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Finite Mathematics : An Applied Approach

Finite Mathematics : An Applied Approach - 3rd edition

ISBN13: 978-0321173348

Cover of Finite Mathematics : An Applied Approach 3RD 04 (ISBN 978-0321173348)
ISBN13: 978-0321173348
ISBN10: 0321173341
Cover type: Hardback
Edition/Copyright: 3RD 04
Publisher: Addison-Wesley Longman, Inc.
Published: 2004
International: No

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Finite Mathematics : An Applied Approach - 3RD 04 edition

ISBN13: 978-0321173348

Paul E. Long, Paula Grafton Young, Todd Lee and Jay Graening

ISBN13: 978-0321173348
ISBN10: 0321173341
Cover type: Hardback
Edition/Copyright: 3RD 04
Publisher: Addison-Wesley Longman, Inc.

Published: 2004
International: No
Summary

Finite Math is often a required course, taken by students who come with a weak math background and struggle with the subject. Young/Lee's Finite Mathematics: An Applied Approach 3rd Edition is written with these students in mind. Despite the excellent variety of drill, practice and conceptual problems laced with relevant real-world applications, students in finite math often struggle, prompting them to lean on the chapter's examples for help.

In this text, the authors provide examples that are not just quick recipes to be applied to a particular problem, but rather they offer actual insight into the problem at hand, as well to the general concept being developed. The examples help the students retain important concepts and then apply them in the exercises that follow. Using color in a way that carries the student's eye into the exposition that surrounds an example, the student is led, gently, to generalization and understanding. Young/Lee have found that delicate balance between accurate, precise and useful mathematics and aiding the struggling student towards successfully learning it.

Features

  • Pedagogical use of color. Careful, innovative use of color links the examples with surrounding exposition to carefully build student understanding of concepts.
  • Chapter Problems. Each chapter begins with a relevant problem to show the type of problem that the material in the chapter can address. Each of these problems is completely solved later in the chapter.
  • Technology Opportunities. Each chapter begins with a brief discussion about the uses of graphing calculators and spreadsheets for the topics about to be covered. Detailed instructions for using the TI-83 Plus and MS Excel are incorporated into examples near the end of each relevant section in order to help instructors determine when and how to use technology.
  • Applications. Applications in a variety of fields are found throughout the examples and exercises. An applications index is provided for reference. Effort has been made to include applications from many different disciplines, including accounting, agriculture, biological sciences, communication and media studies, computers, economics, education, finance, fine arts, health sciences, management, marketing, physical science, production and service, social and behavioral sciences, sports and recreation. Current data from many sources, including governmental agencies and private organizations, has been used in the construction of these applications.
  • Historical Notes. Throughout the text, historical notes are included, usually in the form of biographical sketches, related to the material being discussed. These notes "humanize" the mathematics and can be used to foster class discussions or as starting points for writing assignments.
  • In-Depth Applications. New to this edition, longer, more in-depth applications have been included at the end of most chapters. These applications can be used in a variety of ways, such as group projects or extra credit assignments. Each incorporates the mathematics developed in the respective chapter and involves a series of questions that are related to a timely, interesting topic. Some of the topics are sports ranking systems (Chapter 3), shadow pricing (Chapter 5), credit consolidation (Chapter 6), genetics (Chapter 7), and message routing through the Internet (Chapter 12).
  • Chapter Summaries and Chapter Tests. Each chapter ends with a summary of the keywords and topics covered, as well as a set of exercises which can be used as a review. The sample tests included at the end of each chapter can also be used to test the student's knowledge of the chapter material. The answers to all questions in the sample tests are included at the back of the text.


New To This Edition

  • Algebra review and spreadsheet appendixes have been added.
  • Mathematics of Finance has been moved to the center of the text.
  • Linear Programming has been divided into two separate chapters.
  • Sections on logic have been enhanced to emphasize the subtle skills needed to precisely translate sentences into their mathematical counterparts.
  • Spreadsheet technology has been added to reflect the needs of students and current pedagogy.
  • The graphing calculator usage has been updated to the TI-83 Plus model.
  • Detailed instructions are provided for technology when technology use is appropriate and instructive
  • An In-Depth Application, reflecting current issues and real data, has been added to the end of most chapters.
  • Four color design.
  • New exercises and examples using real data.
  • New Art. The graphs are extended, colorized, and standardized.

Author Bio

Young, Paula Grafton : Salem College


Lee, Todd : Elon University


Long, Paul E. : University of Arkansas


Graening, Jay : University of Arkansas

Table of Contents

1. Applications of Linear Functions.

The Cartesian Plane and Graphing.
Equations of Straight Lines.
Linear Modeling.
Two Lines: Relating the Geometry to the Equations.
Regression and Correlation.

2. Systems of Linear Equations.

Linear Systems as Mathematical Models.
Linear Systems Having One or No Solutions.
Linear Systems having Many Solutions.

3. Matrix Algebra.

Matrix Addition and Applications.
Matrix Multiplication and Applications.
The Inverse of a Matrix.
More Applications of Inverses.

4. Linear Programming: The Graphical Method.

Modeling Linear Programming Problems.
Linear Inequalities in Two variables.
Solving Linear Programming Problems Graphically.

5. Linear Programming: The Simplex Method.

Slack Variables and Pivoting.
The Simplex Algorithm: Maximization.
The Simplex Algorithm: Minimization.
Nonstandard Problems: Crown's Rules.
The Dual Problem.

6. Mathematics of Finance.

Simple and Compound Interest.
Ordinary Annuities.
Consumer Loans and Amortization.

7. Logic, Sets, and Counting Techniques.

Logic.
Truth Tables.
Sets, Set Operations, and Venn Diagrams.
Applications of Venn Diagrams.
Counting: The Multiplication Principle.
Permutations.
Combinations.

8. Basic Concepts of Probability.

Sample Spaces with Equally Likely Outcomes.
Outcomes with Unequal Probability; Odds.
Discrete Random Variables and Expected Value.

9. Additional Topics in Probability.

Addition Rules for Probability and Mutually Exclusive Events.
Conditional Probability.
Multiplications Rules Probability and Independent Events.
Bayes' Theorem.
The Binomial Distribution.

10. Statistics.

Organizing Data; Frequency Distributions.
Measures of Central Tendency.
Measures of Dispersion.
Continuous Random Variables and the Normal Distribution.

11. Markov Chains.

Markov Chains as Mathematical Models.
State Vectors.
Regular Markov Chains.

12. Game Theory: Two Player, Zero-Sum Games.

Strictly Determined Games.
The Expected Value of Games with Mixed Strategies.
Solving Mixed-Strategy Games.

Appendices.
Appendix I: Algebra Review.
Appendix II: Introduction to Spreadsheets.
Appendix III: Standard Normal Table.
Appendix IV: Solutions to Odd Numbered Exercises.
Index.