confidence and competence when doing homework or exam problems. Previous editions of this text have been described as "user friendly" by students.

In the Ninth Edition

In writing this ninth edition, our purpose was three-fold: (1) to maintain the elements of the previous edition that proved successful; (2) to judiciously incorporate, when and where deemed appropriate, suggestions or recommendations from the National Council of Teachers of Mathematics' (NCTM) Standards 2000: Principles and Standards for School Mathematics, as well as the American Mathematical Association of Two-Year Colleges' (AMATYC) position statement on Standards for Introductory College Mathematics Before Calculus; and (3) to reflect many of thethoughtful comments and suggestions from colleagues and students who have used previous editions of the book. We believe we have succeeded in accomplishing our goals.

Key Content Changes

Chapter 1: Fundamentals of Problem Solving combines Sections 1.2 and 1.3 from the eighth edition into a new section called Problem Solving Traits and Methods, which presents various human traits as well as specific techniques and strategies used in most problem solving endeavors. Problem solving strategies such as pattern recognition, reasoning, estimation, and working backwards are first presented in this section and then expanded in subsequent sections. This chapter also includes a completely new and comprehensive section on estimation, which examines several aspects of estimation as a problem solving technique, including various ways in which estimates can be obtained, over- and underestimates, and estimation accuracy. Section 1.4 from the eighth edition was revised to better facilitate pattern recognition and inductive reasoning concepts. Finally, the use of inductive reasoning as a strategy for solving problems involving sequences and series was revised and tagged as an optional section.

Chapter 2: Sets includes two new biographies (Cantor and Euler), and includes information about blood typing as an application of sets.

Chapter 3: Logic contains new information that relates logic to technology, including: Internet search strategies; logic gates, which form the basic building blocks of digital circuits; and fuzzy logic, which is an extension of conventional logic. New examples and related exercises have also been added that involve finding the truth value of a statement without using a truth table.

Chapter 4: Probability includes new information that contrasts theoretical and empirical probability, as well as new information that illustrates how probability is applied to the field of genetics.

Chapter 5: Statistics has updated exercises and includes an expanded exercise set in the section on uses and misuses of statistics.

Chapter 6: Mathematical Systems provides information on how mathematical systems can be used to create geometric patterns, and new information on how modular systems are applied in the field of computer science to encode and decode messages.

Chapter 7: Systems of Numeration contains a new section on early counting and calculation systems that includes a detailed discussion on the Roman numeral system of numeration, the abacus, and Napier's rods. We also combined sections 7.2 and 7.3 from the eighth edition into a single section called Grouping Systems, and sections 7.6 and 7.7 (sans the base 2 material) from the eighth edition are combined into a single section called Base 5 Arithmetic and Other Bases. The base 2 material from the previous section 7.7 is incorporated into a new section on binary and hexadecimal bases to reflect the language of computers.

Chapter 8: Sets of Numbers and Their Structure contains a revised section 8.2 (Natural Numbers—Primes and Composites), which was rewritten for clarity and provides information about the laws of natural numbers. Application problems involving the greatest common divisor and least common multiple are incorporated into section 8.3, and in section 8.4, the discussion on integers is expanded to include division of integers as well as the order of operations. Section 8.5 provides a discussion of mixed numbers and improper fractions, and section 8.7 includes new information about the laws of real numbers.

Chapter 9: An Introduction to Algebra includes anew section, 9.2 (Basic Concepts of Algebra) that pulls together key introductory algebraic concepts and vocabulary such as variable, constant, factor, term, and coefficient, which were scattered throughout the chapter in the eighth edition. This section also provides a review of some of the material from Chapter 8, including the various sets of numbers, the laws of real numbers, integer arithmetic, and the order of operations. Section 9.2 of the eighth edition (Open Sentences and Their Graphs) was renumbered 9.3 but maintains its intuitive (first) approach to solving equations. Section 9.4 (More Open Sentences) was revised to incorporate simplifying algebraic expressions.

Chapter 10: Selected Topics in Algebra includes information about linear models as well as functions.

Chapter 11: An Introduction to Geometry includes information about transformational geometry and fractals.

Chapter 12: Consumer Mathematics was updated in various places to reflect current business practices and vocabulary. The chapter also includes information about inflation and provides Internet links to several different financial planning Websites that contain Java-based calculator tools to help determine the costs of mutual funds, home mortgages, home improvement loans, and life insurance.

Chapter 13: An Introduction to the Metric Systemwas updated in various places to reflect the current state of metric affairs in this country. New Notes of Interests were also added that highlight the use of the metric system in different applications.

