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.
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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.
NEWIntegration of AMATYC and NCTM Standards
NEWText 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.
- 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).
NEWUsing 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.
NEWChapter 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.
NEWOptional 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.
NEWChapter Tests are included at the end
of each chapter for more review and reinforcement.
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.
Real world sourced data, interpretation of data and visualization
is fully integrated.
- 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).
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.
(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
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
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
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
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.