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Foundations of Mathematics

Foundations of Mathematics - 04 edition

Foundations of Mathematics - 04 edition

ISBN13: 9780321168566

ISBN10: 0321168569

Foundations of Mathematics by Marvin L. Bittinger and Judith A. Penna - ISBN 9780321168566
Edition: 04
Copyright: 2004
Publisher: Addison-Wesley Longman, Inc.
Published: 2004
International: No
Foundations of Mathematics by Marvin L. Bittinger and Judith A. Penna - ISBN 9780321168566

ISBN13: 9780321168566

ISBN10: 0321168569


Foundations of Mathematics is a unique offering from a trusted publisher and authors. This text covers all of the core material that is typically found in a 3-semester developmental mathematics sequence--basic mathematics, introductory algebra, and intermediate algebra. And, as you have come to expect when you see the Bittinger name, Foundations of Mathematics offers you and your students a completely integrated text and supplements package that will help your students to succeed not only in this course, but in future courses as well. Foundations of Mathematics brings students the Bittinger hallmark five-step problem-solving process, a clear easy-to-read writing style, real-data applications, and exceptional design and artwork to make learning interesting and fun.

Features :

  • Student-oriented Applications This text encourages students to see and interpret the mathematics that appears every day in the world around them. Throughout the writing process, an energetic search for real-data applications was conducted, and the result is a wide variety of examples and exercises that connect the mathematical content with the real world.
  • Chapter Openers open on a two-page spread with exceptional artwork that is tied to a motivating real-world application to engage students and prepare them for the upcoming chapter material.
  • Chapter Pretests allow students to test themselves before beginning each chapter, helping them to identify material that may be familiar as well as targeting material that may be new or especially challenging.
  • Objective Boxes At the beginning of each section, a boxed list of objectives is keyed by letter not only to section subheadings, but also to the exercises in the Pretest, section-level exercise sets, and Summary and Review, and the answers to the Chapter Test. This correlation enables students to easily find appropriate review material if they need help with a particular exercise or skill.
  • Caution Boxes Found at relevant points throughout the text, boxes with the "Caution!" heading warn students of common misconceptions or errors made in performing a particular mathematical operation or skill.
  • Calculator Corners Where appropriate throughout the text, students see optional Calculator Corners. This feature is designed specifically with developmental mathematics students in mind, giving them keystrokes as appropriate, and is accompanied by exercises for students to try on their own.
  • Discussion and Writing Exercises Designed to help students develop deeper comprehension of critical concepts, two Discussion and Writing exercises (indicated by a DW symbol) are found in each exercise set and Summary and Review to encourage students to think about, write, and verbalize key mathematical ideas in the chapter. Discussion and Writing exercises are suitable for either individual or group work.
  • Skill Maintenance Exercises Found in each exercise set, these exercises review concepts from other sections in the text to prepare students for their final examination. Section and objective codes appear next to each Skill Maintenance exercise for easy reference, and in response to user feedback, the overall number of Skill Maintenance exercises has been increased.
  • Synthesis Exercises Appearing in most exercise sets, Synthesis Exercises help build critical-thinking skills by requiring students to synthesize or combine learning objectives from the current section as well as from preceding text sections.
  • Study Tips A variety of Study Tips throughout the text gives students pointers on how to develop good study habits as they progress through the course. At times short snippets and at other times more lengthy discussions, these Study Tips encourage students to input information and get involved in the learning process. These features can also be used in conjunction with Bittinger's "Math Study Skills for Students" videotape.
  • Art Program Today's students are often visually oriented and their approach to a printed page is no exception. To appeal to students, the artwork in Foundations of Mathematics is dynamic, and photographs and art pieces enhance the emphasis on real data and applications. To encourage students to understand the relevance of mathematics, many applications are enhanced by graphs and drawings similar to those found in today's newspapers and magazines.
  • MyMathLab Ideal for lecture-based, lab-based, and distance-learning courses, this state-of-the-art on-line course provides students with a centralized point of access to the wide variety of multimedia resources available with this text. The pages of the actual book are loaded into MyMathLab, and as students work through a section of the on-line text, they can link directly to tutorial exercises, interactive animations, and audio and video clips that provide instruction, exploration, and practice beyond what is offered in the printed book. Complete course-management capabilities, including a host of communication tools for course participants, provide a user-friendly and interactive on-line environment.

Author Bio

Bittinger, Marvin L. : Indiana University - Purdue University Indianapolis

Penna, Judith A. : Indiana University - Purdue University Indianapolis

Table of Contents

Table of Contents

(All chapters begin with a Pretest and end with a Summary and Review, and Chapter Test.)

1. Whole Numbers
Standard Notation; Order.
Addition and Subtraction.
Multiplication and Division; Rounding and Estimating.
Solving Equations.
Applications and Problem Solving.
Exponential Notation and Order of Operations.
Least Common Multiples.