New or Enhanced Features

In addition to the various content changes, the ninth edition of Fundamentals of Mathematics also includes several new features as well as enhancements to the material.

  • New Examples and Exercise Sets. Nearly every chapter contains at least one section that has been updated with new examples and corresponding exercise sets. Approximately 20% of the exercises are revised and another 20% of new problems added.
  • Extended Exercise Sets. The exercise sets of every section of every chapter were extended to include three new sets of problems: Writing Mathematics, Challenge Problems, and Group/Research Activities.
  • Tables and Graphs. Approximately half of the chapters now include examples and exercise sets that present data in tables or graphs, including bar, circle, and line graphs, so that students can gain experience in reading and analyzing data given in different forms.
  • Math Notes. New boxed text items, called Math Note, are provided in every chapter. The notes are designed specifically to enhance student learning by helping students make connections among a variety of topics as well as understand how mathematics can be applied to other disciplines.
  • Biographies. New biographical profiles of key mathematicians have been added. Additionally, many of the historical notes from the eighth edition that were biographical in nature are renamed as biographies.

Retained Features

Although several pronounced changes have been made to this ninth edition, we were also careful to retain the hallmarks of Fundamentals of Mathematics that have made it an effective and engaging resource for liberal arts mathematics students. Key among them are:

  • Intuitive Approach. Throughout the book, the material is written specifically for nonmathematics majors. The exposition is clear, patient, and friendly. We present the mathematics in a non-intimidating manner and limit the introduction of new material to one or two concepts at a time.
  • Development. The material is carefully and thoroughly developed. We refrain from using shallow statements or phrases such as "as you can see," "obviously," and "clearly, it follows that." Instead, we provide full explanations to facilitate student understanding and meaningful learning.
  • Examples. The text contains an abundance (more than 600) of completely worked-out examples with systematic step-by-step solutions; there are no gaps or "magic" solutions.
  • Exercises. The exercises are plentiful (don't let the numbering system fool you). Moreover, they are graded in difficulty (from basic to moderately difficult) and parallel in nature so that an instructor may independently assign either odd- or even-numbered problems to cover the material in a section.
  • Chapter Openers. Each chapter contains a photo that is representative of the chapter material, a set of objectives, a chapter outline, and a list of symbols (and their meaning) that are used in the chapter.
  • End-of-Chapter Material. Each chapter concludes with a summary, a list of key terms or phrases, a set of chapter review exercises, and a chapter quiz.
  • Illustrations. There are more than 1200 illustrations and photos that help students visualize mathematics and use that visualization in solving mathematical problems.
  • Biographies, Historical Notes, Notes of Interest, and Just for Funs. Throughout the text, specially designed sidebars or problems supplement the exposition. Biographies provide vignettes about people who have made important contributions to mathematics; Historical Notes embellish a discussion by providing a historical context for a particular math concept or topic; Notes of Interest contain adjunct information about a topic that students might find interesting; and Just for Funs are problems that range from serious extensions of mathematical ideas to light-hearted puzzles, recreational mathematics, or brain teasers.
  • Glossary: A 250-word glossary of key mathematical terms or phrases is provided at the end of the book.

Answers to the exercises appear in the back of the text for all the odd-numbered problems. Fully worked out solutions for the odd-numbered problems are found in the Student Study Guide and Solutions Manual, and the even answers are located in the Instructor's Resource and Solutions Manual. For a closer look at the text's many features, turn to the Text Walk-Through on pages xxii-xxv.

Instructor Supplements

Instructor's Resource and Solutions Manual. Contains complete step-by-step worked out solutions to all exercises in the textbook.

Test Item File. With over 1000 questions, this test bank allows easy creation of full tests and quizzes for your students.

TestGenEQ (computerized test generator—cross platform). This easy to use test generator contains all the questions from the written test item file.

Student Supplements

Student Study Guide and Solutions Manual. This combined Study Guide and Solutions Manual contains step-by-step worked out solutions to all the odd-numbered exercises in the textbook and a comprehensive study guide. This is helpful for your students to obtain instant feedback while studying.

Instructor and Student Supplement

PH Companion Website. Designed to complement and expand upon the text, the PH Companion Website offers a variety of interactive teaching and learning tools including: links to related Websites, practice work for students, and the ability for instructors to monitor and evaluate students' work on the Website. For more information, contact your local Prentice Hall representative.

www.prenhall.com/setek

For more information on any of the supplements, please contact your Prentice Hall representative.

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