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Introductory Algebra for College Students, 2/e

Robert Blitzer, Miami-Dade Community College

Published July, 1997 by Prentice Hall Engineering/Science/Mathematics

Copyright 1998, 744 pp.
Cloth
ISBN 0-13-275745-1


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Summary

For a one-semester undergraduate introductory algebra course. The goal of this text is to provide students with a strong foundation in Basic Algebra skills; to develop students' critical thinking and problem-solving capabilities and prepare students for Intermediate Algebra and some “service” math courses. Topics are presented in an interesting and inviting format incorporating real world sourced data modeling.

Features


NEW—Integration of AMATYC and NCTM Standards

  • Over 50 % of the applications and many of the examples have been extensively researched and rewritten to incorporate current, real-world data drawn from familiar sources such as the 1995 Statistical Abstract of the U.S. published by the Census bureau.
  • Graphing is introduced and integrated earlier, starting in Section 1.3. (and fully explored in Chapter 4).
NEW—Text organization reflects an emphasis on problem solving. Section 2.5 is now “An Introduction to Problem Solving,” and Chapter 3 “Problem Solving” fully explores problem solving strategies.
NEW—Using Technology, Study Tips, and Discover for Yourself boxes have been added as pedagogical enrichment features to encourage student success. Study Tips in particular, make mathematical content more accessible.
NEW—Chapter Projects, extended one-page applications, conclude each chapter. Some activities feature related websites (available to students via the Prentice Hall/Blitzer website) for student research and exploration.
NEW—Optional Graphing utility opportunities have been added in appropriate sections and exercise sets. These sections, examples and exercises feature explorations, many with real screen grabs from the TI-83.
NEW—Chapter Tests are included at the end of each chapter for more review and reinforcement. FEATURES
An abundance of interesting and varied exercises are included (50% have been rewritten) to appeal to the modern (often non-traditional) student. The exercises, examples and writing style have been carefully and extensively reviewed and revised to better meet the level of student taking a developmental math course.
Modeling is introduced in Chapter 1 and emphasized throughout.
  • Section 1.9 (Order of Operations; Mathematical Models).
  • Section 2.4 (Mathematical Models).
  • Section 6.3 (Special Products; Modeling with Polynomials).
  • Section 8.7 (Modeling with Rational Expressions).
Real world sourced data, interpretation of data and visualization is fully integrated.
The use of fine art, historical notes and interdisciplinary connections are introduced in the context and applicability of algebra.
  • For example, Warhol's well-known Campbell's Soup piece illustrates the concept of integer exponents. Other artists featured include Escher, Magritte, Picasso, Mondrian, Matisse, and Jasper Johns.


Table of Contents
(NOTE: Each chapter ends with a Summary, Review Problems, Chapter Project, and Chapter Test section.)
    1. The Real Number System.

      Fractions. The Real Numbers. Graphing and Ordered Pairs. Basic Rules of Algebra. Addition of Real Numbers. Subtraction of Real Numbers. Multiplication of Real Numbers. Exponents; Division of Real Numbers. Order of Operations; Mathematical Models.

    2. Linear Equations and Inequalities in One Variable.

      The Addition Property of Equality. The Multiplication Property of Equality. Solving Linear Equations. Mathematical Models. An Introduction to Problem Solving. Solving Linear Inequalities.

    3. Problem Solving.

      Strategies for Solving Problems. Ratio and Proportion. Geometry Problems. Cumulative Review Problems.

    4. Linear Equations and Inequalities in Two Variables.

      Graphing Linear Equations and Linear Functions. More on Graphing Linear Equations. Graphing Other Types of Equations and Functions. Slope. The Slope-Intercept Equation of a Line. The Point-Slope Equation of a Line. Graphing Linear Inequalities in Two Variables. Cumulative Review Problems.

    5. Systems of Linear Equations and Inequalities.

      Solving Systems of Linear Equations by Graphing. Solving Systems of Linear Equations by the Addition (Elimination) Method. Solving Systems of Linear Equations by the Substitution Method. Problem Solving Using Systems of Equations. Solving Systems of Inequalities. Cumulative Review Problems.

    6. Exponents and Polynomials.

      Adding and Subtracting Polynomials. Multiplying Polynomials. Special Products; Modeling with Polynomials. Polynomials in Several Variables. Dividing Polynomials. Dividing Polynomials by Binomials. Negative Exponents and Scientific Notation. Cumulative Review Problems.

    7. Factoring Polynomials.

      Factoring Polynomials with Common Factors. Factoring Trinomials Whose Leading Coefficient is 1. Factoring Trinomials Whose Leading Coefficient is Not 1. Factoring Special Forms. A General Factoring Strategy. Solving Quadratic Equations by Factoring. Cumulative Review Problems.

    8. Rational Expressions.

      Rational Expressions, Rational Functions, and Their Simplification. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions with the Same Denominator. Adding and Subtracting Rational Expressions with Different Denominators. Complex Fractions. Solving Rational Equations. Modeling with Rational Expressions. Cumulative Review Problems.

    9. Roots and Radicals.

      Finding Roots. Multiplying and Dividing Radicals. Operations with Radicals. Rationalizing Denominators; Simplified Radical Form. Equations Containing Radicals. Fractional Exponents. Cumulative Review Problems.

    10. Quadratic Equations and Functions.

      Solving Quadratic Equations by the Square Root Property. Solving Quadratic Equations by Completing the Square. The Quadratic Formula. Complex Numbers as Solutions of Quadratic Equations. Quadratic Functions and Their Graphs.

    Appendix: Review Problems Covering the Entire Book.


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