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