[Book Cover]

Fundamentals of Mathematics, 8/e

William M. Setek, Monroe Community College
Michael A. Gallo, Florida Institute of Technology

Published October, 1998 by Prentice Hall Engineering/Science/Mathematics

Copyright 1999, 726 pp.
Cloth
ISBN 0-13-778341-8


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Summary

For courses in Liberal Arts Mathematics. This text succeeds at what other texts only attempt: it demystifies mathematics. It presents the fundamentals of a variety of mathematical disciplines in a straightforward, easy-to-understand manner. The emphasis is on developing skills and confidence in mathematics for students with a wide range of abilities. The only prerequisite is a working knowledge of arithmetic.

Features


NEW—Expanded problem-solving coverage (Ch. 1).

  • The more students understand the logic of problem solving, the better they will be at applying mathematical principles to real life situations.
NEW—New introduction to Euler Circles.
  • By discussing both Euler and Venn diagrams the text introduces students to both major camps of organizational logic.
NEW—New material on logic
  • Text explores both contemporary and traditional approaches to give professors and students added flexibility.
NEW—Expanded chapter on probability includes more real life problems.
NEW—New discussions on statistics (Ch. 5)—Introduces stem-and-leaf displays and a new section on uses and misuses of statistics.
NEW—Broadened introduction to algebra (Ch. 9)—Features an expanded introduction to the chapter, new vocabulary terms and new exercises.
NEW—Updated chapter on consumer mathematics—Uses up to date interest rates, dates, prices, etc....
  • The text is more relevant when key components to problems and examples are consistent with actual real life values.
Self-contained organization—Provides chapters designed to be independent of one another.
  • Offers instructors the flexibility to cover topics in any order they wish.
Polya's 4-step problem-solving framework—Offers introductions to this and several other techniques and strategies that facilitate the problem-solving process.
  • Eases students through guidelines and examples that develop the sound problem-solving skills essential for success in math.
Solid instructional support—Begins chapters with learning objectives and a list of the symbols that will be introduced in that chapter, then concludes with a summary, vocabulary check, review exercises, and a chapter quiz.
  • Offers students frequent opportunities to reinforce, challenge, and apply their understanding of newly acquired concepts and techniques.
Clear, accessible approach—Presents material in a thorough, patient manner with over 600 fully worked-out examples and systematic step-by-step solutions.
  • Encourages students to participate actively and learn mathematics by working through examples and problems.
Historical Notes and Notes of Interest—Provides insights into the development of mathematics and additional tidbits of noteworthy information.
  • Enhances student learning by placing principles and practices within relevant contexts, allowing students to make connections with personalities and events in mathematics.
WWW applications—Provides web-based online exercises in each chapter denoted by a unique icon for easy identification.
  • Extends understanding beyond the classroom and past the printed page, engaging students in relevant assignments using today's hottest medium.
Team work projects—Devotes a full page of each chapter to collaborative learning.
  • Develops the collaborative, team-based problem-solving skills students will need throughout their academic and professional lives.


Table of Contents
(NOTE: Each chapter ends with a Summary, Vocabulary Check, Review Exercises, and Chapter Quiz.)
    1. Fundamentals of Problem Solving.

      Introduction. Problem-Solving Tools. Understanding Symbols and Context. Decisions and Pattern Recognition. Inductive Reasoning. Problem-Solving Strategies.

    2. Sets.

      Introduction. Notation and Description. Subsets. Set Operations. Pictures of Sets (Venn Diagrams). An Application of Sets and Venn Diagrams. Cartesian Products.

    3. Logic.

      Introduction. Statements and Symbols. Dominance of Connectives. Truth Tables. More Truth Tables — Conditional and Biconditional Statements. De Morgan's Law and Equivalent Statements. The Conditional (Optional). Valid Arguments. Picturing Statements with Venn Diagrams (Optional). Valid Arguments with Venn Diagrams (Optional). Switching Networks (Optional).

    4. Probability.

      Introduction. Definition of Probability. Sample Spaces. Tree Diagrams. Odds and Expectation. Compound Probability. Counting, Ordered Arrangements, and Permutations (Optional). 4.8 Combinations (Optional). More Probability (Optional).

    5. Statistics.

      Introduction. Measures of Central Tendency. Measures of Dispersion. Measures of Position (Percentiles). Pictures of Data. The Normal Curve. Uses and Misuses of Statistics.

    6. Mathematical Systems.

      Introduction. Clock Arithmetic. More New Systems. Modular Systems. Mathematical Systems Without Numbers. Axiomatic Systems.

    7. Systems of Numeration.

      Introduction. Simple Grouping Systems. Multiplicative Grouping Systems. Place-Value Systems. Numeration in Bases Other Than 10. Base 5 Arithmetic. Binary Notation and Other Bases.

    8. Sets of Numbers and Their Structure.

      Introduction. Natural Numbers — Primes and Composites. Greatest Common Divisor and Least Common Multiple. Integers. Rational Numbers. Rational Numbers and Decimals. Irrational Numbers and the Set of Real Numbers. Scientific Notation (Optional).

    9. An Introduction to Algebra.

      Introduction. Open Sentences and Their Graphs. Algebraic Notation. More Open Sentences. Problem Solving. Linear Equations in Two Variables. Graphing Equations. Inequalities in Two Variables.

    10. Selected Topics in Algebra.

      Introduction. The Slope of a Line. The Equation of a Straight Line. Graphing y = ax^2 + bx + c. Linear Programming. Quadratic Equations.

    11. An Introduction to Geometry.

      Introduction. Points and Lines. Planes. Angles. Polygons. Perimeter and Area. Solids. Congruent and Similar Triangles. Networks.

    12. Consumer Mathematics.

      Introduction. Ratio and Proportion. Percents, Decimals, and Fractions. Markups and Markdowns. Simple Interest. Compound Interest. Effective Rate of Interest. Life Insurance. Installment Buying. Mortgages.

    13. An Introduction to the Metric System.

      Introduction. History of Systems of Measurements. Length and Area. Volume. Mass (Weight). Temperature.

    Appendix A.

      Introduction to Computers. History of Computers. How a Computer System Works. Using BASIC. More BASIC Statements.

    Appendix B.
    Glossary.
    Answers to Odd-Numbered Exercises, All Review Exercises, and Chapter Quizzes.
    Photo Credits.
    Index.

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