2. Fraction Notation.
Fraction Notation and Simplifying.
Multiplication and Division.
Addition and Subtraction; Order.
Mixed Numerals.
Applications and Problem Solving.
Order of Operations; Estimation.

3. Decimal Notation.
Decimal Notation, Order, and Rounding.
Addition and Subtraction.
Converting from Fraction Notation to Decimal Notation.
Applications and Problem Solving.

4. Percent Notation.
Ratio and Proportion.
Percent Notation.
Percent and Fraction Notation.
Solving Percent Problems Using Percent Equations.
Solving Percent Problems Using Proportions.
Applications of Percent.
Sales Tax, Commission, Discount, and Interest.
Interest Rates on Credit Cards and Loans.

5. Geometry.
Basic Geometric Figures.
Volume and Surface Area.
Relationships Between Angle Measures.
Congruent Triangles and Properties of Parallelograms.
Similar Triangles.

6. Introduction to Real Numbers and Algebraic Expressions.
Introduction to Algebra.
The Real Numbers.
Addition of Real Numbers.
Subtraction of Real Numbers.
Multiplication of Real Numbers.
Division of Real Numbers.
Properties of Real Numbers.
Simplifying Expressions; Order of Operations.

7. Solving Equations and Inequalities.
Solving Equations: The Addition Principle.
Solving Equations: The Multiplication Principle.
Using the Principles Together.
Applications of Percent.
Applications and Problem Solving.
Solving Inequalities.
Applications and Problem Solving with Inequalities.

8. Graphs of Linear Equations.
Graphs and Applications.
Graphing Linear Equations.
More with Graphing and Intercepts.
Slope and Applications.

9. Polynomials: Operations.
Integers as Exponents.
Exponents and Scientific Notation.
Introduction to Polynomials.
Addition and Subtraction of Polynomials.
Multiplication of Polynomials.
Special Products.
Operations with Polynomials in Several Variables.
Division of Polynomials.

10. Polynomials: Factoring.
Introduction to Factoring.
Factoring Trinomials of the Type x² + bx + c.
Factoring ax² + bx + c, a 1, FOIL Method.
Factoring ax² + bx + c, a 1, ac-Method.
Factoring Trinomial Squares and Differences of Squares.
Factoring Sums or Differences of Cubes.
Factoring: A General Strategy.
Solving Quadratic Equations by Factoring.
Applications of Quadratic Equations.

11. Rational Expressions and Equations.
Multiplying and Simplifying Rational Expressions.
Division and Reciprocals.
Least Common Multiples and Denominators.
Adding Rational Expressions.
Subtracting Rational Expressions.
Complex Rational Expressions.
Solving Rational Equations.
Applications Using Rational Equations and Proportions.
Variation and Applications.

12. Graphs, Functions, and Applications.
Functions and Graphs.
Finding Domain and Range.
Linear Functions: Graphs and Slope.
More on Graphing Linear Equations.
Finding Equations of Lines; Applications.

13. Systems of Equations.
Systems of Equations in Two Variables.
Solving by Substitution.
Solving by Elimination.
Solving Applied Problems: Two Equations.
Systems of Equations in Three Variables.
Solving Applied Problems: Three Equations.
Business and Economics Applications.

14. More on Inequalities.
Sets, Inequalities, and Interval Notation.
Intersections, Unions, and Compound Inequalities.
Absolute-Value Equations and Inequalities.
Systems of Inequalities in Two Variables.

15. Radical Expressions, Equations, and Functions.
Radical Expressions and Functions.
Rational Numbers as Exponents.
Simplifying Radical Expressions.
Addition, Subtraction, and More Multiplication.
More on Division of Radical Expressions.
Solving Radical Equations.
Applications Involving Powers and Roots.
The Complex Numbers.

16. Quadratic Equations and Functions.
The Basics of Solving Quadratic Equations.
The Quadratic Formula.
Applications Involving Quadratic Equations.
More on Quadratic Equations.
Graphing Quadratic Equations: f(x) = a(x - h)² + k.
Graphing Mathematical Quadratic Equations: f(x) = ax² + bx + c.
Modeling with Quadratic Functions.
Polynomial and Rational Inequalities.

17. Exponential and Logarithmic Functions.
Exponential Functions.
Inverse and Composite Functions.
Logarithmic Functions.
Properties of Logarithmic Functions.
Natural Logarithmic Functions.
Solving Exponential and Logarithmic Equations.
Mathematical Modeling with Exponential and Logarithmic Functions.
American Units of Measure.
Metric Units of Measure.
Mean, Median, and Mode.
Tables and Pictographs.
The Distance and Midpoint Formulas.
Nonlinear Inequalities.
Sequences and Series.
Applying Reasoning Skills.
TASP Correlation and Practice Test.

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